Mathematical Conversations

Jan 24 2018

Zeroes of Laplace eigenfunctions

Speaker: Aleksandr Logunov
6:00pm | White-Levy
The classical Liouville theorem claims that any positive harmonic function in $R^n$ is a constant function. Nadirashvili conjectured that any non-constant harmonic function in $R^3$ has a zero set of infinite area. The conjecture is true and we will discuss the following...
Jan 17 2018

Connections between homotopy theory and number theory

Speaker: Irina Bobkova
6:00pm | Dilworth Room
For a formal group law G the group of automorphisms Aut(G) acts on the space of deformations Def(G). The invariants of this action miraculously recover an object of huge interest to algebraic topologists, and this connection led to much progress in homotopy theory. However,...
Dec 08 2017

Proofs from algorithms, algorithms from proofs

Speaker: Pravesh Kothari
6:00pm | Dilworth Room
Constructive vs Pure Existence proofs have been a topic of intense debate in foundations of mathematics. Constructive proofs are nice as they demonstrate the existence of a mathematical object by describing an algorithm for building it. In computer science, we, in fact, have...
Nov 29 2017

Approximate prime numbers

Speaker: James Maynard
6:00pm | Dilworth Room
Unfortunately counting prime numbers is hard. Fortunately, we can cheat by counting 'approximate prime numbers' which is much easier. Moreover, this allows us to say something about the primes themselves, and works in situations which seem well beyond the reach of the...
Nov 01 2017

The three pillars of statistical machine learning: then and now

Speaker: Nadav Cohen
6:00pm | Dilworth Room
In this (short and informal) talk I will present the three fundamental factors that determine the quality of a statistical machine learning algorithm. I will then depict a classic strategy for handling these factors, which is relatively well understood, and until recently...
Oct 25 2017

How deep is your proof?

Speaker: Toniann Pitassi
6:00pm | Dilworth Room
There is a very short proof that a graph is 3-colorable: you simply give the coloring - it is linear in the size of the graph. How long a proof is needed that a given graph is *not* 3-colorable? The best we know is exponential in the size of the graph. Proving that there is...
Oct 18 2017

Spectral gaps without frustration

Speaker: Marius Lemm
6:00pm | Dilworth Room
In spin systems, the existence of a spectral gap has far-reaching consequences. "Frustration-free" spin systems form a subclass that is special enough to make the spectral gap problem amenable and, at the same time, broad enough to be physically relevant. We discuss "finite-...