Mirror Symmetry (MAT 1739, Fall 2004)
Mirror symmetry plays a central role in the study of geometry of
string theory.
In mathematics, it reveals a surprising connection between symplectic
geometry and algebraic geometry.
In physics, it provides a conceptual guide as well as powerful
computational tools, especially in compactifications to four-dimensions.
Room: Fields Institute 230
Hours: Tuesdays 1:00-4:00
Instructor:
Kentaro Hori
McLennan Laboratory 1113
(416)978-4784, familyname@physics.utoronto.ca
Outline:
1. Background:
* Supersymmetry and homological algebra
* Non-linear sigma models (NLSM)
* Landau-Ginzburg models
* topological field theory and topological strings
2. Linear sigma models, moduli space of theories
3. Mirror Symmetry
4. Mirror Symmetry involving D-branes
* B-branes in NLSM - holomorphic bundles, coherent sheaves
* B-branes in LG models - level sets, matrix factorizations
* A-branes in NLSM - Lagrangian submanifolds, Floer homology
* A-branes in LG models - vanishing cycles and Picard-Lefschetz monodromy
References:
The course does not follow a textbook but the following may be useful.
1. K. Hori, S. Katz, A. Klemm, R. Pandharipande, R. Thomas, C. Vafa,
R. Vakil and E. Zaslow, ``Mirror Symmetry''
Clay Mathematics Monographs Vol 1 (AMS, 2003).
2. P. Deligne, P. Etingof, D. Freed, L. Jeffrey, D. Kazhdan,
J. Morgan, D. Morrison, E. Witten, ``Quentum Fields and Strings:
A Course for Mathematicians'' (AMS 1999).
Lecture notes: (with audio:
here)