Kloosterman sums are explicit exponential sums which occur in several contexts in number theory and arithmetic geometry. Bessel functions encode a great deal of representation-theoretic information about finite groups of Lie type, but they are difficult to compute in general. In this talk, we will carefully define these objects and describe a direct relationship between […]
Abstract: Edge ideals of graphs provide a fertile ground for uncovering combinatorial expressions for algebraic invariants of squarefree monomial ideals. Many algebraic invariants of these edge ideals directly reflect combinatorial properties […]
We showcase Diophantine Representation of the Set of Prime Numbers by Jones, Sato, Wada and Wiens. Link: https://www.jstor.org/stable/2318339 For questions about the event, please contact your NTLS Organizers: Maxwell Kooiker (Maxwell.Kooiker@cgu.edu) or Prof. Edray Goins (Edray.Goins@pomona.edu)
A Belyĭ pair \bigl( S,\, z(w) \bigr) is a compact, connected Riemann surface S together with a rational function z \colon S \to \mathbb{P}^1(\mathbb{C}) which has at most three critical values \bigl\{ 0,\, 1,\, \infty \bigr\}. The preimage z^{-1}\bigl( \bigr) \subseteq S \hookrightarrow \mathbb{R}^3 is a bipartite graph called a Dessin d'Enfant. When S = \mathbb{P}^1(\mathbb{C}) […]
The unique minimal generating set for a semigroup of lattice points in an n-dimensional polyhedral cone is called its Hilbert basis. In the case when the cone is spanned by lattice points, this Hilbert basis is finite, however its cardinality can be much larger than n. Nevertheless, a conjecture of Sebö states that each point […]
Speaker: Sam Nelson (CMC) Title: Permutation Jones Polynomials Abstract: The Jones Polynomial is an important invariant of knots with applications in physics, quantum computation and more. In this talk I will introduce a family of generalizations of the Jones polynomial associated to permutations of finite sets and discuss their properties. _______ We especially welcome all […]
Flyer for Kim's talk. Abstract: The logistic map is one of the most famous examples in dynamical systems. Originally introduced as a simple model of population growth, it exhibits a […]
A wide variety of medical imaging methods exist for research and diagnostic procedures on the Central Nervous System (CNS), among them Magnetic Resonance Imaging (MRI) and Optical Imaging. Mathematical modeling and simulation contribute significantly to an improved understanding of image data and the intricate transport, diffusion, and metabolic processes in the brain. This is of […]
Extremal graph theory asks how many edges a graph can have while avoiding a given substructure. We will begin with a brief, accessible introduction to this area, before turning to a natural variant, the bipartite Turan number $(m,n;H)$, which restricts the host graph to be bipartite. This setting is especially natural when $H$ itself is […]
Speaker: Helen Wong (CMC) Title: Introduction to the colored Jones polynomial Abstract: This is a learning seminar. We will present an accessible definition of the colored Jones polynomial for knots and links and discuss the Volume Conjecture, which relates the colored Jones polynomial of K with the volume of its complement S^3 \K. _______ We […]
Abstract: Stable Khovanov homology Kh(T(n, \infty)) is an algebraic limit of the Khovanov homology groups of torus links T(n, k) on a fixed number of strands n, when more and […]
We showcase Functions Which Represent Prime Numbers. Presented by Joy Shin. Link: https://www.jstor.org/stable/2032078 For questions about the event, please contact your NTLS Organizers: Maxwell Kooiker (Maxwell.Kooiker@cgu.edu) or Prof. Edray Goins (Edray.Goins@pomona.edu)
