SUMMER SCHOOL ON COMBINATORIAL MODELS IN GEOMETRY AND TOPOLOGY OF FLAG MANIFOLDS

Objectives
The main objective of the school is to provide an interactive environment where interested people (graduate students, postdocs, young researchers) can learn results and understand techniques concerning various aspects of flag manifolds. The subject is an interplay between differential geometry, algebraic geometry, Lie theory, and combinatorics, and the school will focus on combinatorial models and algorithms which have been developed in connection with the study of various geometric and topological aspects of flag manifolds.

Topics of Study
Young tableaux, Schubert polynomials, the Goresky-Kottwitz-MacPherson graph for equivariant cohomology of flag manifolds (with emphasis on the results of Guillemin and Zara), cohomology of weight varieties (via the Kirwan surjectivity theorem and the Tolman-Weitsman description of the kernel of the Kirwan map), Bott-Samelson manifolds, equivariant K-theory of flag manifolds (the method of Willems for computing the structure constants and his Chevalley type formula), the puzzle rule of Knutson and Tao, the formulas of Buch, Kresch, and Tamvakis for the Gromov-Witten invariants of the Grassmannian, the combinatorial quantum cohomology ring of the flag manifolds G/B via Peterson's operators, quantum Schubert polynomials, and formulas of Kim and Mihalcea concerning the equivariant quantum cohomology of flag manifolds.

Lecturers
Leonardo Mihalcea, Duke University
Matthieu Willems, University of Toronto
Catalin Zara, University of Massachusets-Boston
Liviu Mare, University of Regina


Registration
Interested people are asked to contact Liviu Mare

SCHEDULE

June 5 (Tue.)
Arrival of participants
June 6 (Wed.) Leonardo Mihalcea
Grassmannians and their (equivariant) cohomology Abstract
Two lectures in the morning (9 - 10:15 and 10:30 - 11:45, room ED 612) and a discussion session in the afternoon (3:30 - 4:30,
room ED612)
June 7 (Thu.) Liviu Mare
Cohomology of flag manifolds Abstract
Two lectures in the morning (9 - 10:15 and 10:30 - 11:45, room ED 612) and a discussion session in the afternoon (3:30 - 4:30,
room ED612)
June 8 (Fri.) Catalin Zara and Liviu Mare
Equivariant cohomology of flag manifolds Abstract
Two lectures in the morning (9 - 10:15 and 10:30 - 11:45, room ED 612) and a lecture in the afternoon (3:30 - 4:45, room ED612)
June 9 (Sat.) Catalin Zara and Liviu Mare
Equivariant cohomology of flag manifolds Abstract (TBA)
A lecture (9:30 - 10:45, room ED 612) and a discussion session (11 - noon, room ED612).
June 10 (Sun.)
No lectures
June 11 (Mon.) Leonardo Mihalcea
(Equivariant) quantum cohomology of Grassmannians Abstract
Two lectures in the morning (9 - 10:15 and 10:30 - 11:45, room RC285) and a discussion session in the afternoon (3:30 - 4:30,
room RC285)
June 12 (Tue.) Matthieu Willems
K-theory of flag manifolds Abstract
Two lectures in the morning (9 - 10:15 and 10:30 - 11:45, room RC285) and a discussion session in the afternoon (3:30 - 4:30,
room RC285)
June 13 (Wed.) Liviu Mare
Quantum cohomology of complete flag manifolds Abstract
Two lectures in the morning (9 - 10:15 and 10:30 - 11:45, room ED 612) and a discussion session in the afternoon (3:30 - 4:45, room ED612)
June 14 (Thu.) Liviu Mare
Symplectic quotients of flag manifolds and their cohomology Abstract
Two lectures in the morning (9 - 10:15 and 10:30 - 11:45, room ED 612) and a discussion session in the afternoon (3:30 - 4:45, room ED612)
June 15 (Fri.)
Departure of participants



Last updated May 30, 2007.