Title: First eigenvalue estimates on asymptotically hyperbolic manifolds and their submanifolds. Abstract: I will report on joint work with Samuel Pérez-Ayala. We derive a sharp upper bound for the first eigenvalue $lambda_{1,p}$ of the $p$-Laplacian on asymptotically hyperbolic manifolds for $1<p<infty$. We then prove that a particular class of conformally compact submanifolds within asymptotically hyperbolic […]
Title: The simply typed 2λ-calculus Abstract: 2λ-calculus is a language with three levels: types, terms, and rewrites. I will explore their properties and give categorical description of the equational theory on the rewrites of the 2λ-calculus
From Stochastic to Deterministic: SGD dynamics of non-convex models in high dimensionsStochastic gradient descent (SGD) stands as a cornerstone of optimization and modern machine learning. However, understanding why SGD performs so well remains a major challenge. In this talk, I will present a theory for SGD in high dimensions when the number of samples and […]
Title: Discrete Series and Infinitesimal Characters Abstract: The infinitesimal character is an important invariant of an irreducible representation of a real group. We expect particularly nice representations of the group will have particularly nice infinitesimal character. We'll first introduce the definition of the infinitesimal character. Then, we discuss a recent application found by Krotz, Kuit, […]