Analysis Seminar

Title: A crash course in Bornologies Abstract: By a bornology on a nonempty set X, we mean a family of subsets that contains the singletons, that is stable under finite […]

Title: What can chicken McNuggets tell us about symmetric functions, positive polynomials, random norms, and AF algebras? Abstract: Numerical semigroups are combinatorial objects that lead to deep and subtle questions. […]

Title: Domains of Quantum Metrics on AF algebras Abstract: Given a compact quantum metric space (A, L), we prove that the domain of L coincides with A if and only […]

Title: Exceptional Sets for Divergent Fourier Series Abstract: A survey of some old and newer results on divergent Fourier series with some comments on how they relate to undergraduate analysis courses and (time permitting) leading to a brief discussion of an open question on the size of exceptional sets in divergence examples and some progress […]

Title: Geometric classification problems with the Bergman metric Abstract: One of the common problems in mathematics is the classification problem: When are two mathematical structures really the same? The classification […]

Title: Transfinite Apollonian metric Abstract: The concept of transfinite diameter of compact sets in the complex plane was introduced by Fekete in 1923. It is a generalization of the standard […]

Abstract: The three-dimensional incompressible Euler equations describe the motion of an ideal fluid, yet the mechanisms that govern the possible loss of regularity of smooth solutions remain only partially understood. […]

Abstract: In general, the objective of algebraic topology is to classify spaces using some algebraic invariants or up to some notion of equivalence. In the area of equivariant homotopy theory, […]

Abstract: Let C be a compact convex set (in a locally convex topological vector space). By Choquet’s theorem, every point in C is the barycenter of a probability measure supported […]

Abstract: We study metrics on completely positive maps, and in particular on quantum channels, induced by seminorms from noncommutative geometry. Using an infinite-dimensional analogue of the Choi–Jamiołkowski correspondence, we construct […]

Abstract: An isometry between two normed vector spaces is a linear map that preserves the norm (i.e., the length of each output agrees with the length of its input). For the classical $p$-norms, isometries have a very concrete description when $p\neq 2$: they are given by signed permutations of the coordinates. In this talk, I […]

Abstract: Consider n independent, biased coins, each with a known probability of heads. Presented with an ordering of these coins, flip (i.e., toss) each coin once, in that order, until […]