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Contact
information:
Previous seminars
2004
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Analysis Seminar 2005 - 2006
Fall
Semester Meeting Schedule (All seminars are Wednesdays at 3:00 pm in NS
234)
If you
would like to speak in the seminar, please send a title, abstract and
proposed date
to thomas.riedel“at”louisville.edu
SPRING 2006
Date:
January 25 and February 1, 2006
Speaker: Susan White,
Department of Mathematics, University of Louisville
Title:
Structure of Generic and AE Mappings in Z^Z and R^R
Abstract:
In this talk, we look at the structure of generic and
almost every (ae) continuous function from Z to Z and from R to
R. Similar results were obtained for the permutation space S_N by
Dougherty and Mycielski.
Date:
February 8, 2006
Speaker: Professor David Swanson,
Department of Mathematics, University of Louisville
Title:
The Navier-Stokes Equations: The equations of fluid
flow
Abstract:
I will discuss the derivation of the Navier-Stokes
equations for an incompressible fluid. This will be the first of
several talks. In subsequent weeks I will discuss recent work
concerning the existence of solutions to the NSE.
Date:
February 15, 2006
Speaker: Professor David Swanson,
Department of Mathematics, University of Louisville
Title:
The Navier-Stokes equations II: The wave-vectors formulation
Abstract:
In
this talk I will show how the Navier-Stokes equations may be cast as an
infinite-dimensional dynamical system, and I will discuss a
general strategy for finding solutions to this and related systems.
Date:
February 22, 2006
Speaker: Professor David Swanson,
Department of Mathematics, University of Louisville
Title:
The Navier-Stokes equations III: The evolution equation
Abstract:
This will be a continuation of the previous two
lectures. I will formulate the Navier-Stokes system as an
abstract evolution equation and discuss methods for its solution.
Date:
March 1, 2006
Speaker: Professor Alica Miller,
Department of Mathematics, University of Louisville
Title:
Disjointness of compact minimal flows
Abstract:
In this talk we will focus our attention on
disjointness and give our criterion for disjointness of compact minimal
flows and sketch the proof of it. (continuation of talk
from November
30, 2005).
Date:
March 30, 2006
Speaker: ProfessorBojana Pejic,
Department of Mathematics, University of Pittsburgh
Title:
Uniqueness of Polish Group Topologies
Abstract:
A Polish group is a topological group with a
separable metrizable topology.
A key problem in the theory of Polish
groups is that of the Automatic Continuity: When can we conclude that a
homomorphismbetween two Polish groups must be continuous? This
problem is related to another question: When does a Polish group
admit only one Polish group topology?
A convenient method for proving
that a group has a unique
Polish group topology is to apply a theorem of Mackey: If G is
a topological group, with a countable point-separating family of sets
that are Borel in *any* Polish group topology on G, then G has a unique
Polish group topology.
This problem inspired the following questions:
1) Algebraically definable sets are analytic; are
they,
in fact, always
Borel?
2) If not, can Mackey’s result be improved to work with analytic
sets?
In this talk I'll give an example of a set defined
algebraically that is analytic but not Borel, showing that not all
algebraically defined sets are Borel. Time permitting, I will talk
about some difficulties in
extending the Mackey's result.
Date:
April 5, 2006 and April 12, 2006
Speaker: Professor Trevor Irwin,
Department of Mathematics, University of Louisville
Title:
A New Characterization of the Pseudo-arc
Abstract:
In
the first meeting we will start with an introduction to the pseudo-arc
and continua theory in general. In the second meeting we will present a
new characterization of the pseudo-arc.
FALL 2005
Date:
August 31, 2005
Speaker: Professor
Udayan
Darji, Department
of Mathematics, University of Louisville
Title:
Faithful representation of free groups in the symmetric group on N.
Abstract: The title is algebraic
but the talk will have some topology/analysis in it.
Date:
September 7, 2005
Speaker: Professor Thomas Riedel,
Department
of Mathematics, University of Louisville
Title:
Limit Properties of Mean Values.
Abstract: This is based on joint
work with R. C. Powers and P. K. Sahoo. We will discuss the behavior of
certain differential and integral mean values as the interval length
shrinks to zero. Example: Let f(t)=t2 on the interval
[1,x], the by the MVT there is hx
Î (1,x) such that (f(x)-f(1))/(x-1)=f¢(hx)
and it turns out that hx=1/2(x-1).
Thus limx® 1+(hx -1)/(x-1)=1/2.
Date:
September 14, 2005
Speaker: Professor David Swanson,
Department of Mathematics, University of Louisville
Title:
Existence and Gevrey class regularity of solutions to the
Kuramoto-Sivashinsky equation, Part I
Abstract: We employ elementary
Banach space techniques to prove the existence of local-time solutions
to the Kuramoto-Sivashinsky equation in any number of spatial
dimensions provided that the initial data lies in an appropriate
Sobolev space. This talk is based on joint work with Animikh
Biswas of UNC-Charlotte.
Date:
September 21, 2005
Speaker: Professor David Swanson,
Department of Mathematics, University
of Louisville
Title:
Existence and Gevrey class regularity of solutions to the
Kuramoto-Sivashinsky equation, Part II
Date:
October 5, 2005
Speaker: Professor Prasanna
Sahoo,
Department of Mathematics, University of Louisville
Title:
Two elementary problems and their solutions
Abstract: The
European Mathematical Society asked me to submit two elementary
problems in functional equations and their solutions to be published in
the journal of EMS. In this talk, I will discuss those problems and
their solutions. Moreover, if time permits I will goover one
generalization of one of the problems. Undergraduate andgraduate
students can easily understand this talk.
Date:
October 12, 2005
Speaker: Professor David Swanson,
Department of Mathematics, University of Louisville
Title:
Boundary values of Sobolev functions on irregular
domains
Abstract:
I will talk about some different ways to make sense of the notion that
a Sobolev function vanishes on the boundary of its domain. The
talk will involve various concepts from BV theory and geometric measure
theory.
Date:
October 26, 2005
Speaker: Professor Thomas Riedel,
Department of Mathematics, University of Louisville
Title:
Operators related to functional equations
Abstract:
We will discuss Cauchy C(f)(x,y)=f(x+y)-f(x)-f(y) , Jensen
and quadratic operators on Xl
spaces, and some of their properties. Here l
³ 0 and Xl
is the space of all functions f from a normed space X into a normed
space Y, such that ||f(x)|| £
M(f) el||x||
for all x Î X; where M(f) is a
constant depending only on f. The Jensen operator and quadratic
operator are similarly defined. See "Functional Equations and
Inequalities in Several Variables" by Stefan Czerwik, World Scientific
Press, p. 229f.
Date:
November 2, 2005 and November 9, 2005
Speaker: Professor Udayan Darji,
Department of Mathematics, University of Louisville
Title:
Chaos
Abstract:
In this talk, we introduce Devaney chaos, Li-Yorke
chaos, positive topological entropy and Bruckner-Ceder chaos. We
discuss relationships between these notions of chaos and some open
problems.
Date:
November 16, 2005
Speaker: Professor Ryan Gill,
Department of Mathematics, University of Louisville
Title:
Faster
computation of the maximum likelihood estimator in generalized
broken-line regression.
Abstract:
Here the problem of finding the global maximizer of
the likelihood function for a gradual change model in which the
canonical parameter of a standard exponential family exhibits the
broken-line behavior qt=a+b(t-n)+ with x+=max{
x, 0 } will be considered. The standard method for computing the
estimator of (a,b,n) will be presented and progress for a new
method which computes the MLE more efficiently will be discussed. The
solution for the normal case will be presented, and open questions for
other exponential families will also be discussed.
Date:
November 30, 2005
Speaker: Professor Alica Miller,
Department of Mathematics, University of Louisville
Title:
Some properties of compact minimal flows
Abstract:
In this talk (1st part) we will introduce some
properties of compact minimal flows, such as: proximality, regional
proximality, distality, almost periodicity, disjointness. We will give
some examples and also some statements (like, for example, the
criterion for minimality of restrictions) needed for the 2nd part
of the talk (next week), where we will focus our attention on
disjointness and give our criterion for disjointness of compact minimal
flows and sketch the proof of it.
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