Regularization of moduli spaces of pseudholomorphic curves


Instructor: Katrin Wehrheim

Office: Evans 907

Email: wehrheim [at] berkeley . edu

Lectures: Mon/Wed 11:10 - 12:30 in Evans 730

Office Hours: after class and by appointment


This course aims to build a knowledge base on regularization techniques for moduli spaces arising from geometric PDE's (in particular pseudholomorphic curves). Regularization techniques of the type discussed here were first developed in the 1980s as part of the construction of Gromov-Witten invariants (from pseudoholomorphic curves) and Donaldson invariants (from Yang-Mills instantons). They have since seen rapid extensions in the construction of a wealth of invariants for symplectic or contact manifolds as well as low dimensional manifolds, such as various Floer theories, Fukaya's A-infty category, symplectic field theory, and gauge theoretic TQFTs. Due to the speed of the development of these applications, the subtleties of the underlying regularization techniques have not been studied systematically yet.

The goals of this course are to

Topics and their weights will depend on the development of the course discussion, but certainly include


The perfect preparation (and motivation) is to have seen the broad outlines of ``counting'' or ``integrating over'' a moduli space of pseudoholomorphic curves, and have some basic familiarity with the underlying Gromov compactness and Fredholm theory. Lecture notes for a course (MIT 18.156 / Berkeley MATH278 in fall 2013) covering these basics can be found at the Resources tab of Piazza. However, I will aim to make the course as self-contained as possible. Minimal prerequisites are familiarity with the language of manifolds, vector bundles, Banach spaces, metric spaces, singular homology, and the willingness to take black boxes for granted or read up on them.


Lectures can be joined in person on Monday/Wednesday at UC Berkeley (11-12:30 PST in Evans 730) or viewed live via browser/tablet/smartphone/room system using during 2-3:30 EST. (Note: You do need to download a plugin, so please test this well in advance.) With some delay, recordings will be made available on this site and become part of a Program at the Simons Center for Geometry and Physics, which is partially supporting this course.
To join the forum use access code jhol101.


At UC Berkeley, course credit can be obtained by enrolling in MATH276-002, and participating actively and regularly. Graduate students at other institutions, who are interested in gaining course credit, should find a local faculty or staff member who can grant course credit, and have them contact Katrin Wehrheim directly.