The slice rank polynomial method, motivated by groundbreaking work of Croot, Lev and Pach and refined by Tao, has opened the door to the resolution of many problems in extremal combinatorics. We survey these results and discuss contributions in several of the speaker's recent papers.
Title: How do mathematicians believe? Speaker: Brian P Katz (BK), Department of Mathematics and Statistics, CSU, Long Beach Abstract: Love it or hate it, many people believe that mathematics gives humans access to a kind of truth that is more absolute and universal than other disciplines. If this claim is true, we must ask: what makes the […]
Let \mathcal{L}(X,Y) denote the normed vector space of all continuous operators from \(X\) to \(Y\), \(X^*\) be the dual space of \(X\), and \(\mathcal{K}(X,Y)\) denote the collection of all compact […]
Title: Approximating Quasi-Stationary Distributions with Interacting Reinforced Markov Chains Abstract: An important question in ecology is what conditions must be met for a population of interacting species to coexist. In […]
Given a lattice L, an extension of L is a lattice M of strictly greater rank so that L is equal to the intersection of the subspace spanned by L with M. In this talk, we will discus constructions of such lattice extensions with particular geometric invariants of M, such as the determinant, covering radius […]
Title: Human Computers in Astronomy: Women Astronomers at Mount Wilson Observatory during the Early Twentieth Century Speaker: Eun-Joo Ahn, Department of History, UC Santa Barbara Abstract: Mount Wilson Observatory was founded by astrophysicist George Ellery Hale in 1904 with funding from the Carnegie Institution of Washington. Since then, it has become one of the most prominent […]
Quantum metrics in the sense of Rieffel were introduced to prove some statements arising in the high-energy physics literature. Since then, the area of quantum metric geometry has been used […]
The relation of accessible points in a projective incidence plane defined by Coxeter in the 1960s is the focus of my narrative. It reveals historical pathways bookending the 19th and […]
Title: Kolmogorov, Onsager and a Dyadic Model for Turbulence Abstract: We will briefly review Kolmogorov’s ( 41) theory of homogeneous turbulence and Onsager’s ( 49 ) conjecture that in 3-dimensional […]
Markov chains have become widely-used to generate random political districting plans. These random districting plans can be used to form a baseline for comparison, and any proposed districting plans that differ significantly from this baseline can be flagged as potentially gerrymandered. However, very little is rigorously known about these Markov chains - Are they irreducible? […]
Title: Frequentist Model Averaging in the Generalized Multinomial Logit Model Speaker: Tonia Zeng, Applied Business Sciences and Economics, University of La Verne Abstract: The generalized multinomial logit (GMNL) model accommodates scale heterogeneity to the random parameters logit (RPL) model. It has been often used to study people's preferences and predict people's decisions in many areas, […]
