Geometry, Topology, and Physics Seminar, UCSB Mathematics Department

Geometry, Topology, and Physics Seminar, Spring 2007

Organizers: Sergei Gukov and Dave Morrison
Meets 3:30 - 5:00 p.m. Fridays in South Hall 6635.

Various topics relating geometry, topology, and physics.

Other Quarters: [ Winter, 2012; Fall, 2011; Spring, 2011; Winter, 2011; Fall, 2010; Spring, 2010; Winter, 2010; Fall, 2009; Spring, 2009; Winter, 2009; Fall, 2008; Spring, 2008; Winter, 2008; Fall, 2007; Spring, 2007; Winter, 2007; Fall, 2006 ]

Apr. 6	Dave Morrison (UCSB) Organizational meeting.
Apr. 13	Sergei Gukov (UCSB) Perturbative gauge theory and arithmetic topology Audio [ mp3, wma ]; Lecture notes.
Apr. 20	Xiaodong Cao (MSRI and Cornell Univeristy) Cross Curvature Flow on Locally Homogenous Three-manifolds (joint meeting with Differential Geometry Seminar) Recently, Chow and Hamilton introduced the cross curvature flow on three-manifolds, which is a weakly parabolic partial differential equation system when the sectional curvatures have a definite sign. They also conjectured the long time existence and convergence of cross curvature flow on closed three-manifolds with negative sectional curvature. In this talk, we will study the cross curvature flow on locally homogenous three-manifolds. We will describe the long time behavior of the cross curvature flow for each case. This is a joint work with Yilong Ni and Laurent Saloff-Coste. Audio [ mp3, wma ]; Lecture notes.
Apr. 27	No meeting
May 4	No meeting
May 11	Mike Anderson (SUNY, Stony Brook) Is Anti deSitter spacetime dynamically stable? MEETS AT 4 PM THIS WEEK. A discussion of the wide open question: is AdS spacetime dynamically stable? This is basically a hyperbolic PDE problem, a bit analogous to Christdoulou-Klainerman theorem on stability of Minkowski spacetime. Audio [ mp3, wma ]; Lecture notes.
May 18	No meeting.
May 21	John Lott (MSRI and University of Michigan) Dimensional reduction and long-time behavior of Ricci flow South Hall 4607, 3:30 p.m. (Differential Geometry Seminar; note unusual day and location) Lecture notes.
May 25	Paolo Cascini (UCSB) Kähler-Ricci flow H. D. Cao introduced the Kähler-Ricci flow for canonical metrics on manifolds with definite first Chern class. In particular he obtained a new proof of Calabi's conjecture on the existence of Kähler-Einstein metrics on manifolds with c₁ < 0. More in general, the Kähler-Ricci flow is expected to provide a deeper understanding of the geometry of the underlying manifold. We will survey on some of its property and applications. Audio, part 1 [ mp3, wma ], audio, part 2 [ mp3, wma ]; Lecture notes.
June 1	James M^cKernan (UCSB) The Sarkisov program MEETS AT 4 PM THIS WEEK. The conjectural output of the minimal model program is either a minimal model or a Mori fibre space. Unfortunately the output in neither case is unique. Kawamata has recently shown that any two minimal models are connected by a sequence of flops. The Sarkisov program aims to factorise any birational map between two Mori fibre spaces into a sequence of elementary links. In the case of surfaces, an elementary transformation of P¹-bundles is an example of such a link, and the Sarkisov program provides a natural framework to prove that the birational automorphism group of P² is generated by a Cremona transformation and PGL(3). We describe recent work with Christopher Hacon where we extend the Sarkisov program to all dimensions.