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 more full twists are added as k \to \infty. Stable Khovanov homology is intimately related to the Jones polynomial because it categorifies the Jones-Wenzl projector, […]
This GEMS session will be facilitated by Professor Chiu-Yen Kao from Claremont McKenna College. Title: The Magic of 0s and 1s Abstract: Have you ever wondered how data in a computer is stored? In this talk, we'll crack open the binary numeral system, the simple code of 0s and 1s that represents everything on your […]
Political scientists forecast elections, not primarily to satisfy public interest, but to validate statistical models used for estimating quantities of scholarly interest. Although scholars have learned a great deal from […]
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.
Speaker: Puttipong Pongtanapaisan (Pitzer) Title: Introduction to Quantum Invariants of 3-Manifolds Abstract: The previous speakers showed us how to distinguish knots and links using techniques involving quantum groups. I will […]
Abstract: In this talk, we study the optimal timing of selling a risky asset within the distribution builder framework. Instead of specifying a utility function or risk-aversion parameter, this approach […]
A classical principle in algebraic geometry is that a general hyperplane section of a variety should have singularities no worse than those of the variety itself. Over the complex numbers, this principle is known to hold for rational singularities. Rational singularities are related via reduction mod p to a notion called F-rationality, which is defined […]
Speaker: Jim Hoste (Pitzer) Title: Enumerating 2-bridge knots Abstract: A new proof of an old theorem. This is joint work with Patrick D. Shanahan (Loyola Marymount University). _______ We especially welcome […]
Abstract: Rings containing a finite field mathbb{F}_p (such as the ring of polynomials with coefficients in mathbb{F}_p) admit a map called the Frobenius homomorphism which sends every element to its […]
