An arithmetical structure on a finite, connected graph G without loops is given by an assignment of positive integers to the vertices such that, at each vertex, the integer there is a divisor of the sum of the integers at adjacent vertices, counted with multiplicity if the graph is not simple. Alternatively, an arithmetical structure […]
Title: An introduction to algebraic statistics Speaker: Luis David Garcia Puente, Department of Mathematics and Computer Science, Colorado College Abstract: Algebraic statistics is an interdisciplinary field that uses tools from computational algebra, algebraic geometry, and combinatorics to address problems in statistics and its applications. A guiding principle in this field is that many statistical models of […]
Noncommutative metric geometry is the study of certain noncommuative algebras in the context of metric geometry. For instance, the Lipschitz constant (which measures the maximum slope obtained by a real-valued continuous function on a metric space (allowed to be infinite)) is a vital tool in metric geometry, and a main feature of noncommutative metric geometry […]
This talk discusses a puzzle called “Spinning Switches,” based on a problem popularized by Martin Gardner in his February 1979 column of “Mathematical Games". This puzzle can be generalized to a two-player game on a finite wreath products. This talk will provide a classification of several families of these generalized puzzles, including a full classification […]
Title: Between Yes and No: making decisions under uncertainty. Speaker: Ami Radunskaya, Department of Mathematics and Statistics, Pomona College Abstract: Often we attempt to answer a question with a “yes” or a “no” by developing predictive models (“Will the small remaining population of axolotls survive outside of their native wetlands?”) or by implementing binary classifiers (“Is this […]
Title: Understanding scientific fields with network analysis and topic modeling Abstract: As scientific disciplines get larger, it becomes impossible for an individual researcher to be familiar with the entire body of literature, which forces them to specialize in a sub-field. Such insulation can hinder the birth of ideas that arise from new connections, eventually slowing down […]
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 operators from \(X\) to \(Y\). Denote by \(T^{*} \in \mathcal{L}(Y^{*}, X^{*} )\) the adjoint operator of \(T\in \mathcal{L} (X, Y)\). The well known theorem of […]
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 realistic models of such populations, after a large enough amount of time has passed, one or more of the species are sure to face extinction. […]
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 […]
