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
3 March 2014
14:15
Giuseppe Tinaglia
Abstract
In this talk I will discuss results on the geometry of constant mean curvature (H\neq 0) disks embedded in R^3. Among other things I will prove radius and curvature estimates for such disks. It then follows from the radius estimate that the only complete, simply connected surface embedded in R^3 with constant mean curvature is the round sphere. This is joint work with Bill Meeks.
  • Geometry and Analysis Seminar
17 February 2014
14:15
Goncalo Oliveira
Abstract
The Monopole (Bogomolnyi) equations are Geometric PDEs in 3 dimensions. In this talk I shall introduce a generalization of the monopole equations to both Calabi Yau and G2 manifolds. I will motivate the possible relations of conjectural enumerative theories arising from "counting" monopoles and calibrated cycles of codimension 3. Then, I plan to state the existence of solutions and sketch how these examples are constructed.
  • Geometry and Analysis Seminar

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