## Transfer operators between relative trace formulas in rank one II

I will introduce a new paradigm for comparing relative trace formulas, in order to prove instances of (relative) functoriality and relations between periods of automorphic forms.

Yiannis Sakellaridis

Rutgers University; von Neumann Fellow, School of Mathematics

December 19, 2017

I will introduce a new paradigm for comparing relative trace formulas, in order to prove instances of (relative) functoriality and relations between periods of automorphic forms.

James Maynard

Member, School of Mathematics

December 13, 2017

Amir Shpilka

Tel Aviv University

December 12, 2017

We study the complexity of constructing a hitting set for the class of polynomials that can be infinitesimally approximated by polynomials that are computed by polynomial sized algebraic circuits, over the real or complex numbers. Specifically, we show that there is a PSPACE algorithm that given nsr in unary outputs a set of inputs from of size poly(nsr), with poly(nsr) bit complexity, that hits all $n$-variate polynomials of degree $r$ that are the limit of size $s$ algebraic circuits.

Yiannis Sakellaridis

Rutgers University; von Neumann Fellow, School of Mathematics

December 12, 2017

Yann LeCun

December 12, 2017

Daniel Kane

University of California, San Diego

December 11, 2017

It is classically understood how to learn the parameters of a Gaussian even in high dimensions from independent samples. However, estimators like the sample mean are very fragile to noise. In particular, a single corrupted sample can arbitrarily distort the sample mean. More generally we would like to be able to estimate the parameters of a distribution even if a small fraction of the samples are corrupted, potentially adversarially.

Matthias Schwarz

Universität Leipzig; Member, School of Mathematics

December 11, 2017

Lenny Ng

Duke University

December 11, 2017

Knot contact homology is a knot invariant derived from counting holomorphic curves with boundary on the Legendrian conormal to a knot. I will discuss some new developments around the subject, including an enhancement that completely determines the knot (joint work with Tobias Ekholm and Vivek Shende) and recent progress in the circle of ideas connecting knot contact homology, recurrence relations for colored HOMFLY polynomials, and topological strings (joint work in progress with Tobias Ekholm).

Alexander Gamburd

The Graduate Center, The City University of New York

December 8, 2017

Markoff triples are integer solutions of the equation $x^2+y^2+z^2 = 3xyz$ which arose in Markoff's spectacular and fundamental work (1879) on diophantine approximation and has been henceforth ubiquitous in a tremendous variety of different fields in mathematics and beyond.

Amit Ghosh

Oklahoma State University

December 8, 2017

We report on some recent work with Peter Sarnak. For integers $k$, we consider the affine cubic surfaces $V_k$ given by $M(x) = x_1^2 + x_2 + x_3^2 − x_1 x_2 x_3 = k$. Then for almost all $k$, the Hasse Principle holds, namely that $V_k(Z)$ is non-empty if $V_k(Z_p)$ is non-empty for all primes $p$. Moreover there are infinitely many $k$'s for which it fails. There is an action of a non-linear group on the integral points, producing finitely many orbits. For most $k$, we obtain an exact description of these orbits, the number of which we call "class numbers".