## Exploring the Galactic Halo with Gaia

Vasily Belokurov

University of Cambridge and Center for Computational Astrophysics (CCA), Flatiron Institute

November 21, 2017

Vasily Belokurov

University of Cambridge and Center for Computational Astrophysics (CCA), Flatiron Institute

November 21, 2017

Shubhangi Saraf

Rutgers University

November 27, 2017

Sanjeev Arora

Princeton University; Visiting Professor, School of Mathematics

November 27, 2017

This talk is going to be an extended and more technical version of my brief public lecture https://www.ias.edu/ideas/2017/arora-zemel-machine-learning

I will present some of the basic ideas of machine learning, focusing on the mathematical formulations. Then I will take audience questions.

Yu-Shen Lin

Harvard University

November 27, 2017

We will explain a definition of open Gromov-Witten invariants on the rational elliptic surfaces and explain the connection of the invariants with tropical geometry. For certain rational elliptic surfaces coming from meromorphic Hitchin system, we will show that the open Gromov-Witten invariants with boundary conditions near infinity (up to some transformation) coincide with the closed geodesic counting invariants defined by Gaiotto-Moore-Neitzke, which are integer-valued.

Greta Panova

University of Pennsylvania; von Neumann Fellow, School of Mathematics

November 28, 2017

Akshay Venkatesh

Stanford University; Distinguished Visiting Professor, School of Mathematics

November 28, 2017

In the lectures I will formulate a conjecture asserting that there is a hidden action of certain motivic cohomology groups on the cohomology of arithmetic groups. One can construct this action, tensored with $\mathbb C$, using differential forms. Also one can construct it, tensored with $\mathbb Q_p$, by using a derived version of the Hecke algebra (or a derived version of the Galois deformation rings).

Hector Pasten

Harvard University

November 28, 2017

Existing unconditional progress on the abc conjecture and Szpiro's conjecture is rather limited and coming from essentially only two approaches: The theory of linear forms in $p$-adic logarithms, and bounds for the degree of modular parametrizations of elliptic curves by using congruences of modular forms. In this talk I will discuss a new approach as well as some unconditional results that it yields.

Marta Volonteri

Institut d'Astrophysique, Paris

November 28, 2017

Tristan Buckmaster

Princeton University

November 29, 2017

For initial datum of finite kinetic energy Leray has proven in 1934 that there exists at least one global in time finite energy weak solution of the 3D Navier-Stokes equations. In this talk, I will discuss very recent joint work with Vlad Vicol in which we prove that weak solutions of the 3D Navier-Stokes equations are not unique in the class of weak solutions with finite kinetic energy.

Oded Regev

New York University

November 29, 2017

Lattices are periodic arrangements of points in space that have attracted the attention of mathematicians for over two centuries. They have recently become an object of even greater interest due to their remarkable applications in cryptography. In this talk we will survey some of this progress and describe the somewhat mysterious role that quantum computing plays in the area.