| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR: |
| MIHNEA POPA (University of Illinois at Chicago): |
| BGG correspondence and the cohomology of compact kaehler manifolds |
| on Tuesday, November 24, 2009, at 3 - 4 pm in Science Center, Room 507 |
| The cohomology algebra of the sheaf of holomorphic functions on a compact Kahler manifold can be naturally viewed as a module over the exterior algebra of a vector space. A well-known result of Bernstein-Gel fand-Gelfand gives a correspondence between such exterior modules and linear complexes of modules over the polynomial ring. I will explain how one can use a modern view on this correspondence, together with the Generic Vanishing theory developed by Green and Lazarsfeld via Hodge-theoretic methods, in order to understand new algebraic structures of the cohomology algebra. As a bonus, homological and commutative algebra tools can be applied on the polynomial ring side to obtain inequalities for the holomorphic Euler characteristic and the Hodge numbers of compact Kahler manifolds. This is joint work with R. Lazarsfeld. |
| DIFFERENTIAL GEOMETRY SEMINAR: |
| MELISSA LIU (Columbia University): |
| Coherent-Constructible Correspondence for Toric Varieties and Toric Orbifolds |
| on Tuesday, November 24, 2009, at 1:30 - 3:00 pm in Science Center, Room 507 |
| SPECIAL SEMINAR: |
| YNG-ING LEE (National Taiwan University): |
| Special solutions to Lagrangian mean curvature flow |
| on Wednesday, November 25, 2009, at 2 - 3 pm in Science Center, Room 507 |
| Organized by Professor Shing Tung Yau. |
| NUMBER THEORY SEMINAR: |
| JOHN VOIGHT (University of Vermont): |
| Algebraic curves uniformized by congruence subgroups of triangle groups |
| on Wednesday, November 25, 2009, at 3 - 4 pm in Science Center, Room 507 |
| Abstract: We construct certain subgroups of hyperbolic triangle groups which we call congruence subgroups. These groups include the classical congruence subgroups of SL(2,Z), Hecke triangle groups, and 19 families of Shimura curves associated to arithmetic triangle groups. We determine the field of muduli of the curves associated to these groups and thereby realize the Galois groups PSL(2,q) and PGL(2,q) regularly in many cases over explicitly given abelian number fields. This is joint work with Pete L. Clark. |
| BASIC NOTIONS SEMINAR: |
| CLARK BARWICK (Harvard University): |
| Descent problems for K-theory |
| on Monday, November 30, 2009, at 3 pm in Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR: |
| GREGORY PEARLSTEIN (Michigan State University): |
| Zero loci of normal functions |
| on Tuesday, December 01, 2009, at 3 - 4 pm in MIT (26-204) |
| I will discuss recent work with Patrick Brosnan on the algebraicity of the zero loci of normal functions, and applications to the study of algebraic cycles. |
| DYNAMICS AND GEOMETRY SEMINAR: |
| GIULIO TIOZZO (Harvard University): |
| The entropy of alpha-continued fractions |
| on Wednesday, December 02, 2009, at 4 - 5 pm in Science Center, Room 507 |