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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

The coarse geometry of geodesic currents

Kidd 238
Geometry and Topology Seminar

Speaker: Didac Martinez Granado

Geodesic currents form the completion of the space of closed curves on a hyperbolic surface. The notion of geometric intersection number carries over continuously to this completion. Among its many interesting features, plenty of geometric structures on the surface can be represented as geodesic currents, such as hyperbolic metrics (Teichmueller space) or more general negatively curved metrics. These are examples of filling currents: geodesic currents that have positive intersection with all other currents. The subspace of filling geodesic currents can be endowed with a natural distance, generalizing a classical notion of distance in Teichmueller space. In this talk we study its coarse geometry. This is joint work in progress with Jenya Sapir. Read more.


Scalar Curvature and Singularities

KIDD 364
Colloquium

Speaker: Mark Wash

A central theme in modern geometry concerns the relationship between the curvature and topology of a smooth manifold. One popular measure of curvature is the scalar curvature, and a well-studied problem is that of determining whether a given smooth manifold admits a Riemannian metric whose scalar curvature is strictly positive (PSC-metric). In the case of manifolds admitting such metrics one can ask about the topology of the space of all PSC-metrics on the underlying manifold. Over the last couple of decades many interesting results, showing non-trivial topology of this space, have been obtained. In this talk, we consider the analogous problems for manifolds with various kinds of singularities and present some recent results. This is based on joint work with Boris Botvinnik. Read more.


Improving the accuracy of coupled physics packages in Earth system models

STAG 112
Applied Mathematics and Computation Seminar

Speaker: Sean Santos

ABSTRACT: Earth system models solve exceedingly complicated multiphysics problems by breaking down the Earth system hierarchically into smaller sub-models (e.g. atmosphere, ocean, land, and sea ice), which are composed of smaller components themselves. This decomposition of an Earth system model (which may require millions of lines of code in its software implementation) into many small modules is a vital part of model development. However, naïve coupling of modular physics packages using first-order methods can significantly reduce model accuracy, or even produce numerical instability. This talk covers two examples from the Energy Exascale Earth System Model (E3SM). First, we will see that “sequential” (Lie-Trotter) splitting is a major source of error for E3SM’s cloud and precipitation physics. We will discuss our evaluation of several proposed alternatives, including Strang splitting and multirate methods. Second, we will see that E3SM is prone to spurious “oscillations” in winds… Read more.


Math For All Conference

TBD
Conference

Math for all in Corvallis has the purpose of fostering inclusivity in mathematics by holding talks and discussions in both research and education. This conference will be targeted to undergraduate and graduate students, post-docs, and faculty members from all institutions in Oregon and provide a friendly, open environment to learn and discuss mathematics. Read more.


Numerical Solution of Double Saddle-Point Systems

TBA
Colloquium

Speaker: Chen Greif

Double saddle-point systems are drawing increasing attention in the past few years, due to the importance of multiphysics and other relevant applications and the challenge in developing efficient iterative numerical solvers. In this talk we describe some of the numerical properties of the matrices arising from these problems. We derive eigenvalue bounds and analyze the spectrum of preconditioned matrices, and it is shown that if Schur complements are effectively approximated, the eigenvalue structure gives rise to rapid convergence of Krylov subspace solvers. A few numerical experiments illustrate our findings. Read more.


Modeling hypothermia, frostbite, and blood flow regulation with a coupled PDE and ODE system (by Fara) and TBA (by Lilly)

STAG 112
Applied Mathematics and Computation Seminar

Speaker: Tyler Fara and Jeremy Lily

Abstract (talk by T. Fara) We present a model simulating human body temperature when the extremities (such as hands or feet) are subject to extreme cold, possibly leading to hypothermia. The model involves (1) a PDE for the temperature in the extremity and (2) a reduced/lumped model of temperature in the body core. More specifically, (1) is a parabolic PDE with a nonlinear term modeling the tissue-vascular energy exchange similar to that derived by homogenization by Deuflhard and Hochmuth, and (2) is a constrained, nonlinear ODE. Phenomenologically, the model accounts for (i) the influence of warmed arterial blood on the extremity, (ii) the effect of cooling through the skin on the blood in the microvasculature, (iii) the resulting cooling of the venous blood and (iv) its impact back on the core temperature. Our model also describes (v) the body's attempt to control the loss of heat in the core during hypothermic crisis by vasoconstriction of the microvasculature. Our model is… 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.