Department of Mathematics - UC Santa Barbara

Geometry, Topology, and Physics Seminar, Spring 2010

Organizers: Andreas Malmendier and Dave Morrison.
Meets 4:00 - 5:30 p.m. Fridays in South Hall 6635.

This quarter, due to the KITP workshop String Theory at the LHC and in the Early Universe, this seminar will only meet occasionally between 03/29/10 and 05/14/10. Watch this space (or the email announcements) for information about upcoming seminars.

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 ]

Apr. 30

David Morrison (UCSB)

A Mathematical Introduction to F-theory

Abstract: "F-theory" is a construction in string theory based on elliptic fibrations in algebraic geometry. The study of F-theory over the past 14 years has raised various new questions in algebraic geometry, not all of which have been completely resolved. A recent resurgence of interest in F-theory among string theorists has renewed the interest in some of these questions.

In this week's lecture, I will introduce this topic in terms intended for both mathematicians and physicists. In subsequent weeks, we will learn about various more specialized questions in mathematical F-theory.

Audio [ mp3, wma ]; Lecture notes.

May 14

David Morrison (UCSB)

A Mathematical Introduction to F-theory, II

Abstract: In the first lecture, I explained (among other things) how Kodaira's theory of singular fibers in elliptic pencils can be used to assign a reductive group to every elliptic fibration (which is the gauge group in the corresponding F-theory model).

In this lecture, the focus will be on assigning a representation of that group to the fibration (which represents the massless matter in the corresponding F-theory model). Along the way, we will meet anomalies in 6-dimensional physical theories and explain what they mean for the elliptic fibration.

Audio [ mp3,wma ]; Lecture notes.

May 21

Sakura Schafer-Nameki (KITP)

An Introduction to F(uzz) Theory

Abstract: I will give an overview of the recent paper Evidence for F(uzz) Theory by Heckman and Verlinde, which argues that F-theory in the decoupling limit MPl → ∞ is described by a Fuzz-theory. The theory of 7-branes wrapping non-commutative four-cycles is developed and phenomenological implications of this setup are analyzed.

Audio [ mp3,wma ]; Lecture notes.

May 28

David Morrison (UCSB)

Contractible Divisors in F-theory

Abstract: Many of the recent applications of F-theory to building explicit models for 4-dimensional physics have been constructed using neighborhoods of contractible divisors as the base of the associated elliptic fibration. We will give an introduction to the mathematics and physics of contractible divisors on the bases of elliptic fibrations, starting with elliptic threefolds (which have an application to 6-dimesional physics) and then proceeding to elliptic fourfolds (which have an application to 4-dimensional physics).

Audio [ mp3,wma ]; Lecture notes.