The Jones polynomial is an invariant of knots in R^3. Following a proposal of Witten, it was extended to knots in 3-manifolds by Reshetikhin-Turaev using quantum groups. Khovanov homology is a categorification of the Jones polynomial of a knot in R^3, analogously to how ordinary homology is a categorification of the Euler characteristic of a […]
Title: The 6 Cs - Covid and the 5 Claremont Colleges Speaker: Maryann E. Hohn, Department of Mathematics and Statistics, Pomona College Abstract: The Claremont Colleges' (5Cs) environment consists of students, faculty, and staff that congregate together in indoor spaces, creating a higher risk for possible COVID-19 infection. Additionally, a majority of the students live on […]
Peg solitaire is a popular one person board game that has been played in many countries on various board shapes. Recently, peg solitaire has been studied extensively in two colors on […]
Skein modules were introduced by Jozef H. Przytycki as generalisations of the Jones and HOMFLYPT polynomial link invariants in the 3-sphere to arbitrary 3-manifolds. The Kauffman bracket skein module (KBSM) […]
Title: Voronoi Tessellations: Optimal Quantization and Modeling Collective Behavior Speaker: Prof. Rustum Choksi, Department of Mathematics and Statistics, McGill University Abstract: Given a set of N distinct points (generators) in a domain (a bounded subset of Euclidean space or a compact Riemannian manifold), a Voronoi tessellation is a partition of the domain into N regions […]
Title: Viscoelastic Effects of Spontaneous Oscillations of Elastic Filaments in the Follower-Force Problem. Abstract: It is well know that microorganisms, such as bacteria and eukaryotes, often move in intricate environments […]
In 1932, Tarski conjectured that a convex body of width 1 can be covered by planks, regions between two parallel hyperplanes, only if the total width of planks is at least 1. In 1951, Bang proved the conjecture of Tarski. In this work we study the polynomial version of Tarski's plank problem. We note that […]
During this student-centered Applied Math Seminar, there will be discussion and presentation about upcoming courses in applied mathematics to help students make their enrollment choices for Fall 2022 and beyond.
In this talk we link discrete Markov spectrum to geometry of continued fractions. As a result of that we get a natural generalization of classical Markov tree which leads to […]
Convex real projective structures generalize hyperbolic structures in a rich way. We will discuss a class of manifolds introduced by Cooper Long and Tillmann, which include finite-volume cusped hyperbolic manifolds […]
Title: Geometry of continued fractions Speaker: Oleg Karpenkov, Department of Mathematical Sciences, University of Liverpool Abstract: In this talk we introduce a geometrical model of continued fractions and discuss its appearance in […]
I will explain how to apply presentations of algebras (together with some classical results from non-commutative algebra) to obtain some 5 polynomial invariants telling us when two pairs of 2x2 […]
