# Computer Science and Discrete Mathematics (CSDM)

## CSDM - On P vs NP, Geometric Complexity Theory, and the Riemann Hypothesis

This series of three talks will give a nontechnical, high level overview of geometric complexity theory (GCT), which is an approach to the P vs. NP problem via algebraic geometry, representation theory, and the theory of a new class of quantum groups, called nonstandard quantum groups, that arise in this approach. In particular, GCT suggests that the P vs. NP problem in characteristic zero is intimately linked to the Riemann Hypothesis over finite fields. No background in algebraic geometry, representation theory or quantum groups would be

assumed.

## CSDM - On P vs NP, Geometric Complexity Theory, and the Riemann Hypothesis - Part I

## Pseudorandomness - Randomness extractors

## Pseudorandomness - Substitution sequences at primes

## Pseudorandomness - When do sparse sets have dense models?

## Pseudorandomness - Exponential sums, equidistribution and pseudo-randomness

## Pseudorandomness in Mathematics and Computer Science Mini-Workshop

In math, one often studies random aspects of deterministic systems and structures. In CS, one often tries to efficiently create structures and systems with specific random-like properties. Recent work has shown many connections between these two approaches through the concept of "pseudorandomness".

Lectures by Bourgain, Impagliazzo, Sarnak and Wigderson (schedule below), will explore some of the facets of pseudorandomness, with particular emphasis on research directions and open problems that connect the different viewpoints of this concept in math and CS.

## CSDM - Lower Bounds for Circuits with $MOD_m$ Gates

Let $CC_{o(n)} \left[ m \right]$ be the class of circuits that have size $o(n)$ and in which all gates are $MOD_m$ gates.