This Week in Mathematics


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Beyond Apr 08, 2023

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Monday April 10, 2023

Mathematics Colloquium [url]
Topological Insulators in Electromagnetic Systems
- Justin Cole, University of Colorado
Time: 3:05pm Room: 101
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Abstract/Desc: This talk will introduce the field of topological insulators in electromagnetic systems. Seminal results will be reviewed. Key concepts such as gauge invariant topological invariants (Chern number), topological protection, and the bulk-edge correspondence will be highlighted in a prototypical discrete system known as the Haldane model. Two different realizations of Chern insulators in electromagnetic systems will be examined. Tight-binding approximations yield tractable dynamical systems that capture the essential behavior. From here, spectral reductions can yield effective PDE models such as the Dirac equation. If time allows, nonlinear effects such as solitons will be discussed.

Thursday April 13, 2023

Financial Mathematics Seminar [url]
Bregman-Wasserstein divergence
- Leonard Wong, University of Toronto
Time: 3:05pm Room: Zoom
Abstract/Desc: Consider the Monge-Kantorovich optimal transport problem where the cost function is given by a Bregman divergence. The associated transport cost, termed the Bregman-Wasserstein divergence here, presents a natural asymmetric extension of the (squared) 2-Wasserstein metric and has recently found applications in statistics and machine learning. On the other hand, Bregman divergence is a fundamental concept in information geometry and induces a dually flat geometry on the underlying manifold. Using the Bregman-Wasserstein divergence, we lift this dualistic geometry to the space of probability measures, yielding an extension of Otto’s weak Riemannian structure of the Wasserstein space to statistical manifolds. We do this by generalizing Lott’s formal geometric computations for the Wasserstein space. In particular, we define generalized displacement interpolations which are compatible with the Bregman geometry, and construct conjugate primal and dual connections on the space of distributions. We also discuss some potential applications. Joint work with Cale Rankin.

Friday April 14, 2023

Mathematics Colloquium [url]
Math Honors Day
- Monica Hurdal, FSU
Time: 3:05pm Room: 101
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Abstract/Desc: Faculty, staff, and students are invited to join us as we celebrate and award our graduate and undergraduate students for their achievements and excellence in academics, teaching, and service.

Thursday April 20, 2023

Financial Mathematics Seminar [url]

- Liming Feng, University of Illinois at Urbana-Champaign
Time: 3:05pm Room: TBA
Abstract/Desc: TBA

Friday April 21, 2023

Mathematics Colloquium [url]
Swimming, buckling, mixing, breaking: adventures with helices at the microscale
- Lisa Fauci, Tulane University
Time: 3:05pm Room: LOV 101
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Abstract/Desc: The motion of passive or actuated elastic filaments in a fluid environment is a common element in many biological and engineered systems. Examples at the microscale include bacterial flagella propelling a cell body and engineered helical nanopropellers designed to penetrate mucosal tissue for drug delivery. Complex fluid environments, such as polymeric networks or confining geometries, can have dramatic effects upon the dynamics of filaments, whether rigid or flexible. In this talk we will present mathematical models of a few intriguing systems: actin-like fibers in straining flows that spontaneously buckle into helices, flexible helical filaments whose swimming performance improve when confined to a narrow tube, and rigid helical filaments that penetrate a polymeric network with the ability to remodel the material properties of the network as it moves through it.

Thursday April 27, 2023

Financial Mathematics Seminar [url]

- Igor Cialenco, Illinois Institute of Technology
Time: 3:05pm Room: zoom
Abstract/Desc: TBA

Friday April 28, 2023

Mathematics Colloquium [url]
Mathematics of malaria transmission dynamics: the renewed quest for eradication
- Abba Gumel, Arizona State University
Time: 3:05pm Room: 101
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Abstract/Desc: Malaria, a deadly disease caused by protozoan Plasmodium parasites, is spread between humans via the bite of infected adult female Anopheles mosquitoes. Over 2.5 billion people live in geographies whose local epidemiology permits transmission of P. falciparum, responsible for most of the life-threatening forms of malaria. The widescale and heavy use of insecticide-based interventions, notably long-lasting insecticidal nets and indoor residual spraying), during the period 2000-2015, resulted in a dramatic reduction in malaria incidence and burden in endemic areas, prompting a renewed quest for malaria eradication. Numerous factors, such as Anopheles resistance to all currently-available insecticides and anthropogenic climate change, potentially pose important challenges to the eradication efforts. In this talk, I will discuss a genetic-epidemiology framework for assessing the impact of insecticide resistance on malaria. Specifically, questions on whether eradication can be achieved using existing insecticide-based control resources will be addressed. There may be a brief discussion on the utility of some of the gene drive-based biological interventions being proposed as a plausible alternative pathway for achieving the laudable malaria eradication goal.

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Department of Mathematics

This Week in Mathematics