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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

Torsion and exceptional units

Online
Algebra and Number Theory Seminar

Speaker: Dino Lorenzini

Associated with an elliptic curve E/K over a number field K is a finite set of integers greater than 1 called the local Tamagawa numbers of E/K. The ratio (product of the Tamagawa numbers)/|Torsion in E(K)| appears in the conjectural leading term of the L-function of E in the Birch and Swinnerton-Dyer conjecture, and we are interested in understanding whether there are cancellations in this ratio when E(K) has a non-trivial torsion subgroup. When N is prime, let us call N-special an elliptic curve E/K with a K-rational torsion point of order N and such that N does not divide the product of the Tamagawa numbers. We will show that the existence of an N-special elliptic curve E/K is intimately linked to the existence of exceptional units in the ring of integers of K. When N > 2d+1, we suggest that there exist only finitely fields K/Q of degree d having (finitely many) N-special elliptic curves E/K. The list of known N-special elliptic curves is surprisingly short when d is at most 7. Read more.

Reduced Floating-Point Precision Simulation of Thermal Radiative Transfer

Applied Mathematics and Computation Seminar

Speaker: Simon Butson

ABSTRACT:The re-emergence of reduced floating-point precision computer architectures has provided greater efficiencies in areas like AI model training. However, scientific computing applications where both accuracy and precision are critical have proven resistant to similar reduced-precision improvements. In this talk, we will review the implementation of a reduced-precision thermal radiative transfer code using the Implicit Monte Carlo method. Several techniques falling under the categories of arithmetic manipulations and scaling methods will be discussed for their ability to enable accurate reduced-precision calculations. Arithmetic manipulations include things such as alternate summation algorithms and automatic order of operations re-arranging, while scaling methods include both dynamic and static re-scaling of variables as well as the use of multiple energy scales. Half (16-bit) and Double (64-bit) precision results for various thermal radiation benchmark problems will be… Read more.

On the classification of generalized pseudo-Anosov homeomorphisms

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

Speaker: Inti Cruz

The classification of generalized pseudo-Anosov homeomorphisms up to topological conjugacy is a central problem in the dynamics and topology of surfaces, with a long history and a variety of approaches developed by A. Zhirov, L. Mosher, M. Bestvina, M. Handel, J. Los, among others. In this talk, we will present a brief historical overview of the problem and describe an alternative approach, initiated by C. Bonatti, R. Langevin, and E. Jeandenans, based on the use of geometric Markov partitions and their geometric types.In this context, we will introduce the notion of classification and the different stages involved in this process. We will conclude by showing that the geometric type is a complete invariant for topological conjugacy of generalized pseudo-Anosov homeomorphisms, which allows for their complete classification. Read more.

Interpolating Classical Schur Algebras

Strand Agricultural (Stag) Hall 212
Algebra and Number Theory Seminar

Speaker: Addison Day

Classical Schur algebras are a family of finite-dimensional algebras discovered by Issai Schur in 1901. They are intimately related to general linear and symmetric groups, and possess combinatorial structure enabling one to concretely study their representation theory. In this talk we will discuss the construction and representation theory of a new family of algebras which in a certain sense interpolate between the classical Schur algebras. Read more.

Almost Non-negative Curvature and Almost Maximal Symmetry Rank in 5 Dimensions

STAG 162
Geometry and Topology Seminar

Speaker: Samuel Bartel

Abstract:The classification of manifolds with a lower sectional curvature bound is an open and difficult problem. The symmetry program seeks to simplify the problem by additionally assuming some "large" amount of symmetries, then gradually reducing these assumptions. Along these lines, this talk discusses a classification of almost non-negatively curved, simply connected, closed 5-manifolds which admit an isometric and effective $T^2$-action. This is joint work with John Harvey and Catherine Searle. Read more.

Fracture-controlled Organization of Mixing and Reaction Hotspots in Porous Media

Applied Mathematics and Computation Seminar

Speaker: Lazaro Perez

Abstract:The talk will include a tutorial on modeling reactive transport. Fractures are ubiquitous features in porous media and exert a strong control on subsurface flow, mixing, and reactive transport by introducing preferential pathways and strong velocity contrasts that fundamentally reorganize how fluids spread, mix, and react. Despite their recognized importance, the mechanisms by which fracture connectivity controls the spatial localization of reactions and the emergence of reaction hotspots at the pore scale remain incompletely understood.Here, we investigate how increasing fracture connectivity reorganizes pore-scale flow, mixing and reaction dynamics using direct numerical simulations of flow coupled with reactive random walk particle tracking. We consider a bimolecular irreversible reaction occurring during the displacement of one reactant by another in two-dimensional heterogeneous porous media with progressively developed fracture networks. Reaction localization is… Read more.