Geometry-Topology Seminar

Organizers: Brian Collier, Christian Zickert
When: Mondays @ 3:15pm
Where: Math 1313

Archives: 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017

  • The Goldman symplectic form on the Hitchin component

    Speaker: Tengren Zhang (California Institute of Technology) - https://sites.google.com/site/tengren85/

    When: Wed, August 30, 2017 - 3:15pm
    Where: Kirwan Hall 1313

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    Abstract: Let S be a closed, orientable, connected surface of genus at least 2. We prove that any ideal triangulation on S determines a symplectic trivialization (with respect to the Goldman symplectic form) of the tangent bundle of the Hitchin component. One can then consider the parallel flows with respect to the flat structure given by this trivialization. We give a geometric description of all such flows in terms of explicit deformations of Frenet curves, and prove that all such flows are Hamiltonian. Applying this to a particular ideal triangulation allows us to find a maximal family of Poisson commuting Hamiltonian flows on the Hitchin component. This generalizes the well-known fact that on Teichmüller space, the twist flows along a pants decomposition of S is a maximal family of Poisson commuting Hamiltonian flows. This is joint work with Zhe Sun and Anna Wienhard.
  • The OPER holonomy map is a holomorphic immersion

    Speaker: Andrew Sanders (University of Heidelberg) - https://www.mathi.uni-heidelberg.de/~asanders/

    When: Wed, September 6, 2017 - 3:15pm
    Where: Kirwan Hall 1311

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    Abstract: TBA
  • Exotic Connected components of the SO(p,q) character variety

    Speaker: Brian Collier (UMD) - http://math.umd.edu/~bcollie2/

    When: Mon, September 18, 2017 - 3:15pm
    Where: Kirwan Hall 3206

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    Abstract: In this talk we will give a complete count of the connected components of the character variety of representations of a closed surface group into SO(p,q). In particular, we will exhibit the existence of "exotic" connected component which are not labeled by a characteristic class of SO(p,q) bundles. Each of these exotic components is parameterized by the space of K^p-twisted SO(1,q-p+1) Higgs bundles with the vector space of holomorphic differentials of degree 2,4,...,2n-2. From this parameterization, the Betti numbers for q=p+1 and q=p+2 can be computed. In the end, we will give evidence that these new connected components consist entirely of geometrically interesting (Anosov) representations.
  • Hitchin systems, Langlands duality, and spin bundles

    Speaker: Richard Wentworth (UMCP) -

    When: Mon, September 25, 2017 - 3:15pm
    Where: Kirwan Hall 3206
  • Finsler metrics of constant curvature

    Speaker: Vladimir Matveev () - http://users.minet.uni-jena.de/~matveev/

    When: Mon, October 2, 2017 - 3:15pm
    Where: Kirwan Hall 1313

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    Abstract: I will mostly speak about Finsler metrics of positive constant flag curvature (I explain what is it) on closed 2-dimensional surfaces. The main result is that the geodesic flow of such a metric is conjugate to that of a Katok metric (recall that Katok metrics is are easy and well-understood examples of two-dimensional Finsler metrics of positive constant flag curvature). In particular, either all geodesics are closed, and at most two of them have length less than the generic one, or all geodesics but two are not closed; in the latter case there exists a Killing vector field. Generalizations for the multidimensional case will be given; in particular I show that in all dimensions the topological entropy vanishes and the geodesic flow is Liouville integrable. I will also show that in all dimensions a Zermelo transformation of every metric of positive constant flag curvature has all geodesics closed. The results are part of an almost finsihed paper coauthored with R. Bryant, P. Foulon, S. Ivanov and W. Ziller.
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    Speaker: Nicolas Tholozan (Ecole Normal Supérieure ) - http://www.math.ens.fr/~tholozan/

    When: Mon, October 9, 2017 - 3:15pm
    Where: Kirwan Hall 1313

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    Abstract: TBA
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    Speaker: Florent Schaffhauser (Universidad de Los Andes) - https://matematicas.uniandes.edu.co/~florent/

    When: Mon, October 16, 2017 - 3:15pm
    Where: Kirwan Hall 1313

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    Abstract: TBA
  • Twisted K-homology of compact Lie groups

    Speaker: Jonathan Rosenberg (UMD) - https://www.math.umd.edu/~jmr/

    When: Mon, October 30, 2017 - 3:15pm
    Where: Kirwan Hall 3206

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    Abstract: TBA
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    Speaker: Andrew Zimmer (William and Mary ) - http://www.math.wm.edu/~amzimmer/

    When: Mon, November 6, 2017 - 3:15pm
    Where: Kirwan Hall 3206

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    Abstract: TBA
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    Speaker: Zeno Huang (City University of New York, CSI and Graduate Center) - http://www.math.csi.cuny.edu/~huang/

    When: Mon, November 20, 2017 - 3:15pm
    Where: Kirwan Hall 1313

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    Abstract: TBA
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    Speaker: Anton Lukyanenko (George Mason) - http://lukyanenko.net/

    When: Mon, December 11, 2017 - 3:15pm
    Where: Kirwan Hall 3206

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    Abstract: Tba