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, new proofs of Dowker duality using various poset fiber lemmas. I will introduce modifications of joins and products of simplicial complexes called relational join and […]
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 in the 1970s in the work of the computer scientist Imre Simon. Since then, the field of tropical geometry has developed rapidly. In this talk, […]
We especially welcome all undergraduates and graduate students to attend topology seminar! Speaker: Morgan Weiler (University of California, Riverside) Title: Anchored symplectic embeddings and 2-parameter persistence Abstract: Symplectic geometry is a generalization of classical mechanics, in which position and momentum coordinates are paired. In two dimensions, symplectic geometry is equivalent to volume-preserving geometry, but in […]
We especially welcome all undergraduates and graduate students to attend topology seminar! Speaker: Shane Rankin (University of California, Riverside) Title: Symplectic Hodge Theory on Lie Algebroids Abstract: Symplectic Hodge Theory was developed in the late 80s to answer a conjecture of Brylinksi. Since then it has been used to understand the gap between Symplectic and […]
We welcome all undergraduate/graduate students and faculty to attend topology seminar! Speaker: Heather Lee Title: Some examples of homological mirror symmetry Abstract: Mirror symmetry is a duality phenomenon between symplectic geometry and complex geometry. The homological mirror symmetry (HMS) conjecture was originally formulated by M. Kontsevich in 1994 to fully capture this phenomenon for mirror […]
We welcome all undergraduate/graduate students and faculty to attend topology seminar! Speaker: Will Hoffer (UC Riverside) Title: Tube Formulae for Fractal Snowflakes Abstract: Fractals like the von Koch snowflake have rough boundaries, often having nowhere defined tangent lines/spaces. However, there is a tool useful for probing the edges of such fractals: tubular neighborhoods. In this […]
