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
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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 and abstract TBA
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, […]
Title: Recovery of time-dependent coefficients in hyperbolic equations on Riemannian manifolds from partial data.Abstract: In this talk we discuss inverse problems of determining time-dependent coefficients appearing in the wave equation in a compact Riemannian manifold of dimension three or higher. More specifically, we are concerned with the case of conformally transversally anisotropic manifolds, or in […]
Title: Analytic stacks
Title: Properties of log canonical singularities in positive characteristic.Abstract: We will investigate if some well known properties of log canonical singularities over the complex numbers still hold true over perfect fields of positive characteristic and over excellent rings with perfect residue fields. We will discuss both pathological behavior in characteristic p as well as some positive results […]
Title: Covers of P^1 and number fields Abstract: Let $n$ be an integer. Via the Minkowski embedding, an order $mathcal{O}$ in a degree $n$ number field can be seen as a lattice. Similarly, given a degree $n$ cover of $mathbb{P}^1$, the pushforward of the structure sheaf is an interesting rank $n$ vector bundle on $mathbb{P^1}$. […]