## 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

Yann LeCun

December 12, 2017

Yiannis Sakellaridis

Rutgers University; von Neumann Fellow, School of Mathematics

December 12, 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.

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).

Matthias Schwarz

Universität Leipzig; Member, School of Mathematics

December 11, 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.

Junho Peter Whang

Princeton University

December 8, 2017

The classical affine cubic surface of Markoff has a well-known interpretation as a moduli space for local systems on the once-punctured torus. We show that the analogous moduli spaces for general topological surfaces form a rich family of log Calabi-Yau varieties, where a structure theorem for their integral points can be established using mapping class group descent. Related analysis also yields new results on the arithmetic of algebraic curves in these moduli spaces, including finiteness of imaginary quadratic integral points for non-special curves.

Ryan Ronan

Baruch College, The City University of New York

December 8, 2017

For integer parameters $n \geq 3$, $a \geq 1$, and $k \geq 0$ the Markoff-Hurwitz equation is the diophantine equation

\[ x_1^2 + x_2^2 + \cdots + x_n^2 = ax_1x_2 \cdots x_n + k.\]