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Texas A&M University

Events for 02/20/2020 from all calendars

Number Theory Seminar

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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.

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Banach and Metric Space Geometry Seminar

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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

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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.