Mathematical Conversations

Feb 06 2019

How to efficiently check proofs

Speaker: Dor Minzer
6:00pm | Dilworth Room
The PCP Theorem states that any mathematical proof can be encoded in a way that allows verifying it probabilistically while reading only a small number of bits of the (new) proof. This result has several applications in Theoretical Computer Science, most notably in hardness...
Jan 30 2019

A mathematical conjecture about crumpling paper

Speaker: Francesco Maggi
6:00pm | Dilworth Room
Understanding the mechanics of crumpling, i.e. of isotropically compressing thin elastic sheets, is a challenging problem of theoretical and applied interest. We will present an interesting conjecture on the order of magnitude of the elastic energy per unit thickness needed...
Jan 23 2019

Bourgain and the sum-product phenomena

Speaker: Avi Wigderson
6:00pm | Dilworth Room
In 2004 Jean Bourgain proved, with Netz Katz and Terry Tao, the "sum-product theorem in finite fields". He referred to this result (and proof technique) as a "goose which lays golden eggs". Indeed, in subsequent years, he has published a couple of dozen papers on...
Dec 12 2018

How to detect a projective space?

Speaker: Jakub Witaszek
6:00pm | Dilworth Room
In 1984, Robert Lazarsfeld solved an old conjecture of Remmert and Van de Ven, which stated that there are no non-trivial complex manifolds that can be covered by a projective space. His result was a consequence of Shigefumi Mori's breakthrough answer to the question "How to...
Dec 05 2018

Two short stories on mathematical uncertainty principle

Speaker: Eugenia Malinnikova
6:00pm | Dilworth Room
The uncertainty principle says that a function and its Fourier transform can not be well-localized simultaneously. We will first discuss a version of this statement for a collection of functions forming a basis for $L^2$ space. Then we will connect Hardy's uncertainty...
Nov 28 2018

The isoperimetric inequality

Speaker: Robin Neumayer
6:00pm | Dilworth Room
The isoperimetric inequality says that balls have the smallest perimeter among all sets of a fixed volume in Euclidean space. We give an elegant analytic proof of this fact.
Nov 14 2018

The stability of atoms and the ionization conjecture

Speaker: Ian Jauslin
6:00pm | Dilworth Room
An atom is made of a positively charged nucleus and negatively charged electrons, interacting with each other via Coulomb forces. In this talk, I will review what is known, from a mathematical perspective, about this paradigmatic model, with a particular focus on questions...
Nov 07 2018

Hodge-Riemann relations for Potts-model partition functions

Speaker: June Huh
6:00pm | Dilworth Room
The multivariate Tutte polynomial, known to physicists as the Potts-model partition function, can be defined for any finite graph. The function has a hidden convexity property that implies several nontrivial results concerning the combinatorics of finite sets. This talk will...
Oct 24 2018

What is a central limit theorem for random groups?

Speaker: Melanie Wood
6:00pm | Dilworth Room
We will recall the central limit theorem for random numbers, and then discuss the general principle of universality and what it might mean specifically in an analog of the central limit theorem for random groups.
Oct 17 2018

Mathematical Structures in the Jungles of Life

Speaker: Misha Gromov
6:00pm | White Levy Room