Title: Review of differential geometry Abstract: 1. Given the embedding of a sphere of radius rho centered at the origin of \R^3 from spherical coordinates, what is the pullback of the flat metric in \R^3? i.e., what is the "round metric" on the 2-sphere of radius rho? 2. If we impose a complex structure on S^2 via […]
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 unions, and that is stable under taking subsets. The prototype for a bornology is the so-called metric bornology: the family of metrically bounded subsets of […]
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 […]
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 […]
