## Some probabilistic ideas at the interface of random matrix theory and zeta

Ashkan Nikeghbali

UZH

April 3, 2014

Ashkan Nikeghbali

UZH

April 3, 2014

Van Vu

Yale

April 3, 2014

Jun Yin

IAS

April 3, 2014

Mark McLean

Stony Brook University

April 4, 2014

Let A be an affine variety inside a complex N dimensional vector space which either has an isolated singularity at the origin or is smooth at the origin. The intersection of A with a very small sphere turns out to be a contact manifold called the link of A. Any contact manifold contactomorphic to the link of A is said to be Milnor fillable by A. If the first Chern class of our link is 0 then we can assign an invariant of our singularity called the minimal discrepancy, which is an important invariant in birational geometry.

Martin Hairer

IAS

April 4, 2014

Herbert Spohn

IAS

April 4, 2014

Aravind Srinivasan

University of Maryland, College Park

April 7, 2014

There has been substantial progress on algorithmic versions and generalizations of the Lovasz Local Lemma recently, with some of the main ideas getting simplified as well. I will survey some of the main ideas of Moser & Tardos, Pegden, and David Harris & myself in this context.

Andrew Drucker

Institute for Advanced Study; Member, School of Mathematics

April 8, 2014

The P != NP conjecture doesn't tell us what runtime is needed to solve NP-hard problems like 3-SAT and Hamiltonian Path. While some clever algorithms are known, they all require exponential time, and some researchers suspect that this is unavoidable. This idea is expressed in the influential "Exponential Time Hypothesis" (ETH) of Impagliazzo, Paturi, and Zane. In this survey talk, I will describe the ETH and its consequences (some of which are rather subtle). We will see that this hypothesis holds considerable explanatory power.

Alexei Skorobogatov

Imperial College London

April 10, 2014

The work of Green, Tao and Ziegler can be used to prove existence and approximation properties for rational solutions of the Diophantine equations that describe representations of a product of norm forms by a product of linear polynomials. One can also prove that the Brauer-Manin obstruction precisely describes the closure of rational points in the adelic points for pencils of conics and quadrics over \(\mathbb Q\) when the degenerate fibres are all defined over \(\mathbb Q\).

Najmieh Batmanglij

April 11, 2014