Feb 06 2019
Speaker: Dor Minzer6:00pm | 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
Speaker: Francesco Maggi6:00pm | 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
Speaker: Avi Wigderson6:00pm | 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
Speaker: Jakub Witaszek6:00pm | 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
Speaker: Eugenia Malinnikova6:00pm | 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
Speaker: Robin Neumayer6:00pm | 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
Speaker: Ian Jauslin6:00pm | 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
Speaker: June Huh6:00pm | 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
Speaker: Melanie Wood6:00pm | 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
Speaker: Misha Gromov6:00pm | White Levy Room