Department of Mathematics - UC Santa Barbara

Geometry, Topology, and Physics Seminar, Winter 2007

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

For the first part of the winter quarter, we will continue our study of Ricci flow on three-manifolds, with the goal of understanding the basics of Thurston's geometrization program, Hamilton's strategy for completing that program using Ricci flow, Perelman's technical and conceptual advances in Ricci flow which allow the program to be completed, and relations to physics including the analogy with the renormalization flow in two-dimensional quantum field theory.

Other Quarters: [ Fall, 2021; Winter, 2020; Fall, 2019; Spring, 2018; Winter, 2018; Fall, 2017; Spring, 2017; Wnter, 2017; Fall, 2016; Spring, 2016; Winter, 2016; Fall, 2015; Spring, 2015; Winter, 2014; Fall, 2013; Fall, 2012; Fall, 2011; Winter, 2011; Spring, 2010; Winter, 2010; Fall, 2009; Spring, 2009; Winter, 2009; Fall, 2008; Spring, 2008; Winter, 2008; Fall, 2007; Spring, 2007; Winter, 2007; Fall, 2006 ]

Jan. 12, 19, and 26

No meeting on these dates.

Feb. 2

Dave Morrison (UCSB)

Ricci Flow and Renormalization, II

25 years ago, Friedan calculated the one-loop renormalization of a two-dimensional sigma-model with target space an arbitrary Riemannian manifold and found that the metric should evolve by Ricci flow. We will explain this result and its connections to the recent work of Perelman on Ricci flow. Since the first lecture of this series, the connection between Perelman's work and renormalization has been extended by Tseytlin (, and we will discuss this new work as well.

Audio (incomplete: sorry!) [ mp3, wma ]; Lecture notes version 1; Lecture notes version 2.

Feb. 9

No meeting this week

Feb. 16

Dave Morrison (UCSB)

Ricci Flow and Membrane Theory

Feb. 23

No meeting this week

Mar. 2

Shing-Tung Yau (Harvard University)

Complex Manifolds with Torsion

Audio [ mp3, wma ]; Slides.

Mar. 9

Dave Morrison (UCSB)

Regularization and Renormalization of Sigma Models

In a lecture in December, I briefly discussed the dimensional regularization of sigma models, which is the technical tool underlying the calculation of Ricci flow as the one-loop approximation to renormalization flow on the space of Riemannian metrics on a manifold. In this week's lecture will I give a detailed presentation of dimensional regularization and the renormalization calculations.

Audio [ mp3, wma ]; Lecture notes.

Mar. 16

No meeting.