Department of Mathematics - UC Santa Barbara

Geometry, Topology, and Physics Seminar, Spring 2018

Part of the NSF/UCSB ‘Research Training Group’ in Topology and Geometry

Organizers: Dave Morrison and Zhenghan Wang.
Meets 4:00 - 5:30 p.m. on selected Fridays in South Hall 6635.

Other Quarters: [ 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 ]

April 6

Dave Morrison (UCSB)

Geometry, supersymmetry, and Seiberg-Witten theory

Abstract: I will explain how geometry and supersymmetry are related to the physics of Seiberg-Witten theory. The topological implications of this physical theory will not be discussed.

Audio; Lecture notes v1, Lecture notes v2.

April 27

Dave Morrison (UCSB)

Limits of K3 metrics

Abstract: In March of 2017, I gave a preliminary discussion of the possible limits of a sequence of Ricci-flat metrics on the K3 manifold. I will now give a more thorough discussion of the problem, including recent work of Hein-Song-Viaclovsky-Zhang.

Audio; Slides.

May 4

No meeting

Everyone is encouraged to attend the conference ``Geometry and Analysis on Manifolds 2018'' instead.

May 11

Matt Brown (UCSB)

More about Seiberg-Witten theory

Abstract: I will continue where Dave left off last time with the solution of Seiberg-Witten theory. The topological implications of the theory will still not be discussed.

Audio; Lecture notes.

May 18

Joint meeting with Differential Geometry seminar: 3:00 p.m.

Jeffrey A. Viaclovsky (UC Irvine)

Nilpotent structures and collapsing Ricci-flat metrics on K3 surfaces

Abstract: I will discuss a new construction of families of Ricci-flat Kahler metrics on K3 surfaces which collapse to an interval, with Tian-Yau and Taub-NUT metrics occurring as bubbles. There is a corresponding singular fibration from the K3 surface to the interval, with regular fibers diffeomorphic to either 3-tori or Heisenberg nilmanifolds. This is joint work with Hans-Joachim Hein, Song Sun, and Ruobing Zhang.