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 mathematical graphs. We will present our rules for multiple color peg solitaire on graphs. We will present some student and faculty results classifying the solvability of the game […]
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 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 […]
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 rather different research areas: -- values of quadratic forms (Perron Identity for Markov spectrum) -- the 2nd Kepler law on planetary motion -- Global relation […]
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 […]
Title: Linear independence, counting, and Hilbert's syzygy theorem Speaker: Youngsu Kim, Department of Mathematics, Cal State San Bernardino Abstract: Linear independence is an essential concept in mathematics and one of the most fundamental notions in linear algebra. Linear algebra studies the solutions of linear equations. Algebraic geometry studies the solutions of polynomial equations (of arbitrary degree). […]
Title: Data science and applications in dynamic topic modeling Abstract: The shockwaves of the big data boom have thrown into sharp relief the critical need for domain-driven, large-scale data analytic […]
