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Science and Mathematics

Mathematics Faculty Candidate: Triangulations, mechanisms, and visualizations

January 21, 2020 at 4:00pm5:00pm

Carnegie Library, 122

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Henry Segerman, Ph.D., from Oklahoma State University, is a candidate for a faculty position in the Department of Mathematics, part of the cluster hiring initiative in the BioInspired Institute.

Abstract: I will talk about my research in three related areas: triangulations of three-dimensional manifolds, physically realizable mechanisms, and mathematical visualization.

In triangulations I will focus on veering triangulations, which were introduced by Agol to canonically represent pseudo-Anosov surface bundles. I will describe two projects with Saul Schleimer: building a census of veering triangulations, and providing a converse to an extension of Agol’s work by Agol and Guéritaud. The latter shows that veering triangulations are a perfect combinatorialisation of pseudo-Anosov flows, and with the former is the first step in the combinatorial study of these flows.

One of the goals of my work in visualization is to make abstract mathematical ideas more accessible, by making physical and/or interactive illustrations. I will discuss projects in 3D printing and virtual reality, including simulating the eight Thurston geometries using ray-marching, with Rémi Coulon, Sabetta Matsumoto, and Steve Trettel.

My work in mechanisms grew from adding movement to 3D printed visualizations. My pure mathematics perspective on three-dimensional geometry has led to some novel constructions, including joint work with Sabetta Matsumoto in constructing auxetic linkages and unusual  geared mechanisms.

 

Refreshments at 3:30 in Room 111

This event was published on January 8, 2020.


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