
THEMATIC PROGRAMS 

January 31, 2015  
Symplectic Topology, Geometry, and Gauge Theory Program

Registration  Taking the course for credit  Financial Assistance 
Courses offered in association with the Program on Symplectic Topology, Geometry and Gauge Theory
Held in conjunction with the program on InfiniteDimensional Lie Theory and Its Applications and the Program on Symplectic Topology, Geometry and Gauge Theory
Instructor: Boris Khesin, University of Toronto
Time: Wednesdays 10:3011:30 am and Fridays 1:003:00 pm
Start Date: January 15, 2001
Location: Room 210 or 230 at the Fields Institute
The course is an introduction to the classical theory of gauge groups and connections on real lowdimensinonal manifolds and new techniques in theory of double loop groups and connections on K3 surfaces and CalabiYau manifolds. Topics to be covered include:
References and suggested reading:
Pressley & Segal (1986). Loop Groups. (Oxford)
Atiyah. Collected Works, 5th Volume, Gauge Theory.
Koyobashi (1987). Differential Geometry of Complex Vector Bundles, (Iwanami Shoten and Princeton University Press)
Held in conjunction with the program on InfiniteDimensional Lie Theory and Its Applications and the program on Symplectic Topology, Geometry and Gauge Theory.
Instructor: L. Jeffrey, University of Toronto
Time: Tuesday and Thursday 3:30  5 pm.
Start Date: week of January 15, 2001
Location: Room 210 or 230 at the Fields Institute
A symplectic manifold (a manifold equipped with a nondegenerate closed twoform) is the natural mathematical generalization of the phase space considered in classical machanics. Hamiltonian group actions are a special case of Hamiltonian flows, which are a natural generalization of Hamilton's equations. Coadjoint orbits are natural examples of symplectic manifolds equipped with Hamiltonian group actions. The course treats the following topics:
References and suggested reading:
Audin (1991). The Topology of Torus Actions on Symplectic Manifolds. (Birhauser)
Berline & Getzler & Vergne(1992). Heat Kernels and Dirac Operators. (SpringerVerlag)
Guillemin & Sternberg (1984). Symplectic Techniques in Physics. (Cambridge)
Guillemin (1994). Moment Maps and Combinatorial Invariants of Hamiltonian T^nspaces. (Birkhauser)
Guillemin & Lerman & Sternberg (1996). Symplectic Fibrations and Multiplicity Diagrams. (Cambridge)
Held in conjunction with the Program on Symplectic Topology, Geometry and Gauge Theory.
Instructor: E.Meinrenken, University of Toronto
Time: Tuesdays and Thursdays 1:30  3 pm
Start Date: January 16, 2001
Location: Room 210 or 230 at the Fields Institute
Moduli Spaces of flat connections on 2manifolds are encountered in areas so diverse as Algebraic Geometry, Representation Theory, Knot Theory, Quantum Cohomology, and Conformal Field Theory. In this course we will give an overview from the perspective of Symplectic Geometry and (to a lesser extent) Mathematical Physics. Among other things, we will describe fixed point formulas for loop group actions which imply formulas for volumes, intersection pairings, and quantum dimensions of the moduli spaces.
Topics to be covered include:
References and suggested reading:
Atiyah (1990). The Geometry and Physics of knots. (Cambridge)
Thaddeus (1995). 'An introduction to the topology of the moduli space' and In: Geometry
Held in conjunction with the Program on Symplectic Topology, Geometry
and Gauge Theory
February 12, 19: Preparatory lectures (by M.Abreu)
*February 26March 2: Ya. Eliashberg, Stanford University
March 1214: A. Givental, University of California at Berkeley  Coxeter
lectures
*Schedule for February 26March 2
Monday 1:00  3:00 pm
Tuesday 3:30  5:30 pm
Wednesday 1:00  3:00 pm
Thursday 3:30  5:00 pm
Friday 1:00  3:00 pm
Location: Room 230 at the Fields Institute
This course covers the following areas:
Held in conjunction with the Program on Symplectic Topology, Geometry and Gauge Theory
Instructor: E.Meinrenken, University of Toronto
Time: Mondays, Wednesdays, Fridays at 11:00 am  12:00 pm
Start Date: September 11, 2000
Location: Sidney Smith Hall, Room 2128. Offered by the Math Dept.
This course will be an introduction to basic concepts of symplectic geometry, covering the following topics:
The course will be accompanied by lecture notes. References and suggested reading:
McDuff & Salamon (1997). Introduction to Symplectic Topology. (Oxford)
Libermann & Marle (1987). Symplectic Geometry and Analytical Mechanics. (Reidel)
Guillemin & Sternberg (1990). Symplectic Techniques in Physics (2nd.Ed.). (Cambridge)
Applications for financial support should be received by the following deadlines: April 15, 2000 for the Fall term and September 15, 2000 for the Winter term.