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Geometry and Topology Seminar

We meet Thursdays at 2:50–3:50 pm in WH-100E followed by refreshments served from 4:00–4:25 pm in WH-102. This semester's organizer is Jonathan Williams.

Some seminar speakers will also give a colloquium talk at 4:30 pm on the same day as the seminar talk. This seminar is partly funded as one of Dean's Speaker Series in Harpur College (College of Arts and Sciences) at Binghamton University.

The seminar has an announcement mailing list open to all. There is also a Google calendar with the seminar schedule (also in iCal).

Spring 2019

  • March 7
    Speaker: Yash Lodha (Ecole Polytechnique federale de Lausanne)
    Title: Finitely generated simple left orderable groups, commutator width and orderable monsters

    Abstract: In 1980 Rhemtulla asked whether there exist finitely generated simple left orderable groups. In joint work with Hyde, we construct continuum many such examples, thereby resolving this question. In recent joint work with Hyde, Navas, and Rivas, we demonstrate that among these examples are also so called ``left orderable monsters”. This means that all their actions on the real line are of a certain desirable dynamical type. This resolves a question from Navas's 2018 ICM proceedings article concerning the existence of such groups.

  • March 14
    Speaker: Mayank Goswami (Queens College, CUNY)
    Title: Computing Extremal Quasiconformal Mappings

    Abstract: By the Riemann mapping theorem, one can bijectively map the interior of an n-gon P to that of another n-gon Q conformally (i.e., in an angle preserving manner). However, when this map is extended to the boundary it need not necessarily map the vertices of P to those of Q. For many applications it is important to find the “best” vertex-preserving mapping between two polygons, i.e., one that minimizes the maximum angle distortion (the so-called dilatation) over all points in P. Teichmuller (1940) proved the existence and uniqueness of such maps, which are called extremal quasiconformal maps, or Teichmuller maps. There are many efficient ways to compute or approximate conformal maps, and a result by Bishop computes a (1+ϵ)-approximation of the Riemann map in linear time. However, there is currently no such algorithm for extremal quasiconformal maps (which generalize conformal maps), and only heuristics have been studied so far.

    We solve the open problem of finding a finite time procedure for approximating Teichmuller maps in the continuous setting. Our construction is via an iterative procedure that is proven to converge quickly (in O(poly(1/ϵ)) iterations) to a (1+ϵ)-approximation of the Teichmuller map, and in the limit to the exact Teichmuller map. Furthermore, every step of the iteration involves convex optimization and solving differential equations, two operations which may be solved in polynomial time in a discrete implementation. Our method uses a reduction of the polygon mapping problem to the punctured sphere problem, thus solving a more general problem. Building upon our results in the continuous setting, we give a discrete algorithm for computing Teichmuller maps.

  • March 21 - No seminar (Spring break)
  • March 28
    Speaker: TBA (Institution)
    Title: TBA

    Abstract: TBA

  • April 4 - Peter Hilton Memorial Lecture
    Special time and place: LH 9, 3pm
    Speaker: Shmuel Weinberger (University of Chicago)
    Title: How hard is algebraic topology? Between the constructive and the non.

    Abstract: In algebraic topology one studies geometric problems and problems of constructing and deforming highly nonlinear functions by means of algebra. If one knows that two maps are homotopic (i.e. can be deformed to one another) because a certain calculation says they both lie in the trivial group, then what has one learned? (A striking example of this is Smale's turning the sphere inside out, which now can be seen after much highly nontrivial effort, on youtube.) The question I shall discuss is how hard is it to understand what the algebraic topologists tell us.

  • April 11
    Speaker: Matt Zaremsky (Albany)
    Title: Bestvina-Brady Morse theory on Vietoris-Rips complexes

    Abstract: Discrete Morse theory is a powerful tool for leveraging “local” topological information about a cell complex to make “global” topological conclusions. One prominent incarnation is the version developed by Bestvina and Brady, which has proven invaluable in the study of topological finiteness properties of groups. In this talk I will discuss a generalization of Bestvina-Brady Morse theory that is tailor-made for analyzing Vietoris-Rips complexes of certain metric spaces. I will also discuss some applications to topological data analysis and geometric group theory.

  • April 18
    Speaker: Elizabeth Field (UIUC)
    Title: TBA

    Abstract: TBA

  • April 25
    Speaker: Hyunki Min (Georgia Tech)
    Title: TBA

    Abstract: TBA

  • May 2
    Speaker: Kate Ponto (Institution)
    Title: TBA

    Abstract: TBA

  • May 9
    Speaker: Jacob Russell-Madonia (CUNY)
    Title: TBA

    Abstract: TBA

seminars/topsem.txt · Last modified: 2019/03/14 11:00 by sapir