APRIL 28 - APRIL 30, 2004 |
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| Department Colloquium | |
| Topic: | A deformation of Hodge theory |
| Presenter: | Jean-Michel Bismut, Universite Paris-Sud |
| Date: | Wednesday, April 28, 2004, Time: 4:30 p.m., Location: Fine Hall 314 |
| Topology Seminar | |
| Topic: | Bounded cohomology and hyperbolic groups |
| Presenter: | Igor Mineyev, University of Illinois, Urbana and IAS |
| Date: | Thursday, April 29, 2004, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: | Gromov hyperbolic groups generalize fundamental groups of closed negatively curved manifolds. Bounded cohomology, due to B. E. Johnson, is defined as the usual (singular or bar-construction) cohomology with the additional boundedness assumption on cochains. I will remind both definitions and will discuss the construction of homological bicombings on hyperbolic graphs. With some extra work this provides a cohomological characterization of hyperbolic groups: a finitely presentable group G is hyperbolic if and only if, in dimension 2, the map from the bounded cohomology of G to the usual cohomology is surjective for all bounded QG-modules as coefficients. This surjectivity also holds for all higher dimensions, a result used by Connes and Moscovici for a proof of the Novikov conjecture for hyperbolic groups. In the recent joint work with N. Monod and Y. Shalom, we construct and use ideal bicombings on hyperbolic graphs. An ideal bicombing is a homological version of the classical geodesic flow on hyperbolic manifolds. |
| Geometric Analysis Seminar | |
| Topic: | Moduli spaces of critical Riemannian metrics in dimension 4 |
| Presenter: | Jeff Viaclovsky, MIT |
| Date: | Friday, April 30, 2004, Time: 3:00 p.m., Location: Fine Hall 314 |
| Abstract: | I will discuss some joint work with Gang Tian in which we study the moduli space of anti-self-dual metrics on four-manifolds and also extremal Kahler metrics. We show that, with certain natural geometric assumptions, the moduli space can be compactified by adding metrics with orbifold singularities. |
| Math Graduate Student Seminar | |
| Topic: | A stability approach to hypergraph Turàn problems |
| Presenter: | Peter Keevash, Princeton University |
| Date: | Friday, April 30, 2004, Time: 4:00 p.m., Location: Fine Hall 322 |
| Abstract: | I will discuss the stability method for solving extremal problems, as illustrated by some results from my thesis. The method consists of the following two-step process. In order to show that a given configuration is a unique optimum for an extremal problem, we first prove an approximate structure theorem for all constructions whose value is close to the optimum and then use this theorem to show that any imperfection in the structure must lead to a suboptimal configuration. Benny Sudakov and I recently used this approach to resolve two conjectures of S\'os and Frankl. |
MAY 3 - MAY 7, 2004 |
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| Special Geometry Seminar | |
| Topic: | Asymptotic expansions of Bergman kernel |
| Presenter: | Xianzhe Dai, University of California at Santa Barbara |
| Date: | Monday, May 3, 2004, Time: 1:00 p.m., Location: Fine Hall 224 |
| Algebraic Geometry Seminar | |
| Topic: | The Enriques conjecture; or, How canonical is the canonical bundle? |
| Presenter: | Joe Harris, Harvard University |
| Date: | Tuesday, May 4, 2004, Time: 4:30 p.m., Location: Fine Hall 322 |
| Abstract: | The question we're dealing with is this: Is there any way of associating to each smooth curve C of genus g ---or at least to each C in an open subset of moduli---a line bundle on C, other than by taking powers of the canonical bundle? (The answer, by the way, is no: the canonical bundle is truly canonical.) This question was posed almost a century ago; a bogus proof was given by Franchetta in the '40s (as a result of which the statement is usually called Franchetta's conjecture, and a correct proof was given in the '80s by Harer and Mestrano, based on a topological argument of Harer's. In fact, the statement is immediately implied by a stronger conjecture made by Enriques decades earlier. Enriques claimed (or suggested; it's not always clear) an analogous statement for the Severi variety, namely that the only ways of choosing a line bundle on a general plane curve C of degree d and genus g are combinations of the canonical bundle K_C and the hyperplane bundle O_C(1). In this talk I'll discuss a little of the history of the Enriques conjecture, and variants of it; but the main purpose of the talk will be to give a proof of the conjecture that Deepee Khosla and I found recently. |
| Joint Institute for Advanced Study and Princeton University Complex Geometry Seminar | |
| Topic: | Singular reduction in special Lagrangian geometry and almost complex geometry |
| Presenter: | Robert Bryant, Duke University |
| Date: | Wednesday, May 5, 2004, Time: 2:00 p.m., Location: Fine Hall 322 |
| Abstract: | Special Lagrangian manifolds with symmetry can be studied by the method of symplectic reduction, suitably generalized, and this construction yields many of the known examples. The cohomogeneity one case was essentially completed by Harvey and Lawson in their original paper on calibrated geometries, but the cohomogeneity two case is still not well understood, leading to the study of almost complex curves in almost complex surfaces with singularities. In this talk, after an introductory discussion, the focus will be on some existence and uniqueness questions raised by Dominic Joyce for almost complex curves in the resulting singular spaces. The resolution of these questions requires the use of techniques from singular PDE that generalize regular singular ODE techniques and these will be introduced and discussed during the talk. Reference: arXiv:math.DG/0402201 |
| Geometry, Representation, and Moduli Seminar | |
| Topic: | TBA |
| Presenter: | Alexander Braverman, Brown University |
| Date: | Wednesday, May 5, 2004, Time: 3:00 p.m., Location: Fine Hall 214 |
| Geometric Analysis Seminar | |
| Topic: | Deforming mappings by Mean Curvature Flow |
| Presenter: | Mao-Pei Tsui, Columbia University |
| Date: | Friday, May 7, 2004, Time: 3:00 p.m., Location: Fine Hall 314 |
MAY 10 - MAY 14, 2004 |
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| Joint Princeton University/Institute for Advanced Study Number Theory Seminar | |
| Topic: | TBA |
| Presenter: | David J. Burns, King's College, London |
| Date: | Monday, May 10, 2004, Time: 4:00 p.m., Location: Fine Hall 322 |
| Department Colloquium | |
| Topic: | Long arithmetic progressions of primes |
| Presenter: | Ben Green, University of British Columbia |
| Date: | Wednesday, May 12, 2004, Time: 4:30 p.m., Location: Fine Hall 314 |
MAY 17 - MAY 21, 2004 |
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| Geometry, Representation, and Moduli Seminar | |
| Topic: | TBA |
| Presenter: | R. Thomas, Imperial College |
| Date: | Wednesday, May 19, 2004, Time: 3:00 p.m., Location: Fine Hall 214 |