[Mathclub-members] math talk tomorrow! and Monday

Michael Pelsmajer pelsmajer at gmail.com
Thu Nov 8 14:46:19 CST 2007


Tomorrow's talk should be a good one.  Refreshments will be served
before the talks.

During the meeting today, Rick mentioned a certain talk Monday, so
I'll list Monday's talks here as well.
We actually have speakers all the time (see
math.iit.edu/academics/sem_coll.html) but some talks are not so good
for undergrads.

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Discrete Applied Mathematics Seminar
Friday 11/9 - Kathryn Nyman of Loyola University - Chicago
E1 103 3:00 pm
Title: Descent Algebras, rising sequences, and a good card trick done
poorly, if at all
Abstract:  We will take a short look at how one might model card shuffling
with permutations. This leads to a study of the descent algebra, and finally
we will introduce a subalgebra (close to my heart) known as the peak
algebra. We find a lovely connection between the peak algebra and descent
algebra and explore some of its properties.

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Stochastics and Computation Seminar
Monday 11/12 - Aijun Du of IIT AM Graduate Program
E1 129 12:45 pm
Title: Deviation, Ergodicity, and Reduction for Stochastical Dynamical
Systems

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AM Dept Colloquium & Mathematical Finance Seminar
Monday 11/12 - Erhan Bayraktar of University of Michigan
E1 106 4:40 pm
Title: On the Finite Horizon American Option Pricing Problem:  A Proof of
Smoothness and an Exponentially Fast Converging Scheme
Abstract:  We give a new proof of the fact that the value function of the
finite time horizon American put option for a jump diffusion, when the jumps
are from a compound Poisson process, is the classical solution of a
quasi-variational inequality and it is $C^1$ across the optimal stopping
boundary. Our proof only uses the classical theory of parabolic partial
differential equations of Friedman and does not use the theory of vicosity
solutions, since our proof relies on constructing a sequence of functions,
each of which is a value function of an optimal stopping time for a
diffusion. (Also, the previous proof holds only for a certain range of
parameters.) The sequence is constructed by iterating a functional operator
that maps a certain class of convex functions to smooth functions satisfying
variational inequalities (or to value functions of optimal stopping problems
for a geometric Brownian motion). The approximating sequence converges to
the value function exponentially fast, therefore it constitutes a good
approximation scheme, since the optimal stopping problems for diffusions can
be readily solved using the well-know numerical schemes such as SOR.


-- 
Michael J. Pelsmajer             http://www.iit.edu/~pelsmaje
Applied Mathematics, E1 Room 206       pelsmajer at iit.edu
Illinois Institute of Technology         (312)567-5344
Chicago, IL 60616


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