 

Spring 2015 Mathematics Colloquia
(in reverse chronological order)
Colloquium
Friday, April 3^{rd}, 2014 at 3:00 PM, NS 334
(Refreshments afterwards in room 334)
"Semianalytical time differencing methods for stiff problems"
ChangYeol Jung
Ulsan National Institute of Science and Technology/Indiana University
Abstract: A semianalytical method is developed based on conventional integrating factor (IF) and exponential time differencing (ETD) schemes for stiff problems. The latter means that there exists a thin layer with a large variation in their solutions. The occurrence of this stiff layer is due to the multiplication of a very small parameter with the transient term of the equation. Via singular perturbation analysis, an analytic approximation of the stiff layer, which is called a corrector, is sought for and embedded into the IF and ETD methods. These new schemes are then used to approximate the nonstiff part of the solution. Since the stiff part is resolved analytically by the corrector, the new method outperforms the conventional ones in terms of accuracy. In this paper, we apply our new method for both problems of ordinary differential equations and some partial differential equations. Colloquium
Friday, March 27^{th}, 2014 at 2:00 PM, NS 334
(Refreshments afterwards in room 334)
"Paradoxes in Voting: A mathematical
explanation"
Don Saari
Center for Mathematical Behavioral Sciences,
University of California Irvine
Abstract: Voting paradoxes are everywhere, and they have been affecting election outcomes for millennia. Finally, and thanks to mathematics, we are understanding how and why these difficulties arise. Fall 2014 Mathematics Colloquia
(in reverse chronological order)
Colloquium
Wednesday, September 17^{th}, 2014 at 3:30 PM, NS 333
(Refreshments afterwards in room 334)
"Acoustic propagation in a saturated piezoelastic, porous medium"
Robert P. Gilbert
University of Delaware
Abstract: We study the problem of derivation of an effective model of acoustic wave propagation in a twophase, nonperiodic medium modeling a fine mixture of linear piezoelastic solid and a viscous Newtonian, ionic bearing fluid. Bone tissue is an important example of a composite material that can be modeled in this fashion. We develop twoscale homogenization methods for this system, and discuss also a stationary random, scaleseparated microstructure. The ratio $\varepsilon$ of the macroscopic length scale and a typical size of the microstructural inhomogeneity is a small parameter of the problem. Another possibly small parameter is the Peclet number which influences the type of effective equations which are obtained. Colloquium
Friday, September 12^{th}, 2014 at 3:00 PM, NS 333
(Refreshments afterwards in room 334)
"Divergent Series: The work of the devil?"
Harry Miller
International University of Sarajevo
Abstract: The book "Divergent Series" by G. H. Hardy, Oxford(1949) is a classic. In his introduction Hardy states that some mathematicians thought, in the early 19th century, that any argument based on nonconvergence should be considered the work of the devil. Hardy states several examples of highly nonrigorous arguments that led people (for example Euler) to correct conclusions. In classical mathematics it is often the case that "averages" rather than individual terms are shown to converge, for example the theorem of Fejer in Fourier analysis and the laws of large numbers and the central limit in probability theory come to mind. Here we present results of the speaker, some joint with Lejla Miller, from this field (which is once again quite active). Spring 2014 Mathematics Colloquia
(in reverse chronological order)
Colloquium
Monday, February 24^{th}, 2014 at 1:00 PM, NS 333
(Refreshments afterwards in room 334)
"The center of rings associated to directed graphs"
Jonathan Brown
Kansas State University
Abstract: In 2005 Abrams and Aranda Pino began a program studying rings constructed from directed graphs. These rings, called Leavitt Path algebras, generalized the rings without invariant basis number introduced by Leavitt in the 1950's. Leavitt path algebras are the algebraic analogues of the graph $C^*$algebras and have provided a bridge for communication between ring theorists and operator algebraists. Many of the properties of Leavitt path algebras can be inferred from properties of the graph, and for this reason provide a convenient way to construct examples of algebras with a particular set of attributes. In this talk we will explore how central elements of the algebra can be read from the graph. Colloquium
Friday, February 21^{st}, 2014 at 3:00 PM, NS 333
(Refreshments afterwards in room 334)
"Fluidstructure interactions and multiphase flow:
Applications to the biological sciences"
Shilpa Khatri
University of North Carolina at Chapel Hill
Abstract: To understand the fluid dynamics of marine phenomena, for example particles settling, droplets rising, and pulsating coral, fluidstructure and multiphase flow problems must be solved. Challenges exist in developing analytical and numerical techniques to solve these complex flow problems with boundary conditions at fluidstructure and fluidfluid interfaces. I will present details of two different problems where these challenges are handled: (1) development of a numerical method for two phase flows with insoluble and soluble surfactants and (2) modeling of porous particles settling in density stratified fluids. These problems will be motivated by field and experimental work in the marine sciences. I will discuss these related experiments and provide comparisons with the modeling. Finally, I will briefly present some further work in this field. Colloquium
Tuesday, February 18^{th}, 2014 at 2:00 PM, NS 333
(Refreshments afterwards in room 334)
"The isomorphism problem for rank1 measurepreserving transformations"
Aaron Hill
University of North Texas
Abstract: Measurepreserving transformations of standard Lebesgue spaces are of fundamental importance ergodic theory. Von Neumann asked how one could determine whether two measurepreserving transformations are isomorphic. There are important classification theorems for certain classes of measurepreserving transformations, but also important anticlassification theorems which show that certain types of classification cannot work for all (or in some cases even most) measurepreserving transformations. In this talk I'll discuss some of this history and describe efforts, joint with Su Gao, to understand isomorphism on the class of rank1 transformations. Rank1 transformations are of particular interest because they are generic (so in some sense almost every measurepreserving transformation is rank1) and because the isomorphism relation is known to be Borel on this class (so in some sense there must be good classification for these transformations). Colloquium
Friday, February 7^{th}, 2014 at 3:00 PM, NS 212C
(Refreshments afterwards in room 334)
"Models for Large Complex Spatial Datasets"
Avishek Chakraborty
Texas A&M University
Abstract: Modeling and inference for geographicallyindexed datasets are getting increasingly frequent in current literature. This type of datasets arises in diverse applications from biology, environmental sciences and engineering. The task of statistical inference for these problems consists of finding the strength of association in measurements across adjacent regions in the maps and utilizing it to enhance the predictive performance of the model. Available covariates are often insufficient in this regard and one needs to introduce locationdependent random effects. We start our discussion with a classification of the spatiallyreferenced datasets based on the geographical resolution, nature of available information, existing modeling techniques and challenges. We specifically cover two important features that are of prime interest in current research. First, the variable of interest can exhibit complex pattern of association or clustering across different parts of the region. Second, spatial datasets are often massive  either they come from a large region or they are sampled at a high resolution. This poses a significant challenge for modeling because of the computational demand. We shall discuss approaches that can potentially increase the flexibility of these models and improve computational efficiency. The talk will be complemented with real examples for illustrating key concepts. Colloquium
Thursday, February 6^{th}, 2014 at 2:00 PM, NS 333
(Refreshments afterwards in room 334)
"Motion of fluids in the presence of a boundary"
GungMin Gie
Indiana University
Abstract: In most practical applications of fluid mechanics, it is the interaction of the fluid with the boundary that is most critical to understanding the behavior of the fluid. Physically important parameters, such as the lift and drag of a wing, are determined by the sharp transition the air makes from being at rest on the wing to flowing freely around the airplane near the wing. Mathematically, the behavior of such flows at small viscosity is modeled by the NavierStokes equations. In this talk, we discuss some recent results on the boundary layers of the NavierStokes equations. Colloquium
Wednesday, February 5^{th}, 2014 at 2:00 PM, NS 333
(Refreshments afterwards in room 334)
"Heat Kernels for a family of Grushin type operators"
DerChen Chang
Georgetown University, Departments of
Mathematics and Computer Science
Abstract: In this talk, we will construct the heat kernel for the secondorder operator Δ_{X}, which is a degenerate elliptic operator. Obviously, this operator is closed related to the Grushin operator L_{G}=1/2(∂/∂x)^{2}+1/2(x^{m}∂/∂y)^{2} with m∈N.
In this paper, we first study the geometry induced by the operator L_{G}. Given any two points in the space, the number of geodesics and the lengths of the geodesics are calculated. Then we find modified complex action functions and show that the critical values of this function will recover the lengths of the corresponding geodesics. We also find the volume element by solving a generalized transport equation. Finally, the formula for the heat kernel of the diffusion operator $∂/∂t–Δ_{X} is obtained. The formula involves an integral of a product between the volume function and an exponential term. Colloquium
Tuesday, February 4^{th}, 2014 at 2:00 PM, NS 333
(Refreshments afterwards in room 334)
"A new apprach to generalize the normal
distribution and its applications on unimodal and bimodal data"
Ayman Alzaatreh
Austin Peay State University
Abstract: The idea of generating skewed distributions from normal has been of great interest among researchers for decades. The initial work by Azaalini (1985) on skew normal distributions has motivated researchers in developing general or different approaches to generate skew normal distributions. In this paper, a technique proposed in Alzaatreh, Lee & Famoye (2013) is used for generating the Tnormal family of generalized normal distributions. Comparisons of this method and existing methods suggest that many existing methods can be derived using this framework. Some general properties including moments, mean deviations and Shannon entropy of the Tnormal family are studied. Some new generalizations of the normal distribution, which are members of the Tnormal family, are presented. Some applications of these generalized normal distributions are provided to illustrate their flexibility. Colloquium
Monday, February 3^{rd}, 2014 at 3:00 PM, NS 333
(Refreshments afterwards in room 334)
"Stochastic properties of dynamical systems"
Kevin McGoff
Duke University
Abstract: This talk concerns both statistical and probabilistic aspects of dynamical systems. On the statistical side, one observes data that is believed to be generated by a dynamical system from within a class of model systems, and the problem is to infer the generating system from the data. First, I will discuss recent work with S. Mukherjee, A. Nobel, and N. Pillai, in which we show that maximum likelihood estimation provides a consistent inference procedure for some classes of systems. Additionally, I will discuss some recent related work on the inference of gene regulatory networks from timeseries gene expression data. In a separate project joint with R. Pavlov, we consider dynamical systems from a probabilistic perspective. In particular, we study random shifts of finite type, which are dynamical systems whose rules of evolution are chosen at random. In this setting, we describe some likely properties of a system chosen at random. Fall 2013 Mathematics Colloquia
(in reverse chronological order)
Colloquium
Thursday, October 3^{rd}, 2013 at 2:30 PM, NS 333
(Refreshments afterwards in room 334)
"Generalized Oligarchies and congruences on finite lattices"
Melvin F. Janowitz
DIMACS, Associate Director
Abstract: In cases of a medical, terrorist, or natural emergency there often is a need to simultaneously reach multiple but possibly related decisions relating to public safety. A recent newsworthy event involves the explosions at the Boston Marathon. This suggests a study of the direct product of oligarchies involving the same collection of agents, but analyzing different but possibly related issues. The talk will relate conditions that normally involve social networks with conditions that have arisen in developing the fundamentals of the structure of finite lattices. The need for a simultaneous analysis of related conditions is that a solution to one problem may adversely affect the possible solutions to some other related problem. Tine permitting, there will be a discussion of how certain results for congruences on a finite lattice may be established without ever referring to the underlying lattice. Spring 2013 Mathematics Colloquia
(in reverse chronological order)
Colloquium
Friday, March 29^{th}, 2013 at 3:00 PM, NS 212C
"Some Elementary Number Theory Results and
Algorithms Are Revisited"
Peter Hamburger
Western Kentucky University
Abstract: Starting from a wellknown graph theory conjecture, (CaccettaHäggvist conjecture), I became interested in the behavior of the products of matrices with 0 or 1 entries, their eigenvalues and eigenvectors, and thus the roots of polynomials with integer coefficients. The deeper I went into these problems, I realized that I personally and the rest of the mathematics community do not know much about real numbers. While discussing these facts with a colleague, David Neal, he asked me a loosely related question about the normal distribution in statistics that I found intriguing. I also recognized that to answer either the graph theory conjecture or the question in statistics we need to know a lot more about elementary number theory. I also realized that even the facts that we should know are not conveyed to our students in algebra, calculus, discrete mathematics, and number theory classes. I believe we sacrifice the simplicity for efficiency; we miss out on elementary proofs in order to show more sophisticated approaches. In this talk I will address these issues. Unfortunately, as I dug into these problems further I recognized that I am much farther from solving my original problem than I believed before. Since I am old enough to collect Social Security benefits, I still remember the beginning of the famous Midwest Graph Theory (MIGHTY) meetings when researchers were not embarrassed to talk about mathematics in which they were interested but did not yet have significant results. This experience gives me the courage to present this talk to you. I believe my discussion is suitable for students, teachers, and researchers in mathematics and statistics. Some of the results are joint work with György Petruska, Department of Computer Science, Indiana University Purdue University Fort Wayne, Fort Wayne, Indiana Colloquium
Friday, February 23^{rd}, 2013 at 3:00 PM, NS 212C
(Refreshments in room 334 afterwards)
"US Navy Mathematicians vs JN25"
Chris Christensen
Northern Kentucky University
Abstract: As World War II loomed over the United States, the US Navy began searching college campuses for mathematicians with "cipher brains." The Navy offered these mathematicians a correspondence course in elementary cryptanalysis. When the US declared war, those who had successfully completed the course were commissioned into the Navy and assigned to OP20GM, the research section of Naval Communications in Washington, DC. At GM, these mathematicians applied the skills that they had learned as mathematicians to attack German, Italian, and Japanese codes and ciphers. One of the ciphers that they attacked was JN25, the primary Japanese naval cipher. Using mathematical ideas, the codebreakers at GM designed machines to attack JN25. These machines were engineered at National Cash Register in Dayton, OH. In this presentation, we will consider some of the cryptologic problems faced by the Navy's mathematiciancodebreakers and how they applied mathematical ideas to design machines to attack JN25. Fall 2012 Mathematics Colloquia
(in reverse chronological order)
Colloquium
Friday, November 9^{th}, 2012 at 3:00 PM, NS 333
(Refreshments in room 334 at 2:30 PM)
"Modeling Interepidemic Persistence of Rift
Valley Fever in Kruger Park's African Buffalo"
Carrie Manore
Tulane University
Abstract: Rift Valley fever virus (RVF) is an emerging zoonotic disease that cycles between wildlife, livestock, and people in Africa, causing significant loss. It is spread primarily by mosquitoes and emergence in Europe and North America is a risk. Current literature has focused on correlating large epidemics of RVF with weather events. However, little attention has been given to the underlying mechanisms driving epidemics and persistence, such as transmission from mosquitoes to wildlife and the persistence of the virus between wet seasons. It is unclear how RVF virus persists during the interepidemic periods, but there are two potential nonexclusive explanations for RVF virus persistence: 1) RVF is maintained in the mosquito population via vertical transmission, or 2) RVF circulates undetected in some wildlife reservoir population. We design and analyze a mathematical model for the dynamics of RVF to address the role of freeliving African buffalo in Kruger National Park in the persistence of RVF. We found that a combination of vertical transmission and circulation in an alternate reservoir is the most likely explanation of persistence of RVF in Kruger. This implies that exploration of vertical transmission rates and mosquito dynamics as well as transmission in alternate hosts is needed in order to understand RVF dynamics. Colloquium
Friday, October 12^{th}, 2012 at 3:00 PM, NS 333
(Refreshments in room 334 at 2:30 PM)
"Free resolutions of bracket powers of ideals"
Hamid Rahmati
Miami University
Abstract: To study modules over a commutative ring one can approximate them by modules from some standard class C. This leads to algebraic construction known as resolutions. Using resolutions, one can determine how close a module is to being an element of C. In this talk, we will discuss free resolutions of modules, and we will explain how properties of the ring impose uniform behavior on resolutions of certain modules. In some cases, we will also provide explicit description of these resolutions. Colloquium
Monday, September 17^{rd}, 2012 at 4:00 PM, NS 333
(Refreshments in room 334 at 2:30 PM)
"Lagrange interpolation, divided differences,
splines and Sobolev spaces"
Bogdan Bojarski
Polish Academy of Sciences
Abstract: I will discuss the characterization of Sobolev spaces in terms of pointwise inequalities and the concepts described in the title. This approach seems to be closely connected with the numerical analysis and effective description and approximation of Sobolev functions in terms of B splines of higher degree. Basic properties of Sobolev functions are discussed without Riesz potentials and Fourier transform. Presumably some new (??) formulas will be given. Colloquium
Friday, September 7^{rd}, 2012 at 3:00 PM, NS 333
(Refreshments in room 334 at 2:30 PM)
"The retreat of the less fit allele in a model
for population genetics"
Hans F. Weinberger
University of Minnesota
Abstract: It is shown that the solutions of a singlelocus diploid model with population control for the spatial and temporal interaction of the three genotypes approach a constantdensity equilibrium in which only the more fit allele is present, provided the fitnesses and the densitydependent per capita birth rate have certain properties. The speed at which this phenomenon spreads is at least as great as that of the linearization of the corresponding FisherKPP equation. A larger upper bound for this speed is also obtained. Spring 2012 Mathematics Colloquia
(in reverse chronological order)
Colloquium
Thursday, February 23^{rd}, 2012 at 1:00, NS 212D
(Refreshments in room 334 at 12:30)
"Modeling Sustained Treatment Effects in Tumor Xenograft
Experiments"
Dianliang Deng
University of Regina
Abstract: In cancer drug development, demonstrated efficacy in tumor xenograft models is an important step to bring a promising compound to human. A key outcome variable is tumor volume measured over a period of time, while mice are treated with certain treatment regimens. The statistical challenges include that sample sizes in xenograft experiments are usually limited because these experiments are costly, tumors in mice without treatment would keep growing until the tumorbearing mice die or are sacrificed, and missing data are unavoidable because a mouse may die of toxicity or may be sacrificed when its tumor volume reaches certain threshold (i.e. quadruples) or the tumor volume is too small and becomes unmeasurable. Furthermore, since the drug concentration in the blood of a mouse or its tissues may be stabilized at a certain level and maintained during a period of time, the treatment effect due to sustained drug release in tumor xenograft models should be taken into account. In this talk I will focus on this issue. We propose a novel comprehensive statistical model that accounts for the sustained release effects in tumor xenograft experiments and parameter constraints with incomplete longitudinal data. The ECM algorithm and Gibbs sampling for incomplete data are applied to estimating the doseresponse relationship in the proposed model. The model selection based on likelihood functions is given and a simulation study is conducted to investigate the performance of the proposed estimator. A real xenograft study on the antitumor agent temozolomide combined with irinotecan against the rhabdomyosarcoma is analyzed using the proposed methods. Colloquium
Friday, February 24^{th}, 2012 at 2:00, NS 212C
(Refreshments in room 334 at 1:30)
"Isomorphic subgraphs in uniform hypergraphs"
Paul Horn
Harvard University
Abstract: We show that any kuniform hypergraph with n edges contains two edge disjoint subgraphs of size Ω̃(n^{2/(k+1)}) for k=4, 5, and 6. This is best possible up to a logarithmic factor due to a upper bound construction of Erdős, Pach, and Pyber who show there exist kuniform hypergraphs with n edges and with no two edge disjoint isomorphic subgraphs with size larger than $Õ(n^{2/(k+1)})$. Furthermore, our result extends results of Erdős, Pach and Pyber who also established the lower bound for k=2 (i.e. for graphs), and of Gould and Rödl who established the result for k=3. In this talk, we'll discuss some of the main ideas of the proof, which is probabilistic, and the obstructions which prevent us from establishing the result for higher values of k. Colloquium
Friday, April 6^{th}, 2012 at TBA
"TBA"
Suion Ih
University of Colorado at Boulder
Colloquium
Friday, January 20^{th}, 2012 at 3:00, NS 333
(Refreshments in room 334 at 2:30)
"Measuring the Security of QuantumResistant Cryptosystems"
Daniel Smith
National Institute of Standards and Technology
Abstract: Since the development by Peter Shor of polytime quantum algorithms for factoring and computing discrete logarithms, it has been clear that new cryptographic primitives resistant to attack in the coming quantum era need to be constructed and standardized. Given the disparate nature of the most promising techniques, a significant challenge in the coming years is the derivation of a method to compare the security of these schemes. One of the leading prospects potentially providing quantumresistance is the multivariate family of public key cryptosystems. We will derive a metric determining the security of such systems against attacks exploiting differential symmetries. We then continue analyzing differential invariant structure, and deriving conditions assuring that a multivariate cryptosystem is immune to differential attack. From these investigations we will derive the necessary properties for a multivariate cryptosystem to provide security in the postquantum world. Colloquium
Monday, January 23^{rd}, 2012 at 1:30, NS 333
(Refreshments in room 334 at 1:00)
"Integervalued martingales or: How I ditched
the change and learned to love the dollar"
Jason Teutsch
Johns Hopkins University
Abstract: The classical randomness notions of Schnorr and Kurtz permit a gambler to bet any amount of money within his means. In this talk we consider a more realistic paradigm in which gamblers must place a minimum bet of one dollar. The corresponding randomness notion turns out to be incomparable with the classical notions. Most casinos operate by exploiting the law of large numbers, however, by examining an even more restrictive model in which we ban excessively large wagers, we discover an alternate principle through which a casino might operate profitably. The open questions and "paradox" at the end of this talk should be accessible to a general audience. Colloquium
Tuesday, January 24^{th}, 2012 at 1:30, NS 333
(Refreshments in room 334 at 1:00)
"Random matrix models and determinantal processes"
Dong Wang
University of Michigan
Abstract: Roughly speaking, a determinantal process is a point process whose correlation functions are in a determinantal form. Although determinantal processes are very special point processes, they are prevalent in practice, Some important physical models are directly related to determinantal processes, and many more physical processes are in the same universality class with some determinantal ones. Random matrix theory provides elegant and solvable examples of determinantal processes. By the analysis of various random matrix models, asymptotic properties of determinantal processes are computed explicitly. In this talk I will review the construction and properties of random matrices, and some determinantal processes that are not directly related to random matrix. Finally I present my own work, jointly with Adler and van Moerbeke, on the new minor processes of random matrices that are related to classical multiple orthogonal polynomials. Colloquium
Wednesday, January 25^{th}, 2012 at 1:30, NS 333
(Refreshments in room 334 at 1:00)
"Braess's Paradox in Expanders"
Stephen Young
University of Californai, San Diego
Abstract: Expander graphs are known to facilitate effective routing and most realworld networks have expansion properties. At the other extreme, it has been shown that in some special graphs, removing certain edges can lead to more efficient routing. This phenomenon is known as Braess's paradox and is usually regarded as a rare event. In contrast to what one might expect, we show that Braesss paradox is ubiquitous in expander graphs. Specifically, we prove that Braess's paradox occurs in a large class of expander graphs with continuous convex latency functions. Our results extend previous work which held only when the graph was both denser and random and for random linear latency functions. We identify deterministic sufficient conditions for a graph with as few as a linear number of edges, such that Braess's Paradox almost always occurs, with respect to a general family of random latency functions. Colloquium
Friday, January 27^{th}, 2012 at 3:00, NS 333
(Refreshments in room 334 at 2:30)
"Behavior of a Droplet on a Thin Fluid Film"
Ellen Peterson
Carnegie Mellon University
Abstract: Cystic Fibrosis is a disease of the lung, which is generally treated with an aerosol medicine. In order to better understand and improve this treatment we explore the spreading of a droplet (the medicine) on a thin liquid film (the lung lining). We assume both fluids are Newtonian, incompressible, and immiscible. We formulate a system of coupled fourth order partial differential equations that models the spreading of this simplified physical system. When a drop is placed on another fluid it may either completely spread over the underlying fluid or it may form a static lens. This behavior is predicted by the spreading parameter, which is a relation of the surface tensions of the fluids. In the case when a static lens forms, we explore the existence and structure of the equilibrium solution. Experimentally, we find that in some cases the spreading parameter predicts complete spreading however a static lens is observed. We compare the size of the static lens from the experiment to that predicted mathematically. The results of this investigation suggest that the lens resists flowing over the escaped layer of the same fluid  the mechanism of autophobing. Colloquium
Tuesday, January 31^{st}, 2012 at 1:30, NS 333
(Refreshments in room 334 at 1:00)
"Central discontinuous Galerkin methods for ideal MHD equations"
Liwei Xu
Rensselaer Polytechnic Institute
Abstract: Maintaining the divergencefree constraint on the magnetic field and preserving the positivity of density and pressure are two challenges in numerical simulation for ideal magnetohydrodynamic (MHD) equations. In this talk, we mainly discuss the design of exactly divergencefree central discontinuous Galerkin (DG) schemes solving ideal MHD equations. We first consider the second and third order divergencefree schemes. Exactly divergencefree magnetic fields are achieved by first approximating the normal component of the magnetic field through discretizing the magnetic induction equations on the mesh skeleton, namely, the element interfaces. Then it is followed by an element by element divergencefree reconstruction with the matching accuracy. The extension of this technique to design arbitrary order schemes is not trivial. We next discuss how this strategy, combined with extra consideration on the magnetic induction equations, can be extended to design divergencefree schemes of arbitrary order of accuracy. Essential analysis on these divergencefree schemes is presented. Colloquium
Tuesday, January 17^{th}, 2012 at 4:00, NS 333
(Refreshments in room 334 at 3:30)
"Limit theorems in stochastic analysis"
Arnab Ganguly
ETH Zurich
Abstract: Limit theorems for stochastic processes have a variety of applications in diverse fields ranging from statistics to biology. They are used in deriving continuous time models from the discrete time ones, analyzing numerical approximation schemes, studying stability of dynamical systems, etc. Two important topics in the area are weak convergence and large deviations. While weak convergence deals with the limiting form of a sequence of probability distributions, large deviation methods involve asymptotic analysis of very rare events. In this talk, I will discuss two approaches, one for weak convergence and the other for large deviations, which provide a systematic way to study limit theorems for a broad class of stochastic differential equations. Colloquium
Thursday, January 12^{th}, 2012 at 1:30, NS 333
(Refreshments in room 334 at 1:00)
"Bounding Projective Dimension and Regularity"
Jason McCullough
University of California, Riverside
Abstract: Given a polynomial ring R=K[x_{1},&ldots;, x_{n}] and a homogeneous ideal I of R, one can measure the computational complexity of the ideal in several ways. One of these, is the projective dimension; that is, the minimal length of a (graded) free resolution. Another is the regularity, which roughly speaking, measures the degrees of the relations that appear in the free resolution. There is great interest in finding bounds on these two invariants of an ideal in terms of various input data, such as the degrees and number of generators, the number of variables of the ring, or the degrees of syzygies (relations) early in the resolution. In particular, Stillman's Question asks for a bound on the projective dimension of an ideal purely in terms of the degrees of the generators. This is an open problem with connections to bounding regularity as well. In my talk I will describe some of my work in defining families of ideals with large projective dimension, thus giving large lower bounds on any answer to Stillman's Question. In particular, my coauthors and I defined a threegenerated ideal with exponential projective dimension relative to the degrees of the generators. I will also talk about how these examples motivated a new kind of bound on regularity in terms of only part of the resolution of the ideal. Colloquium
Tuesday, January 10^{th}, 2012 at 1:30, NS 333
(Refreshments in room 334 at 1:00)
"Measuring Singularities"
Wenliang Zhang
University of Michigan
Abstract: The zerolocus of a polynomial is a primary object in Algebraic Geometry. When we visualize these loci (for example, this is possible when there are two variables), we can see (intuitively) that some are more singular than others. A natural question is, can we quantify how singular different polynomials are? In this talk, I wish to explain an analytic approach (in characteristic 0) and an algebraic approach (in characteristic p>0) to this question. If time permits, I will also discuss results and open problems regarding the connections between these two approaches. Fall 2011 Mathematics Colloquia
(in reverse chronological order)
Friday, November 18^{th}, 2011 at 3:30PM, NS 212C
(Refreshments in room 334 at 3:00)
"Prediction of Tumor Growth and Treatment
Response using Integrated Mathematical/Experimental
Modeling"
Hermann B. Frieboes
University of Louisville Department of
Bioengineering/James Graham Brown Cancer Center
Abstract: Cancer behavior at the system level is complex, involving multifaceted interactions of multiple cell and tissue types within a diverse environment. Many factors contribute to this complexity, including tissue microstructure, inter and intracellular signaling, angiogenesis, vascularization, and the immune response, all of which have effects across a wide range of time and length scales. Models that focus on processes at individual scales from basic science to patient bedside while neglecting to address this multiscale complexity have in many cases proven inadequate for cancer treatment and prognosis, leading to therapies with suboptimal activity. To address this issue, we employ a multidisciplinary methodology that integrates biocomputational modeling with laboratory and clinical data to quantitatively study the effects of cellular and microenvironmental processes on cancers at the system level. This integrative process has led to progressively more accurate and biologypredictive 3D cancer models capable of representing tumor growth through the stages of avascular growth, vascularization, and tissue invasion, and that can be used to interrogate changes in the system dynamics, including those related to therapeutic strategies. Our work suggests that tumorscale growth, invasion, and drug response are predictable processes regulated by heterogeneity in the underlying interactions between genotypic, phenotypic, and microenvironmental parameters. Theoretical and experimental evidence indicates that threedimensional tissue architecture and dynamics are coupled in complex, nonlinear ways to cell phenotype, which in turn is related to molecular phenomena and the microenvironment. This study provides evidence that local gradients in oxygen and nutrient due to impaired vascularization lead to reduction in cell adhesion forces causing instability at the tissuetumor interface and increased invasive behavior. In turn, these invasive characteristics strongly influence both the tumor metastatic potential and local resectability. As a result, treatment that aims for vascular reduction may paradoxically increase invasiveness. These findings are supported by experimental and clinical observations which have shown increased tumor fragmentation and vessel cooption following antiangiogenic therapies. Based on this work, we conclude that by applying a biocomputational multiscale approach we can gain deeper insight into cancer behavior and response to treatment, e.g., antiangiogenic and chemotherapeutic, as well as nanovectorbased regimens. In the future, incorporation of patientspecific data into this biocomputational modeling could enhance treatment prognosis as well as the design of more effective therapies tailored to individual patients. Colloquium
Wednesday, November 9^{th}, 2011 at 2:00PM, NS 212D
(Refreshments in room 334 at 1:30)
Coloring with Distance Constraints: The Packing
Chromatic Numbers of a Graph
Wayne Goddard
Clemson University
Abstract: Let S=(a_{1}, a_{2},...) be an infinite nondecreasing sequence of positive integers. An Spacking kcoloring of a graph G is a mapping from V(G) to {1, 2, ..., k} such that vertices with color i have pairwise distance greater than a_{i} and the Spacking chromatic number S(G) of G is the smallest integer k such that G has an Spacking kcoloring. This concept generalizes both proper colorings and broadcast colorings. In this talk we explore broadcast colorings and this generalization. This includes bounds, exact values, and some surprising complexity results. Spring 2011 Mathematics Colloquia
(in reverse chronological order)
Colloquium
Wednesday, August 24^{th}, 2011 at 2:00PM, NS 333
(Refreshments in room 334 at 1:30)
"Why are Matchings so Important"
David M. Howard
Technion Israel Institute of Technology
Abstract: In this talk I will discuss the idea of a matching in a graph. I will spend time illustrating their importance and connections with other fields of mathematics. I will also go into detail about the idea of rainbow matchings and how they are at the core of some famous conjectures in matching theory. Colloquium
Friday, March 25^{th}, 2011 at 12:30, NS 212D
(Refreshments in room 334 at 12:00)
"New Integer Sequences From the Past Year"
Neil J. A. Sloane
AT&T Shannon Labs
Abstract: I will discuss some interesting new integer sequences contributed by M. LeBrun, J. van Eck, H. van der Sanden, G. Back & M. Caragiu, M. Sapir, and N. Inaba, related to number theory and geometry. There are many unsolved problems. I will also give a brief report on the new OEIS, which thanks to the work of Russ Cox and David Applegate, was successfully launched on Nov. 11 2010, ending two years of struggle (see http://oeis.org). Colloquium
Friday, March 11^{th}, 2011 at 2:00, NS 212D
(Refreshments in room 334 afterwards)
"Distributing medicine using PageRank"
Paul Horn
Emory University
Abstract: Disease breaks out on a graph! Having isolated the source of the breakout, one would like to know how and where to distribute medicine in order to ensure that the disease dies out quickly. On the other hand, cost is an issue and one would like to not distribute medicine to everywhere on the graph if it is not truly necessary. Modeling the spread of disease with the a variant of the contact process, a classical stochastic process designed to model disease spread, we show that an effective strategy is to consider PageRank vectors, the same objects used by Google's search engine. In particular, we show that by giving medicine to vertices with high personalized PageRank we can control the probability that the disease escapes the medicated set while at the same time ensuring that the disease on the medicated set dies quickly with high probability. Colloquium
Friday, March 4^{th}, 2011 at 1:00, NS 212D
(Refreshments in room 334 at 12:30)
"SelfExciting Hurdle Models for Terrorism"
Michael D. Porter
Abstract: The contagiousness of terrorism is investigated by studying the influence that a terrorist attack has on the likelihood of future incidents. Examination of terrorism data from Indonesia and TimorLeste, which has been subjected to 454 terrorist attacks between 1977 and 2007, reveals evidence that terrorist activity does indeed increase following successful attacks.
Our analysis employs a shot noise process to explain the selfexciting nature of the terrorist activities. This model estimates the probability of future attacks as a function of the times since the past events. In addition, the possibility of multiple coordinated attacks on the same day compelled the use of hurdle models to jointly model the probability of an attack day with the number of attacks per day. Interpretation of the model parameters and the suitability of these models for Indonesian terrorism is discussed. Colloquium
Monday, February 28^{th}, 2011 at 3:00, NS 212D
(Refreshments in room 334 at 2:30)
"On Alternative Cauchy Functional Equation on Semigroups"
Valeriy Fayizie
Tver State Agricultural Academy
Abstract: On the 44th ISFE in Louisville, KY, Professors R. Ger and G. L. Forti asked for a solution to the alternative Cauchy functional equation (where $f$ is a realvalued function) on semigroups and groups where the Cauchy equation is not stable. In particular, Professor Forti posed the following problem: Solve the alternative Cauchy equation on free semigroups of rank two where the Cauchy equation is not stable. We present the simplest semigroup where the Cauchy equation is not stable and then solve the above equation on this semigroup. Then we present the solution of this equation on free noncommutative semigroups of arbitrary rank. Fall 2010 Mathematics Colloquia
(in reverse chronological order)
Colloquium
Friday, October 15^{th}, 2010 at 2:30, NS 333
(Refreshments in room 334 at 2:00)
"Multivariate PostQuantum Cryptography"
Daniel Smith
University of Louisville
Abstract: We explore a few interconnected topics in multivariate cryptography, illustrating the history of the field by exploring the development of a particular cryptosystem. We will review the history of the SFLASH signature scheme from its creation to its demise... and eventual rebirth. In this journey we will examine the role of proof in modern algebraic cryptography and highlight possible directions which may guarantee greater information assurance in the coming postquantum era. Spring 2010 Mathematics Colloquia
(in reverse chronological order)
Colloquium
Monday, March 29^{th}, 2010 at 3:30, NS 212F
(Refreshments in room 334 at ***3:00)
"Statistical Convergence and Its Extensions"
Pratulananda Das
Jadavpur University, India
Abstract: The idea of convergence of a real sequence had been extended to statistical convergence by Fast (also by Schoenberg) as follows: If N denotes the set of natural numbers and K⊂N then K_{n} denotes the set {k∈K:k≤n\} and K_{n} stands for the cardinality of the set K_{n}. The natural density of the subset K is defined by d(K)=lim_{n→∞}K_{n}/n$$ provided the limit exists. A sequence {x_{n}}_{n∈ℕ} of points in a metric space (X,ρ) is said to be statistically convergent to ℓ if for arbitrary ε>0, the set K(ε)={k∈ℕ:d(x_{n},ℓ)≥ε} has natural density zero. Very recently Di Maio and Kočinac introduced the concept of statistical convergence in topological spaces as well as uniform spaces and established the topological nature of this convergence as also offered some applications to selection principles theory, function spaces and hyperspaces. This has been further extended to nets using the concept of ideals.It has been observed that two types of convergence, namely $I$convergence and I^{*}convergence can be considered in line of statistical and s^{*}convergence of Di Maio et al but unlike the statistical case, these concepts are not in general equivalent even in first countable spaces (which can be shown by constructing proper examples) and only coincide if and only if the ideal satisfies a condition called condition (DP). In this talk we will discuss some developments in this area. Colloquium
Friday, March 26^{th}, 2010 at 1:00pm, NS
333
(Refreshments in room 334 at 2:00pm)
" Class Groups of Global Function Fields "
Yoonjin Lee
Ewha Womans University
Abstract: The problem of determining the structure of class groups of number fields or function fields dates back to Gauss. In this talk we discuss the structure of class groups of global function fields. We focus on the Scholz Theorem (Reflection Theorem) and the explicit construction methods of infinitely many global function fields of a given field extension degree, a prescribed unit rank and guaranteed class group rank. We also discuss some interesting applications of the Scholz Theorem to other research projects. Colloquium
Thursday, March 25^{th}, 2010 at 2:00, NS 333
(Refreshments in room 334 afterwards)
"The convex hull of a space curve"
Bernd Sturmfels
University of California, Berkeley
Abstract: The boundary of the convex hull of a compact algebraic curve in real 3space defines a real algebraic surface. For general curves, that boundary surface is reducible, consisting of tritangent planes and a scroll of stationary bisecants. We express the degree of this surface in terms of the degree, genus and singularities of the curve. We present methods for computing their defining polynomials, and we exhibit a wide range of examples. Most of these are innocentlooking trigonometic curves such as (cos(t), sin(2t), cos(3t)). This is joint work with Kristian Ranestad (arXiv:0912.2986). Colloquium
Friday, March 12^{th}, 2010 at 4:00, NS 333
(Refreshments in room 334 at 3:30)
"The use of mathematical models in the study of
disease dynamics and control "
Zhilan Feng
Purdue University
Abstract: In this talk I shall present two examples of using mathematical models to study the disease dynamics and control of influenza. The first example focuses on the use of a simple SIR epidemic model to forecast the course of the 2009 H1N1 pandemic influenza in the US. According to CDC 2009 H1N1 confirmed case count data, the model accurately predicted the peak time of the pandemic. The second example concerns a multiplestrain model which can be used to explore influenza medication strategies (preexposure or prophylaxis, postexposure/presymptom onset, and treatment at successive clinical stages) that may affect evolution of resistance (select for resistant strains within or facilitate their spread between hosts). The model results are made accessible via userfriendly Mathematica notebooks. Colloquium
Friday, March 5^{th}, 2010 at 4:00, NS 333
(Refreshments in room 334 at 3:30)
"Nonparametric estimation for a timechanged Lévy model
"
Jose E. FigueroaLopez
Purdue University
Abstract: Exponential timechanged Lévy processes are known to incorporate several stylized features of asset prices. In this talk we analyze the problem of estimating the infinitedimensional parameter controlling the jump behavior of the process as well as the underlying random clock. We attain consistent estimation of the relevant parameters when both the sampling frequency and timehorizon get larger, and illustrate the performance of the estimators with simulated and real data. Colloquium
Friday, February 26^{th}, 2010 at 3:00,
NS 333
(Refreshments in room 334 at 2:30)
"Direct and Inverse Scattering Problems in a
Stratified Medium"
Peijun Li
Purdue University
Abstract: Scattering problems are concerned with the effect an inhomogeneous medium has on an incident wave. In particular, if the total field is viewed as the sum of an incident field and a scattered field, the direct scattering problem is to determine the scattered field from a knowledge of the incident field and the differential equation governing the wave motion; the inverse scattering problem is to determine the nature of the inhomogeneity from a knowledge of the scattered field. Scattering problems are basic in many scientific areas such as radar and sonar (e.g. submarine detection), geophysical exploration (e.g. oil and gas exploration), medical imaging (e.g. breast cancer detection), and nearfield optical microscopy (e.g. detection and spectroscopy of single molecules). In this talk, we consider both the direct and inverse scattering problems for the twodimensional Helmholtz equation, which models a timeharmonic plane wave incident on an inhomogeneity embedded in a stratified background medium. I will present a coupling of the finite element and boundary integral equation method for the direct problem. The wellposedness of the continuous and discrete problems, as well as optimal error estimates for the variational approximation will be discussed. Numerical results will be shown to illustrate the performance of the proposed method. A continuation approach will be reported for the inverse scattering problem. The algorithm requires multifrequency scattering data. Using an initial guess from the Born approximation, each update is obtained via recursive linearization on the wavenumber by solving one forward problem and one adjoint problem of the Helmholtz equation. I will also discuss convergence issues for the continuation algorithm and highlight some ongoing projects for scattering problems in complex and random environment. Fall 2009 Mathematics Colloquia
(in reverse chronological order)
Colloquium
Thursday, December 10^{th}, 2009 at 4:00, NS 333
(Refreshments in room 334 at 3:30)
"Central Limit Theorems for Hilbertspace Valued Random Fields satisfying a Strong Mixing Condition"
Cristina Tone
Indiana University
Abstract: We want to study the asymptotic normality of the normalized partial sum of a Hilbertspace valued random field satisfying the ρ'mixing condition. We proceed by proving a central limit theorem for a ρ'mixing random field of realvalued random variables. Next, we extend the realvalued case to a random field of mdimensional random vectors, m≥1, satisfying the same conditions. Finally, we extend the finitedimensional case to a (infinitedimensional) Hilbert spacevalued random field satisfying the same mixing condition. Colloquium
Wednesday, December 9 ^{th}, 2009 at
4:00, NS 333
(Refreshments in room 334 at 3:30)
"Degree Ramsey Numbers of Graphs"
Kevin Milans
University of Illinois
Abstract: In Ramsey Theory, we study when every partition of a large structure yields a part with additional structure. For example, Van der Waerden's theorem states that every scoloring of the integers contains arbitrarily long monochromatic arithmetic progressions, and the HalesJewett Theorem guarantees that every game of tictactoe in high dimensions has a winner. Ramsey's Theorem implies that for any target graph G, every scoloring of the edges of some sufficiently large host graph contains a monochromatic copy of G. In Ramsey's Theorem, the host graph is dense (in fact complete). We explore conditions under which the host graph can be sparse and still force a monochromatic G. A graph H arrows a graph G if every 2edgecoloring of H contains a monochromatic copy of G. The degree Ramsey number of G is the minimum k such that some graph with maximum degree k arrows G. Burr, Erdős, and Lovász found the degree Ramsey number of stars and complete graphs. We establish the degree Ramsey number exactly for double stars and for C_{4}, the cycle on four vertices. We prove that the degree Ramsey number of the cycle C_{n} is at most 108 when n is even and at most 3890 in general. Consequently, there are very sparse graphs that arrow large cycles. We present a family of graphs in which the degree Ramsey number of G is bounded by a function of the maximum degree of G and ask which graph families have this property. This is joint work with Tao Jiang, Bill Kinnersley, and Douglas B. West. Colloquium
Monday, December 7^{th}, 2009 at 4:00, NS 212F
(Refreshments in room 334 at 3:30)
" Bubbles and Futures contracts in markets with =
shortselling constraints "
Sergio Pulido
Cornell University
Abstract: The current financial crisis, product of the burst of the alleged real estate bubble, has brought back the attention of the financial and academic community to the study of the causes and implications of asset price bubbles. In recent works Jarrow, Protter and Shimbo (2006, 2008) and Cox and Hobson (2005) developed an arbitragefree pricing theory for bubbles in complete and incomplete markets. These papers approach the subject by using the insights and tools of mathematical finance, rather than equilibrium arguments where substantial structure, such as investor optimality and market clearing mechanisms, has to be imposed. In their framework, bubbles occur because the market's valuation measure is a local martingale measure which is not a martingale measure and hence the discounted asset's price is above the expectation of its future cashflows. The existence of bubbles does not contradict the condition of no free lunch with vanishing risk (NFLVR), because shortselling constraints, given by an admissibility condition on the set of trading strategies, do not allow investors to make a riskless profit from the overpriced securities. In an attempt to combat sharp and extreme declines in certain stock prices related to the bursting of these bubbles, both the British and the American government imposed temporary bans on the short selling of certain categories of stocks. This affects the liquidity of stocks, and has other less obvious effects.The aim of this talk is to explain how the previous work extends to models where some assets cannot be sold short whatsoever and explore how financial instruments such as futures contracts behave in such models. Colloquium
Friday, December 4^{th}, 2009 at 4:00, NS
333
(Refreshments in room 334 at 3:30)
"Variational representations, small noise large
deviations and applications"
Vasileios Maroulas
IMA, University of Minnesota
Abstract: Variational representations for infinite dimensional Brownian motions and Poisson random measures are considered in order to establish small noise (uniform) large deviations. Using this approach, a large deviation principle for a class of stochastic reactiondiffusion equations is established under conditions that are substantially weaker than those available in the literature, and large deviation estimates for a family of infinite dimensional stochastic flows of diffeomorphisms that arise in certain image analysis problems are demonstrated. The small noise large deviations results for the stochastic diffeomorphic flows are then applied to a stochastic Bayesian formulation of an image matching problem, and an approximate maximum likelihood property is shown for the solution of an optimization problem involving the large deviations rate function. This talk is based on joint works with A. Budhiraja and P. Dupuis. Colloquium
Wednesday, December 2^{nd}, 2009 at 4:00 pm, NS 212F
(Refreshments in room 334 at 3:30 pm)
"Dimension, correlation, and height sequence in partially ordered sets"
Csaba Biro
University of South Carolina
Abstract: The dimension of a partially ordered set (poset) P is the minimum number of linear extensions, such that their intersection is P. In this talk, we discuss several questions and result related to this concept. First we restrict our attention to certain classes of posets defined by relations of line segments on the plane. Then we introduce an interesting analogy with chromatic number of graphs, and we show graph theoretic results inspired by dimension of posets. Finally we look at posets from a computational point of view: a poset is a result of a halted sorting process. We investigate the probability that a certain point will end up at certain height if the sorting is finished. Colloquium
Thursday, December 3^{th}, 2009 at 4:00
pm, NS 110
(Refreshments in room 334 at 3:30 pm)
"Interval Partitions and Stanley Depth"
Mitchel T. Keller
Georgia Institute of Technology
Abstract: This talk explores a connection between the combinatorics of partially ordered sets and commutative algebra. In 1982, Richard Stanley introduced the concept of what is now know as the Stanley depth of a module over a commutative ring. He also conjectured that a module's Stanley depth is always greater than or equal to its depth. Some cases of Stanley's conjecture have been resolved using algebraic techniques over the years, but the conjecture remains largely open. Recently, a combinatorial approach to the problem was introduced by Herzog, Vladoiu, and Zheng. They established a connection between Stanley decompositions (the structures used to determine Stanley depth) of monomial ideals and interval partitions of finite posets associated to those ideals. This connection has led not only to additional results on Stanley depth but also to interesting and elegant combinatorics. The primary focus of this talk is the combinatorics involved in the research, with the algebraic question discussed to provide the motivation and ideas for future research. This talk contains joint work (in various combinations) with Csaba Biro, David M. Howard, YiHuang Shen, Noah Streib, William T. Trotter, and Stephen J. Young. Colloquium
Friday, November 6^{th}, 2009 at 3:30, NS
333
(Refreshments in room 334 at 3:00)
"Continuous Wavelet Analysis: Introduction and
some applications"
Victor Henner
Department of Physics, University of
Louisville
Abstract: The WA appeared as result of a demand to analyze data which Fourier analysis (FA) couldn't successfully manage. Because of nonlocality of trigonometric functions the information obtained with FA is completely delocalized among all spectral coefficients. Random singularities in data affect all Fourier coefficients. WA allows the extraction of high frequency information from relatively short intervals, and low frequency information from wide intervals, thus providing an optimal compromise with the uncertainty principal. WA is used for studying local structures or for analysis of spectral properties. An important feature of WA is that it is significantly less sensitive to noise than Fourier analysis. Applications to be presented: 1. Some elementary particle data analysis; 2. Interactive software to work with 1D continuous wavelets. Colloquium
Friday, Oct. 16^{th}, 2009 at 3:30, NS 333
(Refreshments in room 334 at 3:00)
"Topological Degree theory and its applications to
traveling wave solutions"
Changbing Hu
University of Louisville
Abstract: In this talk we will survey the classical topological degree theory, and its application to the existence of traveling wave solutions for some reaction diffusion equations and integral difference equations arising from mathematical biology. This talk is based on a series of seminars on the LeraySchauder degree theory held in the year of 20082009. The talk will start from the definition of topological degree, then move on to LeraySchauder theory. For its application in reaction diffusion equations we will follow the theory developed by A. Volpert, V. Volpert and V. Volpert for systems of parabolic equations. The second application is an ongoing project, we will briefly present the problem, outline the steps to be done to prove the existence of traveling waves to the integral difference equations. Spring 2009 Mathematics Colloquia
(in reverse chronological order)
Colloquium
Thursday, April 16^{th}, 2009 at 4:00, NS 234
(Refreshments in room 334 at 3:30)
"Mathematical Analysis of Bursting Oscillations in Nerve and Endocrine Cells"
Richard Bertram
Florida State University
Abstract: Nerve cells convey information through patterns of electrical impulses. Endocrine cells secrete hormones in response to electrical impulses. In both cell types, the impulses often come in periodic bursts, during which a highfrequency series of spikes (active phase) is followed by a quiescent period (silent phase). The dynamic mechanism of bursting has been the focus of attention for more than two decades. In this seminar, I discuss how geometric singular perturbation theory, or fast/slow analysis, is used to understand bursting oscillations. We begin with simple relaxation oscillations, and then progress to ever more exotic behaviors, from bursting to phantom bursting, and finally, to compound bursting. Colloquium
Wednesday, April 8^{th}, 2009 at 2:00, NS 333
(Refreshments in room 334 afterwards)
"Bounded generation of groups and semigroups"
James Mitchell
University of St Andrews
Abstract: If G is a group generated by U, does U necessarily generate G in a bounded way? More precisely, does there exist a number n such that every element of G can be given as a product of length at most n over U. In 2005 George Bergman proved that this is the case for the symmetric group, and the property became known Bergman's propertry. In this talk we will show that many natural semigroups exhibit the same property as the symmetric group, and we will discuss the related notion of the cofinality of a semigroup. Colloquium
Monday, February 23^{rd}, 2009 at 2:00, NS 333
(Refreshments in room 334 afterwards)
"New Formulas for TracyWidom Functions"
Robert Buckingham
Centre de Recherches Mathématiques
Abstract: The TracyWidom functions describe the limiting distribution of a variety of statistical quantities, including the largest eigenvalue of a random matrix drawn from the Gaussian orthogonal, symplectic, or unitary ensembles (GOE, GSE, or GUE), the longest increasing subsequence of a random permutation, and the outermost particle in a sea of nonintersecting Brownian particles. We obtain new formulas for the TracyWidom functions in terms of integrals of Painleve functions. Using these new formulas we find the complete asymptotic expansion of the lefthand tail of the GOE and GSE TracyWidom functions for the first time, as well as a second proof of the recently obtained result for the GUE case. We conclude by discussing progress on a new family of "incomplete" TracyWidom distributions corresponding to the largest observed eigenvalue if each eigenvalue has a fixed probability of being observed. This is joint work with Jinho Baik and Jeffery DiFranco. Colloquium
Friday, February 19^{th}, 2009 at 2:00, NS 333
(Refreshments in room 334 afterwards)
"Association schemes and
the Qpolynomial property"
Jason Williford
University of Colorado, Denver
Abstract: An association scheme can be viewed as a partition of a complete graph into regular subgraphs whose adjacency matrices together with the identity matrix form the basis of a matrix algebra. The theory of association schemes has proven useful in several areas of discrete mathematics such as coding theory, finite geometry, and design theory, to name a few. A distanceregular graph is a graph whose distance graphs form an association scheme. Much attention has been paid to association schemes which are generated by distanceregular graphs; however, the formal dual to this type of scheme, known as a "Qpolynomial" scheme, remains less understood. Though few examples of Qpolynomial schemes which do not arise from distance regular graphs are currently known (and most known examples are linked to exceptional lattices, simple groups, designs and codes) in recent years the number of known examples has been steadily growing. In this talk some introductory material on association schemes will be presented, followed by a description of recent progress toward understanding the structure of Qpolynomial schemes. Colloquium
Friday, February 20^{th}, 2009 at 4:00, NS 333
(Refreshments in room 334 at 3:30)
"On a problem of Erdos plus a little summability"
Professor Harry Miller
International University of Sarajevo
Abstract: I will split the talk into two parts. The first part will give an update of an old problem of Erdos. The second part will deal with statistical convergence  a summability method. Colloquium
Thursday, February 19^{th}, 2009 at 2:00, NS 333
(Refreshments in room 334 afterwards)
"Performance Analysis of Manyserver Queues with Reneging"
Weining Kang
Carnegie Mellon University
Abstract: Motivated by problems of current relevance for call centers, we consider a queuing system with a single pool of N identical servers that process incoming customers who have generally distributed service requirements, and abandon the queue if their waiting time exceeds their socalled patience time. We derive a firstorder approximation of this system and study its asymptotic behavior, as the number of servers goes to infinity. We also discuss the implications of our analysis for the design of a call center. The analysis involves a range of mathematical tools, from measurevalued processes and renewal theory to partial differential equations. Colloquium
Wednesday, February 18^{th}, 2009 at 2:00, NS 333
(Refreshments in room 334 afterwards)
"Rainbow Colorings and Rainbow Connectivity of Graphs"
Professor Futaba Okamoto
University of Wisconsin, La Crosse
Abstract: Let G be an edgecolored graph where adjacent edges may be colored the same. A path P in G is a rainbow path if no two edges of P are colored the same. The graph G is rainbowconnected if every two vertices of G are connected by a rainbow path. Generalizations of these concepts are introduced. Colloquium
Monday, February 16^{th}, 2009 at 2:00, NS 234
(NOTE NONSTANDARD LOCATION)
(Refreshments in room 334 afterwards)
"Coloring and Listcoloring of Graphs"
Dan Cranston
DIMACS
Abstract: Graph coloring is the standard way to model many scheduling problems, and it has applications in areas such as register allocation, radio frequency assignment, secret sharing, and even Sudoku puzzles. We will review some major results in graph coloring and one of its popular variants, listcoloring. I will then discuss open problems in these areas and progress that I have made on them. Colloquium
Wednesday, February 13^{th}, 2009 at 3:30, NS 333
(Refreshments in room 334 at 3:00)
"Serre's Multiplicity Conjecture and Frobenius
Endomorphism"
Professor Jinjia Li
Middle Tennessee State University
Abstract: Intersection multiplicity is an important invariant, arising naturally from the study of the intersection of two varieties. I will discuss a definition of it introduced by Serre and some longstanding conjectures related to it. Frobenius endomorphism is one of the useful tools to attack these problems and many other homological conjectures in the characteristic $p$ case. I will briefly discuss some recent results regarding understanding Frobenius endomorphism from homological point of view. No background in commutative algebra or homological algebra is assumed for the audience. Colloquium
Wednesday, February 11^{th}, 2009 at 2:00, NS 333
(Refreshments in room 334 afterwards)
"Homological Conjectures and Invariant Theory"
Jason McCullough
University of Illinois at UrbanaChampaign
Abstract: The Homological Conjectures are an interconnected set of open problems in the homological theory of modules over commutative rings that have attracted a lot of attention over the past 40 years. In this talk I will discuss Hochster's Direct Summand Conjecture, the Vanishing Maps of Tor Conjecture and the Strong Direct Summand Conjecture. As a window to these problems, I will start with an application to invariant theory. In particular, I will discuss the problem of how to show that the ring of Ginvariant polynomials for a group G is ``nice'' in some way. I will finish the talk by discussing some of my work on the Strong Direct Summand Conjecture. Colloquium
Monday, February 9^{th}, 2009 at 2:00, NS 333
(Refreshments in room 334 afterwards)
"Effectiveness and Computation in Algebra and Geometry"
Professor Wesley Calvert
Murray State University
Abstract: Early in the development of twentiethcentury mathematics, van de Waerden, Dehn, and others asked questions about the existence of "explicit" solutions to many problems. With the introduction of precise definitions of algorithms in the 1930's, these questions were investigated for some time before the revival in recent decades of "computational mathematics." In the present talk I will attempt to describe relationships between the classical logical discipline of "computable mathematics" and the modern field of "computational mathematics." Several nonequivalent definitions of computation will be used. Examples will include fields, rings of integers, homotopy groups, the classification of manifolds, and Serre's conjecture on free modules. Colloquium
Friday, February 6^{th}, 2009 at 4:00, NS 333
(Refreshments in room 334 at 3:30)
""
Professor Prasanna Sahoo
University of Louisville
Abstract: In 1940, S. M. Ulam asked the following questions: Given a group G_{1}, a metric group G_{2} with metric d(•,•) and a positive number ε does there exist a δ>0 such that if f:G_{1}→G_{2} satisfies d(f(xy),f(x)f(y))≤δ for all x,y in G_{1}, then a homomorphism $φ:G_{1}→G_{2}$ exists with d(f(x),φ(x))≤ε for all x∈G_{1}? In this talk, I will present some old and recent results on this Ulam's problem. Fall 2008 Mathematics Colloquia
(in reverse chronological order)
Colloquium
Friday, December 5^{th}, 2008 at 3:00, NS 333
(Refreshments in room 334 at 2:30)
"Modeling the Impact of Climate Change and
Mosquito Transgenes on Malaria Transmission"
Professor Jia Li
University of Alabama, Huntsville
Abstract: In this talk, we start with a simple SEIR model for malaria transmission dynamics, based on a system of ordinary differential equations, as our baseline model. We derive a formula for the reproductive number and investigate the existence of endemic equilibria. We then introduce a simple twostagestructured mosquito population model where the mosquito population is divided into two classes. After a brief investigation on this simple stagestructured mosquito model, we incorporate it into the simple SEIR malaria model. We present basic analysis for the combined model and discuss how this combined model can help us study the impact of climate change on the transmission of malaria and other mosquitoborne diseases. We also show that, using the reproductive number as a bifurcation parameter, the simple malaria model and the mosquitostagestructured model can have a backward bifurcation. We finally talk about the interaction between wild and transgenic mosquitoes and its impact on the malaria transmission. 2 Colloquia
Friday, November 14^{th}, 2008 at 3:00, NS 333
(Refreshments in room 334 at 2:30)
"A model for a population competing for resources"
Professor Daniela Bertacchi
Università di MilanoBicocca, Italy
Abstract: I will discuss a generalized branching random walk as a model for a population breeding and dying in a spatially structured environment. In this model particles are born with higher probability at sites which are not too crowded. I will compare this model with some classical mathematical models. Under general assumptions on the breeding rates we proved the existence of a phase where the population survives without exploding and constructed a nontrivial invariant measure for this case. The results are joint work with G.Posta and F.Zucca. "Survivals for branching random walks"
Professor Fabio Zucca
Politecnico di Milano, Italy
Abstract: The branching random walk on Z^{d} exhibits only two behaviors (depending on the breeding parameter): either the process dies out a.s. or with positive probability each site is visited infinitely many times (strong survival). On general graphs (such as trees) there might be values of the parameter such as the process eventually leaves any finite set but does not die out. This is what is called weak survival. Our aim is to describe the critical values of the breeding parameter and discuss the behavior of the process at these critical values, for branching random walks on weighted graphs. The results are joint work with D.Bertacchi. Colloquium
Thursday, September 19^{th}, 2008 at 3:00, NS 333
(Refreshments in room 334 at 2:30PM)
"Transseries"
Professor Gerald A. Edgar
The Ohio State University
Abstract: From the simplest point of view, transseries are a new kind of expansion for realvalued functions. But transseries constitute much more than that–they have a very rich (algebraic, combinatorial, analytic) structure. The set of transseries is a large ordered field, extending the real number field, and endowed with additional operations such as exponential, logarithm, derivative, integral, composition. Over the course of the last 20 years or so, transseries have emerged in several areas of mathematics: analysis, model theory, computer algebra, surreal numbers. This talk will be an introduction for the nonspecialist mathematician. Colloquium
Thursday, September 18^{th}, 2008 at 3:00, NS 333
(Refreshments in room 334 afterwards)
"Galois Rings and Pseudorandom Sequences"
Professor Patrick Sole
CNRS, Sophia Antipolis
Abstract: We survey our constructions of pseudorandom sequences (binary, Z_{8}, Z_{2l}, …) from Galois rings. Techniques include a local Weil bound for character sums, and several kinds of Fourier transform. Applications range from cryptography (boolean functions, key generation), to communications (multicode CDMA), to signal processing (PAPR reduction). This is a joint work with Dmitrii Zinoviev. Spring 2008 Mathematics Colloquia
(in reverse chronological order)
Colloquium
Friday, April 11^{th}, 2008 at 3:00, NS 333
(Refreshments in room 334 at 2:30)
"Resource quality in population dynamics and its implications"
Professor Yang Kuang
Arizona State University
Abstract: Rising carbon dioxide levels should increase crop yields. But what is their effect on the nutritional value of our food? It is known that elevating the level of carbon dioxide can significantly reduce the leaf nitrogen content and hence leaf mites' reproduction and renders pesticide unnecessary in greenhouse vegetable production. This raises the question of how resource quality impacts the population dynamics in general. Mathematical biologists have built on variants of the LotkaVolterra equations and in almost all cases have adopted the physical science's singlecurrency (energy) approach to understand population dynamics. However, biomass production is essentially a mass transfer process that requires more than just energy. It is crucially dependent on the chemical compositions of both the consumer species and food resources. In this talk, we explore how depicting organisms as built of more than one thing, for example, C to represent energy, and an important nutrient, such as P (or N), to represent quality, results in qualitatively different and realistic predictions about the resulting dynamics. Colloquium
Friday, April 4^{th}, 2008 at 3:00, NS 333
(Refreshments in room 334 at 2:30)
"An Introduction to Mathematical Finance for Mathematicians"
Professor Philip Protter
Cornell University
Abstract: Louis Bachelier invented a mathematical model of Brownian motion in 1900 (five years before Einstein did the same albeit for very different reasons) in order to model the Paris stock market. Bachelier's work forgotten, in the 1960s Paul Samuelson waged a lonely but ultimately successful campaign to convince his peers to use probability to model the stock market, which had always been considered the consequence of actions, and not at all random. The evolution of the last 40 years of these models has been astounding, leading to huge advances in our understanding of risk in the sense of insurance of unusual and often innovative forms, known as financial derivatives. In this talk, we will explain the mathematical interpretation of the economics concept of arbitrage, and en passant we will explain the term and the role of martingales. Colloquium
Friday, March 21^{st}, 2008 at 3:00, NS 333
(Refreshments in room 334 at 2:30)
"Mathematical modeling for flocking phenomena and its analysis"
Professor SeungYeal Ha
Seoul National University
Abstract: Collective selfdriven synchronized motion of selfpropelled particles such as flocking of birds, schooling of fishes, swarming of bacteria, appears in many context in biological organisms, mobile networks and human networks etc. In this talk, I will present kinetic and fluid models derivable from CuckerSmale's flocking model, and also discuss their mathematical structures and possible applications of flocking mechanism to phototaxis problem arising from biology. Colloquium
Friday, March 7^{th}, 2008 at 3:00, NS 333
(Refreshments in room 334 at 2:30)
"Around Nonseparably Connected Metric Spaces"
Professor Michal Morayne
Wroclaw University of Technology
Abstract: It is difficult to find a connected metric space which does not contain any nontrivial separable connected subspace. So far there have been only two such examples given: by R. Pol and P. Simon. We give the third which is a graph of a function from the reals into a nonseparable Banach space. In fact this idea provides a certain more general technique for producing special spaces. We also show a positive result when a regular subset of a Banach space must be separably connected (i.e. each two points are contained in a separable connected subspace) in the weak* topology. This talk is based on a joint paper with Ph.D student Michal Wojcik: "Nonseparably Connected and Punctiform Spaces and Connected Graphs of Functions". Colloquium
Friday, February 8^{th}, 2008 at 3:00, NS 333
(Refreshments in room 334 at 2:30)
"Analytical models for strategic, intermediate, and realtime design and management of warehousing systems"
Professor Sunderesh S. Heragu
University of Louisville, Logistics and
Distribution Institute
Abstract: In this paper, we discuss several models for the design, analysis and realtime control of intraplant logistical problems. With a warehouse as the setting, we present (1) a large scale, mixedinteger programming model that can allocate products to areas in a warehouse and thus determine the size of each area; (2) a queuing network model that can analyze designs quickly and accurately with respect to important operational performance measures; and (3) an intelligent agentbased control mechanism to help a material handling system adapt in realtime and effectively to disturbances  external and internal  to the system. Effectiveness of this approach is illustrated with numerical examples and a realworld application. Fall 2007 Mathematics Colloquia
(in reverse chronological order)
Colloquium
Friday, November 30^{th}, 2007 at 4:00, NS 333
(NOTE NONSTANDARD TIME)
(Refreshments in room 334 at 3:50)
"Bounds on dimension of divisible codes"
Professor Xiaoyu Liu
Wright State University
Abstract: Divisible codes were introduced by H. N. Ward in 1981. A qary divisible code is a linear code over the field of q elements whose codewords all have weights divisible by some integer Δ>1, where Δ is called a divisor of the code. Ward proved a divisible code bound on dimension of a divisible code when the weight spectrum is given. However, bound on dimension of divisible codes in terms of code length and divisibility level answers the most fundamental question in coding theory for divisible codes. In this talk, we will give an exact upper bound for the dimension of binary divisible codes in this sense and prove the uniqueness up to equivalence of the code attaining this bound, given the hypothesis that a certain nonzero weight exists. We will also see that the hypothesis is true for level 3 codes of maximum dimension with relatively short lengths. Colloquium
Friday, October 19^{th}, 2007 at 3:00, NS 333
(Refreshments in room 334 after)
"Stability analysis of stationary solutions for the CahnHilliard Equation"
Professor Peter Howard
Texas A&M University
Abstract: I will discuss recent results on the stability of stationary solutions for the CahnHilliard equation in ℝ^{d}, d≥1. For the case d = 1, there are precisely three types of nonconstant bounded stationary solutions, periodic solutions, pulsetype (reversal) solutions, and monotonic transition fronts. These solutions can be categorized as follows: the periodic and reversal solutions are both spectrally unstable, while the transition fronts are nonlinearly (phaseasymptotically) stable. The cases d≥2 are more complicated, and I will discuss what is known about stationary solutions in these cases. Particular emphasis will be placed on planar transition front (or "kink") solutions. Colloquium
Friday, October 12^{th}, 2007 at 3:30, NS 333
(Refreshments in room 334 at 3:00)
"Markov bases for twoway subtable sum problems"
Professor Ruriko Yoshida
University of Kentucky
Abstract: DiaconisSturmfels developed an algorithm for sampling from conditional distributions for a statistical model of discrete exponential families, based on the algebraic theory of toric ideals. This algorithm is applied to categorical data analysis through the notion of Markov bases. Initiated with its application to Markov chain Monte Carlo approach for testing statistical fitting of the given model, many researchers have extensively studied the structure of Markov bases for models in computational algebraic statistics. In the Markov chain Monte Carlo approach for testing statistical fitting of the given model, a Markov basis is a set of moves connecting all contingency tables satisfying the given margins. It has been wellknown that for twoway contingency tables with fixed row sums and column sums the set of squarefree moves of degree two forms a Markov basis. However when we impose an additional constraint that the sum of a subtable is also fixed, then these moves do not necessarily form a Markov basis. Thus, in this paper, we show a necessary and sufficient condition on a subtable so that the set of squarefree moves of degree two forms a Markov basis. The paper on which this talk is based can be found at http://arxiv.org/abs/0708.2312. Slides will be made available at http://www.ms.uky.edu/~ruriko/pdf/Louisville.pdf Colloquium
Friday, September 14^{th}, 2007 at 2:00pm, NS 333
"Mathematics and Epidemics: Local versus global perspectives"
Regents Professor Carlos CastilloChavez
Arizona State University
Abstract:
In this lecture, I will review the role of mathematics in epidemiology and proceed to outline some of its contributions to the challenges posed by emergent diseases like SARS, tuberculosis and influenza.
Spring 2007 Mathematics Colloquia
Colloquium
Wednesday, March 8^{th}, 2007 at 9:00am, NS 333
(NOTE NONSTANDARD TIME)
"Maximum directed cuts in digraphs with degree restriction"
Professor Jeno Lehel
University of Memphis and Vernon Wilson Endowed Chair at Eastern Kentucky University
Abstract:
Every digraph of size m has a directed cut of size at least m/4
+ Θ(sqrt(m)). This bound eventually improves when a
restricted subfamily of digraphs is taken into consideration. For
instance, if the maximum outdegree of the digraph is k, then it has a
cut of size at least m/4 + m/(8k + 4). We investigate the size of the
maximum directed cut for the larger family of digraphs in which each
vertex has either indegree at most k or outdegree at most k.
Fall 2006 Mathematics Colloquia
Colloquium
Wednesday, October 18^{th}, 2006 at 2:00pm, NS 333
(NOTE NONSTANDARD TIME)
"SelfDual Codes over Z_{8} and Z_{9}"
Professor T. Aaron Gulliver
Department of Electrical and Computer Engineering, University of Victoria
Abstract:
Selfdual codes over finite fields are a widely studied subject.
Recently a great deal of attention has been given to selfdual codes
over a variety of rings. It is known that all selfdual codes over
Z_{m} can be found by applying the Chinese Remainder
Theorem to selfdual codes over Z_{pe} for
p a prime. Hence, it is important to classify selfdual codes
over the integers modulo prime powers, since this classification will
give the classification over Z_{m}.
This presentation will consider selfdual codes over the
rings Z_{8} and Z_{9}. Various weights
and weight enumerators over these rings will be described. The torsion
codes over these rings will be examined to characterize the structure
of selfdual codes. Finally, the classification of selfdual codes of
small lengths over Z_{8} and Z_{9} will
be given.
Colloquium
Friday, October 13^{th}, 2006 at 4:00pm, NS 333
(Refreshments in room 334 at 3:30)
"Analyzing chaotic economic models with illdefined forward dynamics"
Professor Judy Kennedy
University of Delaware
Abstract:
Some economic models, such as the cashinadvance model of
money of overlapping generations model, have the property that the
dynamics are illdefined going forward in time, but well defined going
backward in time, often via a continuous function on a compact metric
space called the "backwards map". We analyze such models using inverse
limit spaces. Specifically, we recall a construction of a measure on
the inverse limit space induced by an invariant measure on the factor
space. We show (1) that if the measure on the factor space is "natural",
then so is the induced measure on the inverse limit space; and (2)
that integration of continuous functions from the inverse limit space
to the reals makes sense with respect to the induced measure. We then
compute the integral of a utility function associated with the
economic model, thus obtaining an expected value for the utility
function; and make some conclusions about what this says for the
economic model.
Spring 2006
Fall 2005 Mathematics Colloquia (in reverse chronological order)
Spring 2005 Mathematics Colloquia (in reverse chronological order)
Fall 2004 Mathematics Colloquia (in reverse chronological order)
 
` 
University of
Louisville, Department of Mathematics. Copyright © 2006. All rights
reserved.
Comments to mailto:kezdy@louisville.edu. 