Geometry and Physics RIT

Web site:
Meeting times: Wednesdays, 3:15 - 5:00, MTH 1311. (We probably won't use the whole time slot but have the room reserved for this period.)
Organizers: Jonathan Rosenberg and Hisham Sati


This will be an informal learning seminar on the general theme of Geometry and Physics. We hope that students will give most of the lectures. Topics will include various areas where modern geometry and topology interacts with ideas from theoretical physics. Examples include loop groups and loop spaces and "string topology" and "string structures", gauge theory and geometry of vector bundles and moduli spaces, etc. Since the subject is interdisciplinary, and involves a mixture of physics, geometry, Lie theory, and topology, we assume the participants have some background in one of these topics but not necessarily in all of them. We will pick out some interesting papers to read and discuss.

More Detailed List of Possible Topics

  1. Seiberg-Witten theory
  2. Electric-magnetic duality and Langlands duality
  3. Conformal field theory and moduli spaces
  4. Topological field theory and TQFTs (topological quantum field theories)
  5. Renormalization theory: topics like the renormalization group and the Hopf algebra structure of Connes, Moscovici, and Kreimer
  6. Geometry of loop spaces and string topology

For the fall semester, we decided to start with #1 (with a little of #2 mixed in). After that we may move to #4.

Tentative plan for the fall semester lectures

  1. Introduction to Yang-Mills theory (1-2 lectures, Richard Wentworth)
  2. Introduction to supersymmetry (1-2 lectures, Gokhan Civan, William Donnelly)
  3. Super-Yang-Mills theory
  4. Dirac's EM duality and Montonen-Olive duality (Rong Zhou)
  5. Seiberg-Witten theory (Ben Sibley)
  6. Topological field theories (if time permits)

Some references for the topics above

Schedule, Fall 2010

9/15Organizational meeting
9/22Richard WentworthAn introduction to Yang-Mills
9/29Gokhan CivanIntroduction to supersymmetry
start time 4:00
William DonnellySUSY from a physics perspective
start time 4:00
Hisham SatiSupersymmetric Yang-Mills in flat space-time
start time 4:00
Rong ZhouElectric-magnetic duality
start time 4:00
Rong ZhouElectric-magnetic duality (cont'd) and the Montonen-Olive conjecture
start time 4:00
Hisham Sati N=2 supersymmetry and super-Yang-Mills
back to regular time
of 3:15 for rest of semester
Hisham SatiExtended supersymmetry and the central charge
11/17Jonathan RosenbergSeiberg-Witten theory, part 1
11/24No meeting because of Thanksgiving
12/1Jonathan RosenbergSeiberg-Witten theory, part 2
12/8Ben SibleyWitten's paper on Seiberg-Witten invariants for 4-manifolds

Schedule, Spring 2011

The new topic for the spring semester is topological quantum field theories (TQFTs). This topic is reasonably self-contained, so you ought to be able to follow even if you didn't attend in the fall. Basic references for this topic include:

Suggested order of reading: Start with Atiyah's paper, then Freed's notes. After that we may do Witten's CMP paper and then Segal's 1999 notes, followed by some of the more recent references.

1/26Organizational meeting
2/2 start time 4:00Ben SibleyAtiyah's definition of a TQFT
2/9Gokhan CivanBasic examples following Freed's notes
2/16Gokhan CivanBasic examples following Freed's notes (cont'd): finite groups
2/23Ben SibleyBasic examples following Freed's notes (cont'd): Lie groups
3/2Rong ZhouTQFTs via the BRST symmetry formalism, I
3/9Rong ZhouTQFTs via the BRST symmetry formalism, II
3/16 start time 4:00Jonathan RosenbergA TQFT connected to Ray-Singer torsion (after A. Schwarz)
3/23Spring break, no meeting
3/30Jonathan RosenbergSegal's notes on TQFTs, I: Frobenius algebras
4/6Steve BaladyDefining TQFTs in dimension > 2