Hunter's theorem ensures that the complete homogeneous symmetric (CHS) polynomials of even degree are positive definite functions. We provide new proofs of Hunter's theorem, applications to operator theory, and a noncommutative (NC) generalization that sheds light even on the commutative case. Surprisingly, this work emerged from a problem in analytic combinatorics.
We welcome all undergraduate/graduate students and faculty to attend topology seminar! Speaker: Indraneel Tambe (UCLA) Title: Steinberg skein relations at roots of unity Abstract: This talk discusses some of the relationships between skein theory and the representation theory of quantum sl2 when q is a root of unity. Specifically, I focus on the Frobenius pullback […]
CCMS Colloquium invites you to a talk by Konstantin Zuev (Caltech) Title: Course-Prerequisite Networks Abstract: An academic curriculum is a complex system of courses and their interactions that lies at the heart of an academic institution and underlies its educational mission. Understanding these systems is essential for providing high-quality education. Course-prerequisite networks (CPNs) are directed […]
This GEMS session will be facilitated by Professor Ryan Aschoff from the Claremont Graduate University. Title: Randomness: Creating Order from Chaos Abstract: From the hiss of white noise to the gentle hum of ocean waves, randomness surrounds us — yet hidden within that chaos lies remarkable order. In this talk, we’ll explore how unpredictable events, […]
Abstract: The talk introduces a conjecture on the first exit time of fractional Brownian motion: the upper-tail probability for a fractional Brownian motion to first exit a positive-valued barrier over time […]
Virtual links can be represented as equivalence classes of Gauss diagrams under Reidemeister moves. The Forbidden Moves are moves which look plausible but change the virtual isotopy class of the knot or link -- indeed, virtual knots are all trivial if we allow forbidden moves. However, virtual links remain non-trivial. In this talk we show […]
Abstract: A proper coloring of a graph is an assignment of colors from \( \{1, 2, \ldots, k\} \) to each node of a graph such that no two nodes […]
CCMS Colloquium invites you to a talk by John Baez (UCR) Title: The mathematics of tuning systems Abstract: Leibniz said "Music is the pleasure the human mind experiences from counting without being aware that it is counting." The first step is choosing a tuning system — the frequency ratios between pitches in a scale. Different kinds […]
We will examine the multiplicative structure of two skein algebras--- the usual Kauffman bracket skein algebra of a surface (generated by loops) and a generalization of it due to Roger-Yang (generated by loops and arcs). In joint work with Chloe Marple, we found a homomorphism between the usual skein algebra for a closed torus and […]
CCMS Colloquium invites you to a talk by Teal Witter (CMC) Title: Exactly Computing do-Shapley Values Abstract: Causal questions lie at the heart of scientific inquiry, from evaluating economic policies […]
This GEMS session will be facilitated by Professor Teal Witter from Claremont McKenna College. Title: Who Can Write Down the Bigger Number? Abstract: If you had fifteen seconds to write the largest distinct whole number possible on an index card, what would you write? While most would look to the physical world for inspiration—counting the […]
Abstract: The three-dimensional incompressible Euler equations describe the motion of an ideal fluid, yet the mechanisms that govern the possible loss of regularity of smooth solutions remain only partially understood. […]
