The gauged symplectic sigma-model

Constantin Teleman
University of California, Berkeley and Oxford University
November 15, 2016
I will recall the construction of the space of states in a gauged topological A-model. Conjecturally, this gives the quantum cohomology of Fano symplectic quotients: in the toric case, this is Batyrev’s presentation of quantum cohomology of toric varieties. Time permitting, I will discuss the role of “Coulomb branches” in gauge theory in relation to equivariant quantum and symplectic cohomology.

Non-malleable extractors for constant depth circuits, and affine functions

Eshan Chattopadhyay
Member, School of Mathematics
November 15, 2016
Seeded and seedless non-malleable extractors are non-trivial generalizations of the more commonly studied seeded and seedless extractors. The original motivation for constructing such non-malleable extractors are from applications to cryptography (privacy amplification and tamper-resilient cryptography). Interestingly, explicitly constructing non-malleable extractors have led to many new connections and progress in pseudoranomness as well.

Eigenvalue bounds on sums of random matrices

Adam Marcus
Princeton University; Member, School of Mathematics
November 14, 2016
For certain applications of linear algebra, it is useful to understand the distribution of the largest eigenvalue of a finite sum of discrete random matrices. One of the useful tools in this area is the "Matrix Chernoff" bound which gives tight concentration around the largest eigenvalue of the expectation. In some situations, one can get better bounds by showing that the sum behaves (in some rough way) like one would expect from Gaussian random matrices.

The mathematics of natural algorithms

Bernard Chazelle
Princeton University
November 14, 2016
I will review some of the recent techniques we've used in our study of natural algorithms. These include Dirichlet series for matrix products, mean-field approximations in opinion dynamics, graph sequence grammars, and tools for renormalizing network-based dynamical systems. If time permits, I will also discuss anti-mixing techniques for self-sustaining iterated learning. The talk will be self-contained and non-technical.