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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

Monotonicity of data along Ricci flow on surfaces

STAG 213
Dynamical Systems Seminar, Mathematical Biology Seminar, Probability and Data Science Seminar

Speaker: Alena Erchenko

Consider a closed surface M of genus greater than or equal to 2. For negatively curved metrics on M and their corresponding geodesic flow, we can study the topological entropy, the Liouville entropy, and the mean root curvature. In 2004, Manning showed that the topological entropy strictly decreases along the normalized Ricci flow if we start with a metric of variable negative curvature and asked whether monotonicity holds for the Liouville entropy. In this talk, we answer Manning's question and show that the Liouville entropy strictly increases along the flow. This talk is based on joint work with Butt, Humbert, and Mitsutani. Read more.

Self-Similar Solutions to the Hele-Shaw Problem with Surface Tension

STAG 111
Analysis Seminar

Speaker: Neel Patel

The Hele-Shaw problem models the dynamics of the interface of a single viscous fluid domain in porous media. While the dynamics around a corner on the fluid interface are known in the absence of surface tension, it is less rigorously studied in the presence of surface tension. In this talk, we will demonstrate the existence of self-similar solutions that initially have a corner, but instantaneously smoothen out. Due to surface tension, the differential equation describing the self-similar solution is a third order nonlocal equation of elliptic type with coefficients that grow at infinity, and thus, requires an interesting linear analysis. Read more.

Geometric flexibility and rigidity of Anosov manifolds

KEAR 212
Colloquium

Speaker: Alena Erchenko

We will discuss the possibility of recovering a metric from the marked boundary distance information on a compact manifold with boundary. It is analogous to the question of whether it is possible to recover a metric from the marked length of closed geodesics on a compact manifold without boundary. We will link these two questions using an isometric extension. This talk is based on joint work with Thibault Lefeuvre as well as joint work with Dong Chen and Andrey Gogolev. Read more.

Richards equation for unsaturated flows, formulation and numerical methods

STAG 112
Applied Mathematics and Computation Seminar

Speaker: Yves Bourgault

ABSTRACT: The Richards equation describes the infiltration of a fluid in a porous media, such as water in soil, under partially saturated conditions. This equation is a strongly nonlinear parabolic PDE, which PDE also becomes doubly degenerate when regions of the porous media are completely desaturated (or dry) and others fully saturated. Appropriate formulations and numerical methods are required to efficiently handle the strong nonlinearities and degeneracies present in Richards equation. The talk will cover few aspects of this problem, illustrated by numerical test cases. This work is joint with Abdelaziz Beljadid, Abderrahmane Benfanich, Sana Keita, Nour-Eddine Toutlini and Azzeddine Soulaı̈mani.BIO: Yves Bourgault obtained his PhD in mathematics from Laval University in 1996, under the supervision of Professor Michel Fortin. In 1995, he joined the Computational Fluid Dynamics Laboratory of Concordia University, initially as a research associate and then as a research assistant… Read more.

Human behavior and uncertainty quantification in the context of epidemiological models

Zoom: Please email Philipp Kunde for the zoom link.
Dynamical Systems Seminar, Mathematical Biology Seminar, Probability and Data Science Seminar

Speaker: Binod Pant

Human behavior has been attributed as one of the major reasons why models perform poorly when forecasting. The first half of this talk will focus on modeling the interplay between human behavior and disease outbreaks. In a retrospective study, we show that models incorporating human behavior change capture disease trajectories better than equivalent models without behavior change. Further, I will present a study characterizing population-level human behavior change, as inferred through survey-collected behavior data from all 50 US states during the first two years of the COVID-19 pandemic.Identifiability issues, a common problem in mathematical biology, have also been attributed to why models fail to forecast properly and struggle to correctly characterize disease transmission even in retrospective studies. Using model-generated synthetic data where ground truth is known, we investigate the inference of epidemiological quantities of interests when only fitting to detected incidence… Read more.

Analysis of a Coupled Flow–Cantilever System Arising in Piezoelectric Energy Harvesting

STAG 111
Analysis Seminar

Speaker: Maria Deliyianni

This talk is motivated by piezoelectric energy harvesting, where cantilevered beams undergo large deflections and interact with a surrounding flow. We begin with the nonlinear beam equation, which provides the analytic foundation for the coupled model. The first part focuses on the linearized flow–beam dynamics under the Kutta–Joukowski coupling and mixed boundary conditions. Within the semigroup framework, we establish well-posedness for this linear system, capturing the effects of the flow coupling on the beam dynamics. The nonlinear problem, studied through a structurally damped version of the beam, is solved via a fixed-point argument, and solutions to the original system are recovered as damping vanishes. The analysis unites nonlinear beam theory with quasilinear PDE methods and offers a pathway toward more realistic models of cantilever-based fluid–structure interactions relevant to piezoelectric energy harvesting. Read more.

Counting Ordinary and Extraordinary Hyperelliptic Curves over a Finite Field

KEAR 212
Colloquium

Speaker: Jeff Thunder

Given a hyperelliptic curve defined over a finite field, there is a quantity called the a-number attached to the curve. This integer ranges from 0 to the genus and curves with a-number 0 are called "ordinary." For example, elliptic curves have genus 1 and those curves with a-number 1 are the supersingular elliptic curves ("extraordinary"). Enumerating hyperelliptic curves with given genus and/or a-number can be accomplished with more modern computing, and this leads one to conjecture probabilities for curves of given genus to have a particular a-number.In this talk we'll discuss finite fields, function fields, what it means to be a hyperelliptic curve over a finite field, and how one computes the genus and a-number. We'll recall previous work regarding the probabilities above and some methods used to address them along with some data indicating these methods may be lacking. We'll then demonstrate a relatively simple counting method, based on the theory of heights in Diophantine… Read more.

The Thue Equation

Weniger 275
Algebra and Number Theory Seminar

Speaker: Jeff Thunder

Suppose F(X,Y) is a homogeneous polynomial with integer coefficients that is irreducible over the rational numbers and has degree at least 3. Fix an integer m. We will discuss integer solutions x and y to the Thue equation F(x,y)=m. We will go over some history of efforts to understand such solutions along with conjectures both old and new(er). We'll demonstrate a geometric approach which gives some insight into a deep conjecture of Stewart regarding the number of possible solutions. No previous knowledge of Diophantine equations/inequalities will be assumed; the talk should be accessible to anyone with an understanding of undergraduate mathematics. Read more.

Space-Time Finite Element Methods - The Good, the Bad and the Ugly

STAG 112
Applied Mathematics and Computation Seminar

Speaker: Tamas Harvath

Partial differential equations posed on moving domains arise in many applications, such as air turbine modeling, flow past airplane wings, etc. The time-dependent nature of the flow domain poses an additional challenge when devising numerical methods for the discretization of such problems. One alternative when dealing with time-dependent domains is to pose the problem on a space-time domain and apply, for example, a finite element method in both space and time. These space-time methods can easily handle the time-dependent nature of the domain. In this talk, we present a space-time hybridizable discontinuous Galerkin method for the discretization of the incompressible Navier-Stokes equations on moving domains. This discretization is pointwise mass conserving and pressure robust, even on time-dependent domains. Moreover, high order can be achieved both in space and time. Numerical experiments will demonstrate the capabilities of the method. Read more.

Exceptional congruences for eta-quotient newforms

Zoom
Algebra and Number Theory Seminar

Speaker: Swati

In 1973, Swinnerton-Dyer completely classified all congruences for coefficients of normalized eigenforms in weights k ∈ {12, 16, 18, 20, 22, 26} on Γ_0(1) = SL_2(Z) using the theory of modular Galois representations. In this talk, we classify congruences of the Type I and Type II considered by Swinnerton-Dyer for the coefficients of eta-quotient newforms in S_k(N, χ), k ≥ 1 and prove them using theory of filtrations modulo primes. Further, we prove extensions of these congruences modulo prime powers.(Joint with Matthew Boylan, Eddie O’ Sullivan, Jin Xiaolan and Henry Stone) Read more.

Polynomials from random walks: accelerating the non-symmetric power iteration

STAG 112
Applied Mathematics and Computation Seminar

Speaker: Peter Cowal

ABSTRACT: In numerical linear algebra, an iterative method that alternates between applying a matrix and taking linear combinations of the result corresponds to applying a polynomial to a matrix. The action of the polynomial on the eigenvalues of the matrix determines the output of the method. In this talk, we'll present a class of polynomial families based on mean-zero random walks which are closely related to Faber polynomials, with useful boundedness and rapid-growth properties on the complex plane. Additionally, we'll present a momentum-based acceleration scheme for the power iteration that significantly outperforms the power iteration for certain classes of non-symmetric matrices with small spectral gaps. Read more.