Date 
Speaker,
Title and
Abstract 
April 11 
Dr.
Qiji J. Zhu
Department of Mathematics Western Michigan University HOW TO MANAGE YOUR PORTFOLIO USING CONVEX ANALYSIS In 1990, Harry Markowitz received the Nobel Price in Economics for developing the theory of portfolio choice in early 1950s. More than one half century later, Markowitz'es theory is still one of the most popular in portfolio management. In this talk we give a convex analyst's introduction to Markowitz'es pioneering work. Time permits, we will also discuss some recent developments. 
April 4 
ON
SPECTRAL RADIUS ALGEBRAS AND NORMAL OPERATORS
It is well known that, if N is a
normal operator, then its commutant {N}' (the set of all operators that
commute with N) has an invariant subspace. We will introduce the
socalled spectral radius algebra B_N associated to N and establish a
strenghtening of the mentioned result. Namely, we'll show that B_N also
has an invariant subspace. In addition, B_N properly contains the
commutant {N}', so the result is, indeed, stronger than the classical
one.

March 28 
INTRODUCTION
TO NONLINEAR FOURIER TRANSFORM
This is a
continuation of the previous talk. We discuss some standard material on
the nonlinear Fourier transform
which is the scattering theory analogue of the more familiar linear
Fourier transform. Our exposition closely follows Terence Lao's (2006
Fields
Medal winner) survey on this subject.(after Terence Tao) 
March 21 
Yuri
S.Ledyaev Department of Mathematics Western Michigan University INTRODUCTION TO NONLINEAR FOURIER TRANSFORM (AFTER TERENCE TAO) We discuss some
standard material on the nonlinear Fourier transform
which is the scattering theory analogue of the more familiar linear
Fourier transform. Our exposition closely follows Terence Lao's (2006
Fields
Medal winner) survey on this subject.

March 14 
Anirban
Dutta Department of Mathematics Western Michigan University FOURIER ANALYSIS ON LOCAL COMPACT ABELIAN GROUPS This is the gourth talk of a
srudentoriented minicourse on
generalization of Fourier Transforms in R^n to any Locally
Compact Abelian (LCA) group. We'll review briefly
some basic concepts of measure theory and functional analysis that are
relevant to the topic. Our final goal is generalization of
classical important results (namely, Inversion Theorem, Plancherel
Theorem, Pontryagin Duality Theorem and Bohr Compactification Theorem)
of classical Fourier Transform to the case of locally compact group.
These results are used in modern physical theories. This course is
primarily intended for graduate students who have some exposure to
graduate level analysis.

February 28 
Anirban
Dutta Department of Mathematics Western Michigan University FOURIER ANALYSIS ON LOCAL COMPACT ABELIAN GROUPS This is the third talk of a
srudentoriented minicourse on
generalization of Fourier Transforms in R^n to any Locally
Compact Abelian (LCA) group. We'll review briefly
some basic concepts of measure theory and functional analysis that are
relevant to the topic. Our final goal is generalization of
classical important results (namely, Inversion Theorem, Plancherel
Theorem, Pontryagin Duality Theorem and Bohr Compactification Theorem)
of classical Fourier Transform to the case of locally compact group.
These results are used in modern physical theories. This course is
primarily intended for graduate students who have some exposure to
graduate level analysis.

February 21 
Vinod
Kumar.P.B Department of Mathematics Rajagiri School of Engineering and Technology India. INTRODUCTION TO CHAOS AND FRACTALS There are events occurring in
nature which are predictable and unpredictable. If such
unpredictability arises because of sensitivity then chaos occurs. The theory of chaos
was originated in the work of a meteorologist Edward Lorenz in
1960's. But an interest to mathematical aspects was stimulated by the
work of Tien Yin Li and James Yorke in 1975. In this talk we'll discuss
and illustrate some forms of chaos.
Most of the objects in the nature are irregular. They do not have a definite shape or size. Fractals are irregular objects. Their theory was originated by the work of Benoit Mandelbrot in 1980's and it became popular with the introduction of self similarity concept by John Hutchinson in 1985. We'll provide a brief introduction to selfsimilarity in this talk. 
February 14 
Anirban
Dutta Department of Mathematics Western Michigan University FOURIER ANALYSIS ON LOCAL COMPACT ABELIAN GROUPS This is the second talk of a
srudentoriented minicourse on
generalization of Fourier Transforms in R^n to any Locally
Compact Abelian (LCA) group. We'll review briefly
some basic concepts of measure theory and functional analysis that are
relevant to the topic. Our final goal is generalization of
classical important results (namely, Inversion Theorem, Plancherel
Theorem, Pontryagin Duality Theorem and Bohr Compactification Theorem)
of classical Fourier Transform to the case of locally compact group.
These results are used in modern physical theories. This course is
primarily intended for graduate students who have some exposure to
graduate level analysis.

February 7 
Anirban
Dutta Department of Mathematics Western Michigan University FOURIER ANALYSIS ON LOCAL COMPACT ABELIAN GROUPS This is a first talk of a srudentoriented minicourse on generalization of Fourier Transforms in R^n to any Locally Compact Abelian (LCA) group. We'll review briefly some basic concepts of measure theory and functional analysis that are relevant to the topic. Our final goal is generalization of classical important results (namely, Inversion Theorem, Plancherel Theorem, Pontryagin Duality Theorem and Bohr Compactification Theorem) of classical Fourier Transform to the case of locally compact group. These results are used in modern physical theories. This course is primarily intended for graduate students who have some exposure to graduate level analysis. 
January 31 
Dr.
Qiji J. Zhu Department of Mathematics Western Michigan University HOW MANY TRICKS DOES A VARIATIONAL ANALYST HAVE It is said that even a great
mathematician has only a few tricks. We will explain that many
important tools in convex and nonsmooth analysis are different facets
of two basic tricks of variational methods: a variational principle and
a decoupling method. We'll also discuss interesting new directions of
research.

January 24 
Yuri
S.Ledyaev Department of Mathematics Western Michigan University FIXED POINTS AND ZEROES OF MAPPINGS AND INVARIANCE (second part of the January 17th talk) 
January 17 
Yuri
S.Ledyaev Department of Mathematics Western Michigan University FIXED POINTS AND ZEROES OF MAPPINGS AND INVARIANCE This is a studentoriented talk
intended to provide them with a survey of classical (and not so
classical) results on existence of fixed points and zeroes of
mappings f: K>R^n on closed subsets K of
R^n. Such results are important in various fields of applied
mathematics including existence of solutions of partial
differential equations or existence of equilibria in mathematical
economics models.
We start with classical fixed points theorems by Brouwer and Kakutani and relate them to results on existence of zeroes of mappings on convex compact sets under some boundary conditions for these mappings. We use invariance properties of some flows generated by these mappings to obtain generalization of existence theorems for zeroes of mappings for nonconvex sets. 
Last modified :April 24, 2007