INSTRUCTOR: Sasha Voronov
OFFICE: VinH 324
PHONE: (612) 624-0355
E-MAIL ADDRESS: voronov@umn.edu. You are welcome to use e-mail to send questions to me.
INTERNET: All class announcements and assignments will be posted on the class homepage http://www.math.umn.edu/~voronov/8270/index.html and NOT handed out in class.
OFFICE HOURS: Mon 1:30-2:20, Wed 12:20-1:10, Fri 12:20-1:10, or by appointment.
TEXT: No text covering the material exists or required, but the following texts may be used as supporting reading material:
CONTENT: This is a one-semester course. The course with the same name, Math 8270, Topics in Algebraic Geometry, offered by Professor Messing in Spring 2017, will be totally independent.
This course is devoted to supergeometry, superschemes and supermanifolds, integration on supermanifolds, introduction to string theory, super Riemann surfaces, supermoduli space, Deligne-Mumford compactification, string theoretic measure on moduli and supermoduli spaces, and super Mumford isomorphism.
On the one hand, a superscheme is just a Z/2Z-graded scheme, a Z/2Z-graded commutative generalization of the notion of a scheme, thereby largely covered by Grothendieck's treatment of algebraic geometry. On the other hand, there are certain aspects of the theory, such as integration on manifolds and the very notion of an algebraic curve as a variety of the least positive dimension, whose generalization to supergeometry is nonobvious. The course will focus on such aspects.
Super Riemann surfaces came from string theory as world sheets swept out by propagating superstrings. The supersymmetric extension of string theory was necessary, because string theory led to some divergences, known as anomalies, which disappear in the presence of ghosts (or odd coordinates).
PREREQUISITES: The course will be suitable for graduate students interested in algebra and geometry with applications to string theory. A basic course on Manifolds and Topology and familiarity with the notion of a scheme. However, I will be reminding various facts about classical notions, depending on the background of the audience. No prior knowledge of physics will be required.
GRADING: Since understanding the material will already present certain challenge, no homework or tests will be given. If you make effort to make sure I remember you by the end of the term, you will get an A.
IMPORTANT DATES:
September 7: First class meeting.
November 24-25: Thanksgiving Break.
December 14: Last class meeting.
Page created on 09/08/2016, updated on 09/27/2016 with publication years for references.