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Department of Mathematics

Upcoming Events

Branwen Purdy at her stall during OMSI meet-a-scientist day.

Branwen Purdy prepares hands-on activities for kids at the OMSI Meet-A-Scientist Day in Portland, to share hands-on learning experiences about her research in topological data analysis.

Join us for these events hosted by the Department of Mathematics, including colloquia, seminars, graduate student defenses and outreach, or of interest to Mathematicians hosted by other groups on campus.

Access our archive of events

Randomized Kaczmarz, Geometric Smoothing, and Momentum

STAG 163
REU Colloquium

Speaker: Nick Marshall

Abstract. This talk discusses the effect of adding geometrically smoothed momentum to the randomized Kaczmarz algorithm, which is an instance of stochastic gradient descent on a linear least squares loss function. We prove a result about the expected error in the direction of singular vectors of the matrix defining the least squares loss. We present several numerical examples illustrating the utility of our result and pose several questions. Read more.

Symmetry, Classification, and Positive Curvature

STAG 163
REU Colloquium

Speaker: Austin Bosgraaf

Classification problems are ubiquitous in mathematics; and in study of Riemannian manifolds with positive sectional curvature, classification is a central theme. In 2003, Wilking introduced a set of topological tools to the study of positive sectional curvature which led to new classification results in the presence of torus symmetry. This talk will overview some classical results in positive sectional curvature, before introducing Wilking's tools and discussing their applications. We will then see recent results in positive sectional curvature due to Kennard, Khalili Samani, and Searle in the case of discrete symmetries, and I will finish by presenting some of my own results. Read more.

q-series Identities Connected to Ideals in Quadratic Fields

STAG 163
REU Colloquium

Speaker: Lucas Perryman-Deskins

A certain $q$-hypergeometric series $\sigma$ was shown by Andrews, Dyson, and Hickerson to have an interpretation in terms of counting ideals in $\mathbb{Z}(\sqrt{6})$. This interpretation was used to demonstrate unique combinatorial and analytic characteristics, along with some interesting $q$-series identities. Some of these identities reflect a correspondence, predicted by class field theory, between characters on the ideals of each quadratic subfield of a biquadratic field. Cohen described that there are many quadratic fields where similar identities are theoretically discoverable, but few have been actually explored. Cohen also constructed from $\sigma$ a related Maass form, with later work generalizing this construction to a class of functions which are mock Maass theta functions, and in special cases Maass forms. In this talk, I will discuss the some background in each of these areas, and the history of research on this problem, as well as my current approach working towards… Read more.