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, […]
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) is the most extensively studied of all. However, computing the KBSM of a 3-manifold is notoriously hard, especially over the ring of Laurent polynomials. With […]
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 […]
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 experiencing mechano-chemical dynamics. These environments consist of rheologically complex substances such as mucus and other biofilms that are more complicated than water. Spermatozoa (sperm), for […]
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 […]
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 an efficient computation of Markov minima for all elements in generalized Markov trees.
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 and other manifolds with well-controlled ends. These manifolds have nice deformation theoretic properties, and we will conclude with an existence theorem for novel structures on […]
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 matrices over a commutative ring are conjugate, assuming that each of these pairs generate the matrix algebra. This talk is based on my joint paper […]
