Week of February 4, 2018

Mon Feb 5, 2018
4:00pm to 5:30pm - RH 440R - Logic Set Theory
Ryan Sullivant - (UCI)
Learning seminar: An introduction to large cardinals and L

In this talk, we will cover the basics of measurable cardinals and their relationship to non-trivial elementary embeddings.  We proceed with basic facts about the constructible universe, L.  After laying this groundwork, we show L cannot have a measurable cardinal.  Time permitting, we will discuss the dichotomy introduced by Jensen's covering lemma: either L is a good approximation to V, or there is a non-trivial elementary embedding from L to L.

 

4:00pm to 5:00pm - RH 306 - Special Colloquium
Mario Micheli - (Harvey Mudd College)
Image processing in an undergraduate curriculum: ideas and experience for teaching and research

In this talk I will illustrate my ideas and plans about the development of an undergraduate curriculum in the broader area of data science that includes, among other things, a course in image
processing. I will give an overview of the field, discuss typical problems that are studied within the discipline, and present an array of applications in medicine, astronomy, atmospheric science, security, navigation systems, and others: this will include a brief exposition of my own research in the recovery of images from videos affected by optical turbulence. I will be drawing ideas from my own experience in teaching courses and doing research with undergraduates at different academic institutions.
 

4:00pm to 5:00pm - RH 340P - Geometry and Topology
Carolyn Abbott - (UC Berkeley)
Ordering actions on hyperbolic metric spaces

Every group admits at least one action by isometries on a hyperbolic metric space, and certain classes of groups admit many different actions on different hyperbolic metric spaces (in fact, often uncountably many).  One such class of groups is the class of so-called acylindrically hyperbolic groups, which contains many interesting groups, such as mapping class groups, Out(F_n), and right-angled Artin and Coxeter groups, among many others.  In this talk, I will describe how to put a partial order on the set of actions of a given group on hyperbolic spaces which, in some sense, measures how much information about the group the action provides.  This partial order defines a "poset of actions" of the given group.  I will then define the class of acylindrically hyperbolic groups and give some structural properties of the resulting poset of actions for such groups.  In particular, I will discuss for which (classes of) groups the poset contains a largest element.

Thu Feb 8, 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
Fri Feb 9, 2018
1:00pm - rh 340N - Mathematical Physics
Yinfun Shi - (Fudan University)
Spectral gaps for quasi-periodic Schrodinger operators
3:00pm to 4:00pm - NS2 2201 - Distinguished Lectures
Curt McMullen - (Harvard University)
Quadrilaterals, billiards and moduli spaces