Past Geometry and Analysis Seminar

19 May 2014
14:15
to
15:30
Julius Ross (Cambridge)
Abstract
<p><span>&nbsp;</span><span>I will discuss joint work with Daniel Greb and Matei Toma in which we introduce a notion of Gieseker-stability that depends on several polarisations. &nbsp;We use this to study the change in the moduli space of Giesker semistable sheaves on manifolds giving new results in dimensions at least three, and to study the notion of Gieseker-semistability for sheaves taken with respect to an irrational Kahler class.</span></p>
  • Geometry and Analysis Seminar
5 May 2014
14:15
Motohico Mulase (UC Davis)
Abstract
<p>I will present a formula that relates a Higgs bundle on an algebraic curve and Gromov-Witten invariants. I will start with the simplest example, which is a rank 2 bundle over the projective line with a meromorphic Higgs field. The corresponding quantum curve is the Airy differential equation, and the Gromov-Witten invariants are the intersection numbers on the moduli space of pointed stable curves. The formula connecting them is exactly the path that Airy took, i.e., from wave mechanics to geometric optics, or what we call the WKB method, after the birth of quantum mechanics. In general, we start with a Higgs bundle. Then we apply a generalization of the topological recursion, originally found by physicists Eynard and Orantin in matrix models, to this context. In this way we construct a quantization of the spectral curve of the Higgs bundle.&nbsp;</p>
  • Geometry and Analysis Seminar
28 April 2014
14:15
to
15:30
David Witt Nystrom (Cambridge)
Abstract
<p><span>By solving the Homogeneous Monge-Ampere equation on the deformation to the normal cone of a complex submanifold of a Kahler manifold, we get a canonical tubular neighbourhood adapted to both the holomorphic and the symplectic structure. If time permits I will describe an application, namely an optimal regularity result for certain naturally defined plurisubharmonic envelopes.</span></p>
  • Geometry and Analysis Seminar

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