Superstring Theory and Related Mathematics

- Jim
Gates, Physics Department.

email`gatess@wam.umd.edu`, phone 301-405-6025 - Jonathan Rosenberg, Mathematics Department.

email`jmr@math.umd.edu`, phone 301-405-5166

The topics discussed will be interdisciplinary, and involve significant interaction between mathematics and physics. In fact, this is probably the field in which there is greatest interaction between mathematicians and physicists. Relevant topics include supersymmetry, conformal, complex, and algebraic geometry, mirror symmetry, topology, and index theory. For the general philosophy of RITs, see here.

As agreed at the organizational meeting on September 11, we will begin with five introductory lectures on topics that are of interest to many of the participants. These will be at a very general level, aimed at non-experts. After that, we may have groups report on some of these areas in greater depth.

Date | Speaker |
Topic |

Sept. 18 | Jim Gates, PHYS | Introduction to supersymmetry |

Sept. 25 | Jonathan Rosenberg, MATH | The mathematical structure of string dualities |

Oct. 2 | No meeting because of Yom Kippur | |

Oct. 9 | Dan Chapman, PHYS, Stefan Mendez-Diez, AMSC, and Isaac Chappell, PHYS | Introduction to conformal field theory |

Oct. 16 | Willie Merrell, PHYS | The Virasoro algebra and its connection with conformal field theory |

Oct. 23 | Ashwin Pande, MATH | Introduction to noncommutative geometry |

Oct. 30 | Greg Landweber, University of Oregon | The mathematics of off-shell supersymmetry |

Nov. 6 | Jim Gates, PHYS | Topological solitons |

Nov. 13 | Calder Daenzer, University of Pennsylvania | What are gerbes and why are they useful in physics? |

Nov. 20 | Dan Chapman and Stefan Mendez-Diez | The Wess-Zumino-Witten-Novikov model |

Nov. 27 | Dan Chapman and Stefan Mendez-Diez | The Wess-Zumino-Witten-Novikov model (cont'd) |

Dec. 4 | Shane McCarthy, PHYS | What are Calabi-Yau manifolds and what are they good for? |

Dec. 11 | end of semester discussion |

The topic for Spring 2007 will be an introduction to mirror symmetry,
following parts of *Mirror
Symmetry*, by Vafa, Zaslow et al. We will begin with Ch. 12
and Ch. 16, then move on to Ch. 20, filling in missing backround as
needed.

Date | Speaker |
Topic |

Jan. 29 | organizational meeting | |

Feb. 5 | Willie Merrell | Noether charges and currents |

Feb. 14Note switch to Wed. | snowed out | |

Feb. 21 | Jonathan Rosenberg | Introduction to mirror symmetry for Calabi-Yaus |

Feb. 28 | Willie Merrell | Noether charges and currents, cont'd |

Mar. 7 | Ashwin Pande | A and B Twists |

Mar. 14 | Ashwin Pande | A and B Twists, cont'd |

- The NOVA program on string theory from a few years ago. Includes some interviews with Professor Gates.
- The arxiv preprint server for new papers on fundamental particle theory. Almost anything currently being done in string theory appears here.
- A recorded public lecture by Ed Witten (1998) on "Duality, Spacetime and Quantum Mechanics".
- A recorded public lecture by Sir Michael Atiyah (2005) on "The Nature of Space".
- A review in the New York Times (9/17/06) by Tom Siegfried of two recent critiques of string theory.
- "The Universe on a String", an op-ed piece (10/20/06) by Brian Greene in the New York Times.

For those who want to participate, here is some suggested background.

- For undergraduates: Some 400-level MATH and/or PHYS courses. For treatment of the subject at a level suitable for undergraduates, see the NOVA website above, especially the suggestions for further reading.
- For MATH graduate students: graduate-level geometry/topology (MATH 730/734). Additional geometry courses, such as MATH 740 (Riemannian geometry) or MATH 606/607 (algebraic geometry) are useful, as is any background in Lie groups (MATH 636 and/or 744) or functional analysis (MATH 632).
- For PHYS graduate students: graduate-level Lagrangian mechanics and quantum mechanics (PHYS 601, 622/623/624). Relativity (PHYS 675), or fundamental particle theory or string theory (PHYS 711, 751/752, 851/852, 859) is useful but not required.