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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

A Tensor-Train Stochastic Finite Volume Method for Uncertainty Quantification

STAG 112
Applied Mathematics and Computation Seminar

Speaker: Svetlana Tokareva

ABSTRACT: Many problems in physics and engineering are modeled by systems of partial differential equations such as the shallow water equations of hydrology, the Euler equations for inviscid, compressible flow, and the magnetohydrodynamic equations of plasma physics. The initial data, boundary conditions, and coefficients of these models may be uncertain due to measurement, prediction, or modeling errors.The stochastic finite volume (SFV) method offers an efficient one-pass approach for assessing uncertainty in hyperbolic conservation laws. The SFV method has shown great promise as a weakly-intrusive PDE solver for uncertainty quantification. However, in many relevant applications, the dimension of the stochastic space can make traditional implementations of the SFV method infeasible or impossible due to the so-called curse of dimensionality. We introduce the Tensor-Train SFV (TT-SFV) method within the tensor-train framework to manage the curse of dimensionality. This integration,… Read more.

CASCADE RAIN

Kidder Hall
Conference

Cascade RAIN is a gathering of researchers for rapid and informal communication of ongoing research activities in computational and applied mathematics in the Northwest region. For the history and the format of the meetings, see https://sites.google.com/site/cascaderainmeetings/There is no registration fee, but we ask participants to register in advance on the conference website:https://sites.google.com/oregonstate.edu/rain2025We ask that the participants register at the latest by April 21 so we can make appropriate local arrangements. We plan to offer minitutorials best suited to graduate students and early researchers on April 25 evening and April 27 morning. There will be a separate registration for these. Please use the email address [email protected] to contact the Organizing Committee. Read more.

Optimal Risk-Sharing Rules in Network-based Decentralized Insurance

STAG 111
Dynamical Systems Seminar, Mathematical Biology Seminar, Probability and Data Science Seminar

Speaker: Heather Fogarty

This talk studies decentralized insurance models with an imposed network structure, extending the existing literature to both define and prove properties of new risk-sharing rules. These rules ensure fairness among participants using properties of the network structure, including graph-theoretic tools such as the graph Laplacian. While maintaining actuarial fairness and convex ordering, the minimization of different risk-sharing metrics is considered. Participants are assumed to share risk with direct neighbors only, with all pre-distributed losses independent, using non-uniform reciprocal contract risk-sharing. Illustrations of this model will be presented, demonstrating the versatility of the risk-sharing rules in a decentralized insurance context. Read more.

Understanding large-time behavior using data assimilation

ROG 332
Analysis Seminar

Speaker: Elizabeth Carlson

One of the fundamental challenges of accurate simulation of turbulent flows is that initial data is often incomplete, which for said flows is a strong impediment to accurate modeling due to sensitive dependence on initial conditions. A continuous data assimilation method proposed by Azouani, Olson, and Titi in 2014 introduced a linear feedback control term to dissipative systems, giving a simple rigorous deterministic method by which to understand the underpinnings of more complex data assimilation algorithms. In this talk, we will focus on how the AOT algorithm and modifications can be improved by knowledge of the dynamics, as well as how the AOT algorithm can yield new insights into the large time behavior of said dynamical systems. Read more.

Where do you put a telescope? How do you understand Covid concentrations?

Kidder 364
Colloquium

Speaker: Matthew Foreman

This talk will discuss dynamical systems - systems that evolve through time. We illustrate differences with two contemporary examples of the qualitative and the quantitative behavior of dynamical systems. These broad, slightly vague categories, usually called the study of the smooth behavior and ergodic theory. We then introduce the technical framework necessary to state the problems mathematically. Finally we show that the problems are unsolvable in a rigorous technical sense. Read more.

40th Annual Lonseth Lecture: Impossibility Results in Mathematics

LaSells Stewart Center Construction and Engineering Hall
Lonseth Lecture

Speaker: Matthew Foreman

Speaker Bio: Matthew Foreman is a set theorist at University of California, Irvine. He has made contributions in widely varying areas of set theory, including descriptive set theory, forcing, and infinitary combinatorics. Foreman earned his PhD in 1980 at University of California, Berkeley under the direction of Robert M. Solovay, with a dissertation on Large Cardinals and Model Theoretic Transfer Properties.Abstract: You can't square the circle! The square root of 2 can't be written as a fraction! The integral of e^{-x^2} can't be written in closed form! Bitcoin is unbreakable! Most of mathematics is about finding solutions to problems or approximating them well. But there is an important collection of results that show certain tasks are mathematically impossible. This talk explains what that means, and the varying notions of impossibility. Read more.

Digital Twins for Wind Energy and Leading Edge Erosion Detection

STAG 112
Applied Mathematics and Computation Seminar

Speaker: Susan Minkoff

ABSTRACT: One of the main sources of renewable energy is wind, which generates tremendous power while also reducing the need for greenhouse gas-emitting traditional power sources such as hydrocarbons and coal. However, many wind turbines installed in the early 2000's are nearing the end of their lifespan, and the problem remains of how to maintain, reduce, or decommission these aging turbines in a cost efficient way. In this talk we describe a digital twin for damage detection and maintenance scheduling of wind turbines which can track the condition of a wind turbine under different operating conditions. A key concern for wind energy that contributes to power production losses and high maintenance costs is deterioration of the turbine blades over time from environmental stressors such as lighting strikes, icing, and accumulation of airborne particles which can result in leading edge erosion of the blades. We will discuss surrogate modeling of the turbines and classification of levels… Read more.

Dedekind had his cuts, Cantor had Cauchy sequences, but what about Weierstrass? The mysterious 'third construction' of the real numbers in the nineteenth century

Owen 102
Colloquium

Speaker: David Pengelley

Precious little of today's mathematics would be possible without the real numbers. Mathematicians all learn about one or both of Dedekind cuts or Cantor's use of Cauchy sequences as nineteenth century constructions of the reals. These constructions, as part of the "arithmetization of analysis", allowed mathematics to move forward, by being assured of the existence and properties of the reals. They put on a firm foundation efforts to forge ahead with a theory of functions, in which rigorous analysis could replace naive geometry and intuition. It turns out, though, that the constructions of Richard Dedekind and Georg Cantor were neither the only, nor the first, such edifices representing the real numbers. It was Karl Weierstrass who provided the very first construction, particularly attuned to his interest in developing function theory via infinite series. Weierstrass never published his construction. I will present his construction and its properties in the context of a somewhat modern… Read more.

Mathematical Strategies for Regional Natural Resource Assessments with Examples for Geothermal Energy

STAG 112
Applied Mathematics and Computation Seminar

Speaker: Erick Burns

Abstract: Under the Energy Act of 2020, the U.S. Geological Survey is tasked with completing assessments for five geothermal resource types: conventional geothermal, enhanced geothermal systems (EGS), low-temperature heating and cooling resources, underground thermal energy storage, and the potential for co-production of conventional hydrothermal with critical minerals. The mathematical tools employed for these assessments range from data-driven methods (e.g., Machine Learning) to process-based physically motivated models, with methods selected to capitalize upon what is known from past study. The goal is to make a best estimate of the resource along with estimates of uncertainty, typically using Bayesian paradigms. The reality of data often conflicts with the idealized assumptions of the underlying mathematical strategies, and understanding the math helps the practitioner understand and address bias (e.g., the use of regularization). As methods become increasingly complex and… Read more.

Two presentations: Mansi Mahajan and Nicholas Slugg

STAG 112
Applied Mathematics and Computation Seminar

Presentation by Mansi MahajanTitle : Spectral Finite Elements for Electromagnetic Metamaterial Models Abstract : Metamaterials are artificially structured materials designed to exhibit electromagnetic properties not found in naturally occurring materials. This talk begins with a brief overview of electromagnetic metamaterials and their applications, such as cloaking, negative refraction, and superlensing. I will then introduce spectral finite element methods for modeling wave propagation in such media, with a focus on dispersive models like the Drude model and the use of edge (Nédélec) elements for accurate discretization of Maxwell’s equations. The talk will also touch on dispersion relations arising from the discretized system and their relevance to wave behavior in metamaterials.Presentation by Nicholas Slugg Read more.