Working Geometry Seminar
Spring 2009
Tuesday at 2:00-3:30 pm in Milner 317
- Part 1: Schubert varieties and their homological rigidity.
- R. Bryant, Rigidity and quasi-rigidity of extremal cycles in Hermitian symmetric spaces.
- B. Kostant, Lie Algebra Cohomology and Generalized Schubert Cells.
- Bernstein-Gelfand-Gelfand, Schubert cells, and the cohomology of the spaces G/P.
- G. Segal, Introduction to the BGG paper.
- Part 2: Index theory and quaternionic Kähler manifolds.
- S. Salamon, Quaternionic Kähler manifolds, Invent. Math. 67 (1982), no. 1, 143--171.
- M. Atiyah & F. Hirzebruch, Spin-manifolds and group actions, from 1970 Essays on Topology and Related Topics, pp. 18--28 Springer, New York.
- H. Herrera & R. Herrera, Â-genus on non-spin manifolds with S1 actions and the classification of positive quaternion-Kähler 12-manifolds, J. Differential Geom. 61 (2002), no. 3, 341--364.
- Part 3: N. Takaka's paper On differential systems, graded Lie algebras and psuedogroups, J. Math. Kyoto Univ, 10 (1970) 1--82.
January 20
J.M. Landsberg
Overview of Bryant's paper and goals.
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January 27
Frank Sottile
On the BGG paper, part 1.
• • • • •
February 3
Frank Sottile
On the BGG paper, part 2.
• • • • •
February 10
Dennis The
On Bryant's paper, part 1.
• • • • •
February 17
Dennis The
On Bryant's paper, part 2.
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February 24
J.M. Landsberg
Introduction to manifolds with special holonomy and Salamon's paper.
• • • • •
March 3
Dennis The
On Bryant's paper, part 3.
• • • • •
March 10
J.M. Landsberg
Curvature of manifolds with special holonomy.
• • • • •
March 17
No seminar: Spring Break
• • • • •
March 24
Igor Zelenko
Tanaka's paper, part 1.
• • • • •
March 31
Jarek Buczynski
Quaterionic-Kähler manifolds, part 1.
• • • • •
April 2 (Thursday)
Jarek Buczynski
Quaterionic-Kähler manifolds, part 2.
• • • • •
April 07
Igor Zelenko
Tanaka's paper, part 2.
• • • • •
April 14
Igor Zelenko
Tanaka's paper, part 3.
• • • • •
April 17 (Friday) at 4:00 in Milner 317
-- joint with Linear Analysis Seminar
Ron Douglas
K-homology and Index Theory
From general principles, there is a generalized homology theory paired with
the K-theory introduced by Atiyah and Hirzebruch. Some time ago, Larry
Brown, Peter Fillmore and I discovered a "realization" of this theory in the
context of operator theory. I will describe this discovery paying attention
to its connection to index theory, particulary the classical theorem of
Atiyah and Singer.
• • • • •
April 21
No seminar: B. Lawson visits as
Frontiers speaker
this week.
• • • • •
April 28
Jarek Buczynski
Quaterionic-Kähler manifolds, part 3.
• • • • •
May 5
Michel Brion
Bott-Samelson Varieties
This will be an expository talk on
Demazure's classic 1974 paper and serve as a
prequel to the TAGS lecture.
Past Working Geometry Seminars:
Fall 2008 • Spring 2008 • Fall 2007 • 2006-2007 • 2005-2006