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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

Recent progress on the well-posedness theory for some kinetic models

Kidder 237
Analysis Seminar

Speaker: Weinan Wang

The Boltzmann and Landau equations are two fundamental models in kinetic theory. They are nonlocal and nonlinear equations for which (large data) global well-posedness is an extremely difficult problem that is nearly completely open. In this talk, I will discuss two more tractable and related questions: (1) Local well-posedness for the Boltzmann equation and (2) Schauder estimates and their application to uniqueness of solutions to the Landau equation. At the end of the talk, I will discuss some open problems and future work. This is based on joint work with Christopher Henderson. Read more.

Volumes of Hyperbolic 3-Manifolds

Kidd 280
Geometry and Topology Seminar

Speaker: Alexander Pierson

It is a result of Thurston that for a large class of knots, there is a unique complete hyperbolic structure on its complement. This leads very naturally to the 3-manifold invariant of hyperbolic volume, the volume of this 3-manifold. In this talk we will discuss motivations of the study of this invariant, as well as examples of how to compute it. We will also discuss drawbacks of volume and introduce further extensions of it, such as the Chern-Simons invariant, and how to describe the volume of families of perturbed manifolds, where the hyperbolic structure is no longer complete. Read more.

Global well-posedness and the stabilization phenomenon for some 2D fluid equations

Kidder 364

Speaker: Weinan Wang

In this talk, I will talk about some recent well-posedness and stability results for three incompressible fluid equations. More precisely, I will first discuss a global well-posedness result for the 2D Boussinesq equations with fractional dissipation and the long-time behavior of solutions. For the Oldroyd-B model, we show that small smooth data lead to global and stable solutions. When the Navier-Stokes is coupled with the magnetic field in the magneto-hydrodynamics (MHD) system, solutions near a background magnetic field are shown to be always global in time. The magnetic field stabilizes the fluid. In the examples for Oldroyd-B and MHD, the systems governing the perturbations can be converted to damped wave equations, which reveal the smoothing and stabilizing effect. If time permits, I will discuss some open problems. Read more.

Type C combinatorics of two-pole centralizer algebras

STAG 263
Algebra and Number Theory Seminar

Speaker: Zajj Daugherty

Hecke algebras arise in one sense as deformations of Weyl groups, but in another sense as quotients of braid algebras. While some types of braid algebras can only loosely be associated to their namesake, some can be concretely imagined as braid diagrams on k strands, possibly in spaces with one or more punctures. The latter produces a connection to quantum group actions on tensor spaces of particular shapes. For example, the finite Hecke algebra of type A has a natural action on a tensor space V^{\otimes k}, which commutes with the natural action of the quantum group of type A (this is precisely the q-deformation of classical Schur-Weyl duality). Closures of braids then correspond to traces of endomorphisms, giving rise to knot and link invariants via Hecke algebras; actions on tensor space have implications for lattice models in statistical mechanics; and on the connections go. Read more.

Investigating Gender Bias in the OpenStax Ebook, College Algebra 2e: An Addition to an Ongoing Conversation

M.S. Defense

Speaker: Kaitlynn Spiker

The purpose of this thesis is to investigate gender bias in the OpenStax online textbook, College Algebra 2e. First, I provide a literature review that details how textbooks have historically been gender-biased, and how this is particularly disheartening for students in science, technology, engineering, and mathematics (STEM) fields. I then summarize research that illustrates the importance of representation in STEM fields. To study whether bias was present in the College Algebra textbook, I created a database of all the applied problems in the textbook and coded them based on different criteria. Next, I aggregated the data into summary tables for each category and created proportions for each of the categories. Finally, I used confidence intervals and Fisher’s Exact Test to compare the different proportions. I did not find evidence of gender bias in the problems, but I did find a lack of representation in the historical figures mentioned in the textbook. This shows improvements from… Read more.

Planar extensions and continuity of entropy for infinitely many 1-parameter families of interval maps

Dynamical Systems Seminar

Speaker: Thomas Schmidt

Abstract: In a series of papers with Calta and Kraaikamp, we associate to each of an infinite number of hyperbolic triangles a one-parameter family of interval maps. We prove that the measure theoretic entropy value is continuous along each one-parameter family. We conjecture that the "first expansive power" of each of the maps arises as a factor of a section to the geodesic flow on the unit tangent space of the corresponding hyperbolic surface. In the talk, I will indicate the history of such investigations, explain basic notions, share some examples, and indicate the methods. Read more.

Nonlinear integrable equation-based generation of random waves in large-scale basins and flumes

STAG 112
Applied Mathematics and Computation Seminar

Speaker: Solomon Yim and Patrik Nabelek

Generation of prescribed, scaled physical time series of large-amplitude (including rogue) waves, as measured at particular ocean sites, are often needed in large-scale wave basin (LSWB) experiments to replicate extreme wave impact loads on offshore structures. Current state-of-the-practice models for wave generation in commercial and academic LSWBs worldwide are limited mostly to linear and second-order-term removal types. However, for large-amplitude wave generation, nonlinear models such as nonlinear Schrodinger (NLS) for deep water, Korteweg-de Vries (KdV) for shallow water, and their associated higher-order equations are deemed more accurate for large-amplitude wave simulations. In this study, some analytical and numerical tools we have developed for wave propagation analysis using the periodic and quasi-periodic inverse scattering transform (a.k.a. finite gap) theory based on the NLS and KdV equations propagation, and a nonlinear wavemaker theory (NWMT) based on NLS for wave… Read more.

Digital Twins for Time Dependent Problems

STAG 112
Applied Mathematics and Computation Seminar

Speaker: Juan Restrepo

ABSTRACT: A digital twin is a set of algorithms that connect the virtual world to the physical worl in a fully bi-directional way: for example, a predictive digital twin will use physics models, machine learned models, constraints as well as observations to make forecasts. A digital twin used as a controller would yield a virtual prescription, taking into account observations, that prescribes changes in the real world aimed at obtaining a certain desired real world outcome. I will describe ongoing work on developing a digital twin that will become central to an artificial intelligence framework for large scale electric grid resilience via adaptation. BIO: Juan M. Restrepo is a Distinguished Member of the R&D staff and the section head of the mathematics in computation section at Oak Ridge National Laboratory. His research concerns foundational aspects of machine learning and the development of new artificial intelligence algorithms for science. He is a Fellow of the Society of… Read more.