Biquandle brackets are skein invariants of biquandle-colored knots, with skein coefficients that are functions of the colors at a crossing. Biquandle power brackets take this idea a step further with state component values that also depend on biquandle colors. This is joint work with Neslihan Gügümcü (IYTE).
Title: Cellular resolutions of the diagonal and exceptional collections for toric Deligne-Mumford stacks Abstract: Beilinson gave a resolution of the diagonal for complex projective space which yields a strong, full exceptional collection of line bundles. Bayer-Popescu-Sturmfels generalized Beilinson's result to a cellular resolution of the diagonal for what they called "unimodular" toric varieties (a more restrictive […]
Title: p-Norm Approval Voting Speaker: Michael Orrison, Professor of Mathematics, Harvey Mudd College Abstract: Approval voting is a relatively simple voting procedure: Given a set of candidates, each voter chooses a subset of the candidates, and the candidate chosen the most is then declared the winner. Interestingly, approval voting can be viewed as an extreme […]
A classic problem in graph theory is to find the chromatic number of a given graph: that is, to find the smallest number of colors needed to assign every vertex a color such that whenever two vertices are adjacent, they receive different colors. This problem has been studied for many families of graphs, including cube-like […]
Title: Cellular resolutions of the diagonal and exceptional collections for toric Deligne-Mumford stacks (Continued) Abstract: Beilinson gave a resolution of the diagonal for complex projective space which yields a strong, full exceptional collection of line bundles. Bayer-Popescu-Sturmfels generalized Beilinson's result to a cellular resolution of the diagonal for what they called "unimodular" toric varieties (a more […]
Title: Building the Fan of a Toric Variety Speaker: Reginald Anderson, Department of Mathematical Sciences, Claremont McKenna College Abstract: Roughly speaking, algebraic geometry studies the zero sets of polynomials, which lead to objects called varieties. Since the zero sets of polynomials do not always pass the vertical line test, we enlist other methods to study […]
Title: Understanding SARS-CoV-2 viral rebounds with and without treatments. Abstract: In most instances, the characteristics of SARS-CoV-2 mirror the patterns of an acute infection, with viral load rapidly peaking around 5 days post-infection and subsequently clearing within 2 weeks. However, some individuals show signs of viral recrudescence of up to 10000 viral RNA copies/mL shortly […]
Beilinson gave a resolution of the diagonal for complex projective space, which gives a strong, full exceptional collection of line bundles as a generating set for the derived category of coherent sheaves. Bayer-Popescu-Sturmfels generalized Beilinson's resolution of the diagonal by giving a cellular resolution of the diagonal for a proper subclass of smooth toric varieties […]
Title: Quantum 4-Manifold Invariants Via Trisections Abstract: I will describe a new family of potentially non-semisimple invariants for compact a 4-manifold whose boundary is equipped with an open book. The invariant is computed using a trisection, along with some additional combing data, and a piece of algebraic data called a Hopf triple. The relationship with […]
Title: Thinking Inside the Box: A combinatorial approach to Schubert Calculus Speaker: Sami H. Assaf, Department of Mathematics, University of Southern California Abstract: Given 2 lines in the plane, how many points lie on both? If we rule out the case where the two lines are the same, and we work in projective space so […]
Title: The Hartman-Watson distribution: numerical evaluation and applications in mathematical finance Abstract: The Hartman-Watson distribution appears in several problems of applied probability and financial mathematics. Most notably, it determines the joint distribution of the time-integral of a geometric Brownian motion and its terminal value. A classical result by Yor (1981) expresses it as a one-dimensional […]
