# Events for 02/20/2020 from all calendars

## Number Theory Seminar

**Time:** 10:30AM - 11:30AM

**Location:** BLOC 220

**Speaker:** Nahid Walji, American University of Paris

**Title:** *On the distribution of Hecke eigenvalues in the complex plane*

**Abstract:** Let r be a cuspidal automorphic representation of non-solvable polyhedral type for GL(2) over a number field. We establish the existence of sets of primes with positive upper Dirichlet density for which the associated Hecke eigenvalues satisfy prescribed bounds on their argument and/or size. For example, if r is not self-dual we show that there is a positive upper density of Hecke eigenvalues in any sector of size 2.64 radians.

**URL:** *Link*

## Banach and Metric Space Geometry Seminar

**Time:** 3:00PM - 4:00PM

**Location:** BLOC220

**Speaker:** Anastasios Sidiropoulos, University of Illinois at Chicago, Theory Group

**Title:** *Robust metric learning via geometric approximation algorithms*

**Abstract:** We study the problem of learning a metric space under discriminative constraints. Given a universe X and sets S, D of similar and dissimilar pairs in X, we seek to find a mapping f: X → Y, into some host metric space M = (Y, ρ), such that similar objects are mapped close together, and dissimilar objects are mapped to points that are far apart from each other. More generally, the goal is to find a mapping of maximum accuracy (that is, fraction of correctly classified examples). We propose approximation algorithms for various versions of this problem, for the cases of Euclidean and tree metric spaces, and for both linear and non-linear mappings. Our problem formulation leads to algorithms that are shown to be robust against poisoning attacks when learning Mahalanobis metric spaces. Finally, we also discuss the problem of learning Mahalanobis metric spaces using depth-2 neural networks. Based on joint works with Diego Ihara Centurion, Bohan Fan, Neshat Mohammadi and Francesco Sgherzi.

## Working Seminar in Groups, Dynamics, and Operator Algebras

**Time:** 3:00PM - 4:00PM

**Location:** BLOC 220

**Speaker:** Konrad Wrobel, Texas A&M University

**Title:** *Ornstein Theory I: Bernoulli Shifts and the Rokhlin Lemma*

**Abstract:** Ornstein theory is a collection of techniques used to prove the Orstein Isomorphism Theorem, a beautiful and deep result which gives a complete classification of Bernoulli shifts by their entropy. Bernoulli shifts arise in many contexts including the theory of flows on manifolds, stochastic processes, transformations of the torus, symbolic coding, statistical mechanics, and ergodic theory. I'll introduce Bernoulli shifts and state the Kolmogorov-Ornstein Isomorphism Theorem. Then, I'll discuss a geometric representation of the Bernoulli shift in the form of the Rokhlin Lemma.