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Department of Mathematics

Upcoming Seminars

Memorial Union on sunny day

Join us for an upcoming seminar featuring mathematics faculty and invited speakers on one of our seven research topics.

You may also see upcoming seminars by topic:

Exploring the Brownian loop measure

STAG 112
Dynamical Systems Seminar, Mathematical Biology Seminar, Probability and Data Science Seminar

Speaker: Greg Lawler

I will review the Brownian loop measure as a limit of random walk loop measures, its relation to Schramm-Loewner evolutions, and discuss some decompositions into boundary bubbles. We give a formulation of the measure on the unit disk in terms of measure-driven Loewner evolutions and something we call “Brownian bubble tea”. This latter work is part of joint work with Frederik Viklund, Yilin Wang, and Catherine Wolfram. Read more.

Heegaard Floer homology, Dehn surgery and (2+1)-dimensional TQFT

Batcheller Hall 250
Geometry and Topology Seminar

Speaker: Ian Zemke

Abstract: Heegaard Floer homology is an invariant for 3-manifolds, as well as knots and links in 3-manifolds. A classical theorem of Lickorish-Wallace states that every 3-manifold can be constructed by Dehn surgery on a link in S^3. Heegaard Floer homology admits useful Dehn surgery formulas, which have played an important role in many applications of the theory. In this talk we will describe some interesting algebraic perspectives on these formulas, as well as some applications of these perspectives. Read more.

Heap Birkhoff polytopes

Zoom
Algebra and Number Theory Seminar

Speaker: Emily Gunawan

Abstract: For each orientation c of a type A Dynkin quiver, we define a c-Birkhoff polytope Birk(H) and show that it is integrally equivalent to the order polytope for poset H, the heap of the c-sorting word of the longest permutation. A consequence of this result is that the volume of the c-Birkhoff polytope is the number of the longest chains in the type A c-Cambrian lattice. We will also discuss current work in type B and a generalization of our result to other Birkhoff subpolytopes Birk(H) corresponding to heaps H of other reduced words of an element in the symmetric group. Read more.

Heterogeneous domain decomposition approach for coupled soil-snow model

STAG 110
Applied Mathematics and Computation Seminar

Speaker: Praveeni Mathangadeera

ABSTRACT: We present a heterogeneous domain decomposition approach for solving nonlinear heat conduction for a snow-soil model in Arctic environments. The snow and soil domains are treated as distinct physical domains, each described by a separate nonlinear heat equation with distinct nonlinear laws for material properties. These two models are coupled across their interface by ensuring the continuity of temperature and the conservation of heat flux. The coupled system is solved iteratively with a Dirichlet to Neumann approach, where the snow and soil models are solved independently, updating the interface conditions within a Richardson scheme until convergence is achieved. We show the basics of analysis, compare with Schur complement calculations, and with the monolithic approach. Read more.

The Arithmetic of Laurent Coefficients of Meromorphic Modular Forms

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Algebra and Number Theory Seminar

Speaker: Eleanor McSpirit

The arithmetic study of Taylor coefficients of modular forms at CM points has its roots in the classical theory of complex multiplication, beginning with the algebraicity the values of the j-function at CM points. The study of Taylor expansions of modular forms at CM points has since developed through work of Shimura on nearly holomorphic modular forms and became more explicit in later work of e.g. Rodriguez-Villegas and Zagier. Recently, Bogo, Li, and Schwagenscheidt studied Laurent expansions of meromorphic modular forms with poles at CM points and observed arithmetic patterns in examples. In this talk, I will discuss ongoing joint work with Rolen aimed at explaining and characterizing the arithmetic behavior of these Laurent coefficients. Read more.