Research Highlights Seminar Schedule
Department of Mathematics
University of Pittsburgh

2010-2011 Academic Year

All talks are on Thursdays in Thackeray 704 at 1 pm unless noted otherwise. If you would like to speak or have a question about the seminar, please contact Anna Vainchtein at

Spring 2011

Speaker and title
January 20
Jon Rubin
The dynamics of bursting (in neurons and networks)

January 27
No talk this week
February 3
Konstantin Zelator
Integral triangles with a 120 degree angle
February 10
No talk this week
February 17
No talk this week
February 24
Reza Pakzad
Regularity, rigidity and matching properties of isometries

Abstract: We will review some classical results on isometric immersions and their rigidity properties before suggesting a new take on the topic inspired by the theory of elasticity.

 Fall 2010

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 Erdos-Heilbronn 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|+|B|-3. 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|+|B|-1 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 Nyman-Beurling criterion for the Riemann Hypothesis, step functions, and  lattice-free simplices