Date 
Speaker,
Title and
Abstract 
December 4 
Dr. D. Steven Mackey Department of Mathematics Western Michigan University ITERATIVE METHODS FOR MATRIX FACTORIZATIONS (continuation of November 15th talk) The
decomposition of matrices into simpler, more structured factors is
central to numerical linear algebra, and hence of great importance for
applications. In this talk we discuss the design and analysis
of iterative algorithms of the form $X_{n+1} =
f(X_n)$ for several such matrix factorizations. In addition
we consider the issue of structure preservation 
if $X_0$ is already structured in some way, can we arrange
that every iterate $X_n$ retains this structure?

November 29 
Dr. Giuseppe Grassi Dipartimento di Ingegneria dell'Innovazione Universita di Lecce, Italy and Department of Electrical and Computer Engineering Western Michigan University GENERATING AND SHAPING CHAOTIC ATTRACTORS In
recent years chaotic phenomena have gradually moved from being an
academic curiosity to a subject of practical significance, due to
potential applications in engineering systems. Since chaos can be
useful, designing chaos (or generating/shaping chaos) becomes an
important issue in many technological applications. This lecture
presents a systematic technique to generate chaotic attractors
characterized by rich dynamic behaviours, that is, multiscroll
attractors with an arbitrarily large number of scrolls located around
specific unstable equilibriums points. Additionally, the lecture
introduces a novel observerbased technique to shape chaotic
attractors, that is, to arbitrarily scale all the chaotic drive system
states using a scalar synchronizing signal only.

November 15 
Dr. D. Steven Mackey Department of Mathematics Western Michigan University ITERATIVE METHODS FOR MATRIX FACTORIZATIONS The
decomposition of matrices into simpler, more structured factors is
central to numerical linear algebra, and hence of great importance for
applications. In this talk we discuss the design and analysis
of iterative algorithms of the form $X_{n+1} =
f(X_n)$ for several such matrix factorizations. In addition
we consider the issue of structure preservation 
if $X_0$ is already structured in some way, can we arrange
that every iterate $X_n$ retains this structure?

November 8 
John
Petrovic Department of Mathematics Western Michigan University ON
THE EXTENDED EIGENVALUES OF SOME
VOLTERRA OPERATORS
For a given operator $A$ it is often of
interest to determine which
operators satisfy the equation $A X = \lambda X A$ for some complex number $\lambda$. In this situation $\lambda$ is said to be
an extended eigenvalue of $A$. Although the case $\lambda = 1$ is much better
understood, even when $\lambda \neq 1$, $X$ shares many properties with $A$. In particular,
when $A$ is compact, $X$ has an
invariant subspace. In this work we focus on the integral operators of the Volterra type. We will exhibit some of
the possible solutions of theoperator
equation above and discuss their significance.

November 1 
Anirban
Dutta Department of Mathematics Western Michigan University BASICS OF STOCHASTIC CALCULUS We
introduce two types of Stochastic Integrals, namely, Stratanovich
and Ito Integral. Then we focus on results involving Ito Integral, for
example, the Ito Formula. If time permits we'll talk about
StroockVaradhan Diffusion Theory, thus revealing a deeper connection
between Brownian Motion and PDE's.

October 25 
Anirban
Dutta Department of Mathematics Western Michigan University BASICS OF BROWNIAN MOTION We
discuss a formalism of Brownian Motion in Euclidean Spaces starting
with definitions and existence theorems. Then, we
study the properties of brownian paths in single dimension along with
occasional generalizations to higher dimensions. If time permits, we
will look at some connection between Brownian Motion and classical
analysis issues, such as, Harmonic measure, PDEs (Heat Equation in
particular) etc.

October 18 
Ovidiu
Furdui Department of Mathematics Western Michigan University LACUNARY SERIES ON FOCK SPACES We
give necessary and sufficient conditions for a holomorphic function
with gaps to belong
to the Fock spaces F. Some applications of these results will discussed. 
October 11 
Dr.Melinda
Koelling Department of Mathematics Western Michigan University REPRESENTATIONAL LEARNING One approach to explain
neural function is to describe how the circuitry of the brain connects
to produce observed properties of the brain. Another approach is to
consider what representations might be developed on the basis of
statistics of the input and what goals might be served by those
representations. In this talk, I will consider some examples of this second
approach.

October 4 
Dr. Sanath Boralugoda Department of Mathematics University of Sri Jayewardenepura Colombo, Sri Lanka EVOLUTION PROBLEMS ASSOCIATED WITH NONSMOOTH FUNCTIONS Recent
results show that the Moreau envelope
functions associated with some classes of nonsmooth functions (eg.
ProxRegular, PrimalLowerNice) have C1 smoothness. In this talk we
discuss the
local existence and uniqueness of absolutely continuous solutions of
some
differential inclusions determined by subdifferentials of
related envelope functions.

September
27

Department of Mathematics
In
1997
Scholes and Merton were awarded the Nobel Prize in economics for their
contribution to the BlackScholes option pricing model (unfortunately
Black had passed away). What is this model and why is it so important?
In this talk I will give a brief introduction following the original
BlackScholes seminal paper published in 1973 and mention some
later developments if time permits.Western Michigan University BLACKSCHOLES OPTION PRICING MODEL 
September 20 
Department
of Mathematics
Western Michigan University OPTION PRICING INTERVAL . An option is a right without obligation. Options are widely used in the financial industry to mitigate risks or to leverage investment opportunities. If you believe that there is no free lunch then an option always come with a price. How to price an option is a highly active area of research in mathematical finance with an extensive literature. We will try to give an elementary introduction to the widely used classical idea of pricing options by replicating portfolios stemming from Black, Scholes and Merton. We then indicate the difficulties of this method in investment practice and propose an alternative based on information theoretical techniques. This talk is accessible to undergraduate students. 
September 13 
Yuri
S.Ledyaev Department of Mathematics Western Michigan University CONVEX SETS ON MANIFOLDS OF NONPOSITIVE CURVATURE Manifolds of nonpositive curvature (
CartanHadamard manifolds) have been studied intensively during last
three decades, in particular, in the framework of a "geometrization" program for solving
some difficult algebraic problems. Notion of convexity plays a
significant role
in these studies. In this talk we discuss generalization of Junge
theorem on a radius of circumscribed ball and new proximal criteria for
convexity of sets on CartanHadamard manifolds by using new analytical
techniques.

Last modified : November 30, 2006