Department of Mathematics and Statistics

Colloquia for Spring 2018

Friday, Mar. 9 -- Holt 175, 3:30pm

Edward Roualdes (CSU Chico)
Introduction to Bayesian Modelling

Abstract: This talk will introduce Bayesian statistics. Throughout, Bayesian statistics will be juxtaposed to the more commonly known, but rarely specified, frequentist statistics. We begin with a brief re-cap of frequentist statistics and use this as motivation for Bayesian statistics. We introduce Bayesian statistics with both a high-level discussion and multiple examples.

We then provide a brief, theoretical comparison between these two branches of statistics, keeping in mind that each branch relies on its own approximations. The talk will conclude with two recent examples of my research in applied Bayesian statistics, each of which should highlight some benefits of Bayesian statistics. 

Thursday, Apr. 5 -- Holt 175, 5:00pm

Matthias Beck (San Francisco State University)
Combinatorial reciprocity theorems

Abstract: A common theme of enumerative combinatorics is formed by counting functions that are polynomials. For example, one proves in any introductory graph theory course that the number of proper k-colorings of a given graph G is a polynomial in k, the chromatic polynomial of G.

Combinatorics is abundant with polynomials that count something when evaluated at positive integers, and many of these polynomials have a (completely different) interpretation when evaluated at negative integers: these instances go by the name of combinatorial reciprocity theorems. For example, when we evaluate the chromatic polynomial of G at -1, we obtain (up to a sign) the number of acyclic orientations of G, that is, those orientations of G that do not contain a coherently oriented cycle. 

Combinatorial reciprocity theorems appear all over combinatorics. This talk will attempt to show some of the charm (and usefulness!) these theorems exhibit. Our goal is to weave a unifying thread through various combinatorial reciprocity theorems, by looking at them through the lens of geometry.

Friday, Apr. 20 -- Holt 175, 3:30pm

Birant Ramazan (University of Nevada Reno)
Groupoids and quantizations

Abstract: A quantization establishes a correspondence between a classical mechanical system given as a Poisson manifold, and a quantum mechanical system given as a certain non-commutative algebra. In the case of strict quantization for different values h of the Planck's constant, a family A_h of C*-algebras is associated, with the requirement that for h->0 the classical system is retrieved.

Groupoids are natural generalizations of groups, and a construction of a C*-algebra of a groupoid can be modeled after the construction of the group C*-algebra. Like a Lie group, a Lie groupoid has an associated "infinitesimal" object, its Lie algebroid.

We introduce a groupoid approach to quantization and using it we show the existence of a strict quantization for the Poisson manifolds which are associated with Lie algebroids. An important role is played by a generalization of Connes's tangent groupoid. No expertise in the area needed, as I will introduce all the relevant concepts from scratch.

Friday, May 11, 2018 -- Holt 175, 3:30pm

Hyoungjun Kim (Ewha Woman's University, Korea)
Intrinsic knotting for spatial graphs

Abstract: Spatial graph theory is the study of graphs embedded in S^3. Most of the work in this area has its roots in Conway and Gordon's results on intrinsic properties. A graph is called intrinsically knotted if every embedding of the graph contains a non-trivially knotted graph. In this talk, I will introduce spatial graph theory, in particular, the intrinsic knotting property and related results.