Topology, akin to geometry, delves into the study of the shapes and structures of mathematical spaces, ranging from simple surfaces to intricate collections of functions and objects. In recent years, […]
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 […]
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 such metrics and show that, under suitable assumptions, they satisfy stability and chaining. I will present the main ideas and explain how spectral triples and […]
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: 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, the goal is the same but now spaces equipped with a group action are considered and algebraic invariants of choice are homotopy groups. It turns […]
We especially welcome all undergraduates and graduate students to attend topology seminar! Speaker: David Bachman (Pitzer College) Title: Learning optimal knot projections Abstract: We use techniques from Reinforcement Learning to find knot projections which minimize crossing number.
We especially welcome all undergraduates and graduate students to attend topology seminar! Speaker: Sam Nelson (Claremont McKenna College) Title: Virtual Biquandle Cocycle Quiver Representations Abstract: We construct a quiver representation valued invariant of virtual knots and links using virtual biquandle homology.
We especially welcome all undergraduates and graduate students to attend topology seminar! Speaker: Sierra Knavel (Georgia Tech) Title: Betti Numbers and Indecomposability of Genus-2 Lefschetz Fibrations Abstract: Symplectic 4-manifolds, smooth 4-manifolds equipped with a closed, nondegenerate 2-form, arise naturally in classical mechanics and have become central objects of study in topology. Following foundational work by […]
We especially welcome all undergraduates and graduate students to attend topology seminar! Speaker: Scott Taylor (Colby College) Title: Genus 1 Bridge Number of Satellite Knots in Lens Spaces Abstract: In the mid-1950s, Horst Schubert introduced two ideas which turned out to have lasting impact in knot theory: satellite knots and bridge number. A Satellite knot […]
We especially welcome all undergraduates and graduate students to attend topology seminar! Speaker: Reginald Anderson (Claremont McKenna College) Title: Kontsevich's Recursive Formula for Rational Plane Curves Abstract: Gromov-Witten theory was developed in the 1990s as a curve-counting theory by integrating cohomology classes against a virtual fundamental class for a moduli space of stable maps. One […]
We especially welcome all undergraduates and graduate students to attend topology seminar! Speaker: Iris Yoon (Wesleyan University) Title: Dowker duality, profunctors, and spectral sequences Abstract: I will present three short, […]
We especially welcome all undergraduates and graduate students to attend topology seminar! Speaker: Carrie Frizzell (Scripps College) Title: A Primer on Tropical Geometry Abstract: Max-plus and min-plus semifields—coined tropical semifields—appeared […]
