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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:

Some Lie (super)algebras generated by reflections

TBD
Algebra and Number Theory Seminar

Speaker: Chris Drupieski

In 2007, motivated by questions from the representation theory of the braid group, Ivan Marin computed the structure of the Lie algebra generated by the transpositions in the group algebra of the symmetric group. In this talk I’ll describe Marin’s results and report on joint work with Jonathan Kujawa investigating analogous questions for arbitrary finite reflection groups, as well as results on the Lie superalgebras generated by the same sets of elements. Read more.

Comparison of Parameter Recovery Methods from Stochastic and Continuous Data Assimilation

STAG 110
Applied Mathematics and Computation Seminar

Speaker: Elizabeth Carlson

ABSTRACT: 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. Data assimilation is the study of different methods used to adaptively correct models towards the data. These methods can be modified to solve the inverse problem of finding incorrect parameters. Parameter recovery is a popular research area, the methods for which, to the best of the speaker’s knowledge, almost exclusively use data uncertainty as a driving factor in finding such parameters. A continuous data assimilation method, known as the Azouani-Olson-Titi (AOT) or Continuous Data Assimilation (CDA) algorithm, introduced a linear feedback control term to dissipative systems, giving a simple and rigorous deterministic method by which to understand the underpinnings of more complex data assimilation algorithms used in the geosciences for, e.g… Read more.

A complete conjugacy invariant for generalized pseudo-Anosov homeomorphisms via symbolic dynamics and combinatorics

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

Speaker: Inti Cruz

In this seminar we review the notion of Markov partitions for generalized pseudo-Anosov homeomorphisms (\gpA) and show how, through the associated incidence matrix, one can construct a subshift of finite type (SFT) that is semiconjugate to the corresponding pseudo-Anosov homeomorphism.We then introduce geometric Markov partitions and the notion of geometric type, a combinatorial object that extends the information contained in the incidence matrix. We discuss how this geometric type allows for a refined combinatorial analysis of the associated SFT, leading to our main result: two \gp-Anosov homeomorphisms admit geometric partitions of the same geometric type if and only if they are topologically conjugate via an orientation-preserving homeomorphism. Read more.

Structure-Preserving Algorithms for Hyperbolic Balance Laws and Related PDE-Based Models

STAG 210 (note unusual day/location)
Applied Mathematics and Computation Seminar

Speaker: Yekaterina Epshteyn

ABSTRACT: Hyperbolic conservation/balance laws and related PDE-based models are essential mathematical apparatus for modeling a variety of complex physical phenomena, including but not limited to wave propagation, fluid flow, biological and materials science phenomena. Over the past few decades there has been enormous progress in designing stable, robust, structure-preserving numerical schemes (such as positivity-preserving and/or well-balanced schemes) that have enabled high-fidelity simulation of phenomena described by nonlinear hyperbolic PDEs. The main goal of our recent work is to extend these capabilities to systems with a stochastic component, which are relevant models in practical real-world situations since precise knowledge of an environment or operating conditions is frequently absent in such scenarios, and naturally results in models where randomness is used to describe the ignorance.In this talk, we will discuss progress in the design of structure-preserving numerical… Read more.

Intransitive Symmetry Groups of 2-Plane Distributions and Darboux Integrable f-Gordon Equations

STAG 161
Geometry and Topology Seminar

Speaker: Brandon Ashley

Abstract: We present a new, (transformation) group-theoretic approach to the classification of a class of Darboux integrable partial differential equations, commonly referred to as f-Gordon equations, generalized wave maps equations, or equations of Liouville type.The main result of our approach asserts that a complete list of all f-Gordon equations which are Darboux integrable at order three can be determined from a complete list of all (real) 2-plane distributions in five dimensions which admit intransitive, 5-dimensional symmetry groups. Through this correspondence, we have uncovered a new class of f-Gordon equations, the addition of which completes the classification of f-Gordon equations Darboux integrable at order three. This talk is based upon joint work with Ian M. Anderson, Utah State University. Read more.

Evolution on graphs and heat- and mass-gradient driven phase transitions

STAG 110
Applied Mathematics and Computation Seminar

Speaker: Malgorzata Peszynska

We describe the basic modeling, analysis and approximation tools for phase transition models which use monotone multi-valued graphs. The PDE models with these feature free boundaries and lack of smoothness. We connect these to real-life applications of solid-liquid and soild-vapor p[hase transitions which are driven by, respectively, temperature and concentration gradients. We also discuss models where these are coupled. This is based on joint work with students and collaborators who will be named in the talk. Read more.