### Week of February 4, 2018

 11:00am to 12:00pm - RH 306P - Probability Yan Shuo Tan - (University of Michigan) Efficient algorithms for phase retrieval in high dimensions Mathematical phase retrieval is the problem of solving systems of rank-1 quadratic equations. Over the last few years, there has been much interest in constructing algorithms with provable guarantees. Both theoretically and empirically, the most successful approaches have involved direct optimization of non-convex loss functions. In the first half of this talk, we will discuss how stochastic gradient descent for one of these loss functions provably results in (rapid) linear convergence with high probability. In the second half of the talk, we will discuss a semidefinite programming algorithm that simultaneously makes use of a sparsity prior on the solution vector, while overcoming possible model misspecification. 3:00pm to 4:00pm - - Number Theory Oleksiy Klurman - (Royal Institute of Technology) Dynamical properties of multiplicative functions. Understanding joint behaviour of $(f(n),g(n+1))$ where f and g are given multiplicative functions play key role in analytic number theory with potentially profound consequences such as Riemann hypothesis, twin prime conjecture, Chowla's conjecture and many others. In the the first part of this talk, I will discuss joint work with A. Mangerel, answering an old question of Katai about distribution of points $\{(f(n),g(n+1))\}_{n\ge 1}\in \mathbb{T}^2,$ where f and g are unimodular multiplicative functions.   In the second part of the talk, which is based on a joint work with P. Kurlberg, answering a question of M. Lemanczyk, we construct deterministic example of multiplicative function $f:{\mathbb{N}\to \{+1,-1\}$ with various ergodic properties with respect to the Mirsky measure and discuss its relation to the interplay between Chowla conjecture and Riemann hypothesis. 4:00pm to 5:00pm - RH 306 - Colloquium Distinguished Lecture by C. McMullen - (Harvard) The behavior of planes in confinement 4:00pm to 5:00pm - RH 306 - Distinguished Lectures Curt McMullen - (Harvard University) The behavior of planes in confinement