Past Seminars- Geometry and Topology

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  • Nick Rozenblyum
    Mon Apr 30, 2018
    4:00 pm
    A classical result of Goldman states that character variety of an oriented surface is a symplectic algebraic variety, and that the Goldman Lie algebra of free loops on the surface acts by Hamiltonian vector fields on the character variety. I will describe a vast generalization of these results, including to higher dimensional manifolds where the...
  • Weiyan Chen
    Tue Apr 17, 2018
    3:00 pm
    It is a classical topic dating back to Maclaurin (1698–1746) to study certain special points on smooth cubic plane curves, such as the 9 inflection points (Maclaurin and Hesse), the 27 sextatic points (Cayley), and the 72 points "of type 9" (Gattazzo). Motivated by these algebro-geometric constructions, we ask the following...
  • Jason Behrstock
    Mon Apr 2, 2018
    4:00 pm
    Hierarchically hyperbolic spaces provide a uniform framework for working with many important examples, including mapping class groups, right angled Artin groups, Teichmuller space, and others. In this talk I'll provide an introduction to studying groups and spaces from this point of view. This discussion will center around...
  • Nir Gadish
    Mon Mar 19, 2018
    4:00 pm
    Hyperplane arrangements are a classical meeting point of topology, combinatorics and representation theory. Generalizing to arrangements of linear subspaces of arbitrary codimension, the theory becomes much more complicated. However, a crucial observation is that many natural sequences of arrangements seem to be defined using a finite amount of...
  • Marc Hoyois
    Mon Mar 12, 2018
    4:00 pm
    The study of vector bundles on algebraic varieties is a classical topic at the intersection of geometry and commutative algebra. In its algebraic form it is the study of finitely generated projective modules over commutative rings. There are many long-standing conjectures and open questions about algebraic vector bundles, such as: is every...
  • Weiwei Wu
    Mon Mar 5, 2018
    4:00 pm
    Seidel's Lagrangian Dehn twist exact sequence has been a cornerstone of the theory of Fukaya categories.  In the last decade, Huybrechts and Thomas discovered a new autoequivalence in the derived cateogry of coherent sheaves using the so-called "projective objects", which are presumably mirrors of Lagrangian projective spaces....
  • Qiongling Li
    Mon Feb 12, 2018
    4:00 pm
    On a complex manifold, a Higgs bundle is a pair containing a holomorphic vector bundle E and a holomorphic End(E)-valued 1-form. In this talk, we focus on nilpotent Higgs bundles, for example, the ones arising from variations of Hodge structures for a deformation family of Kaehler manifolds. We first give an optimal upper bound of the curvature of...