Date

Speaker and title/abstract

October 7

Kiumars Kaveh
Convex polytopes and
systems of algebraic equations
Abstract:
I will discuss a beautiful connection between the theory of convex
polytopes (in Euclidean space) and the question of finding the number
of solutions (over complex numbers) of a system of algebraic equations.
This talk can be thought of as an invitation to the (nowadays very
popular) theory of toric varieties. Only a minimum background in
algebra and geometry is assumed.

October 14

Bard Ermentrout
Patterns in
biology: what can mathematics tell us?

October 21

Anna
Vainchtein
Mathematical
modeling and analysis of nonlinear phenomena in materials

October 28

Brent Doiron
Noisy
brains: the mathematics of neural computation

November 4

Jeffrey Wheeler
A Proof the
ErdosHeilbronn Problem Using the Polynomial Method of Alon, Nathanson,
and Ruzsa
Abstract:
In the early 1960's, Paul Erdos and Hans Heilbronn conjectured that
for any two nonempty subsets A and B of Z/pZ the number of restricted
sums (restricted in the sense that we require the elements to be
distinct) of an element from A with an element from B is at least the
smaller of p and A+B3. This problem is related to independent
results of Cauchy and Harold Davenport which established that there are
at least the minimum of p and A+B1 sums of the form a+b (with the
restriction removed). One thing that makes the problem interesting is
that the results of Cauchy and Davenport were immediately established
whereas the conjecture of Erdos and Heilbronn was open for more than 30
years.
We present the proof of the
conjecture due to Noga Alon, Melvyn Nathanson, and Emre Rusza. This
technique is known as the Polynomial Method and is regarded by many as
a powerful tool in the area of Additive
Combinatorics.

November 11

Christopher Lennard
Open
problems in fixed point theory in Banach spaces

November 18

Greg Constantine
Design,
strategy, and applications

December 2

Juan Manfredi
Games
mathematicians play to solve PDE

December 9

Alexander Borisov
Discrete
NymanBeurling criterion for the Riemann Hypothesis, step functions,
and latticefree simplices
