MAY 4 - MAY 7, 2004 |
|
| 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: | Instanton counting and affine Lie algebras |
| Presenter: | Alexander Braverman, Brown University |
| Date: | Wednesday, May 5, 2004, Time: 3:00 p.m., Location: Fine Hall 214 |
| Abstract: | In this lecture I shall explain an approach to the "instanton counting" problem (introduced by Nekrasov and studied thoroughly by Nekrasov-Okounkov and Nakajima-Yoshioka in the case when the gauge group is equal to SL(n)) via representation theory of affine Lie algebras. This approach works for an arbitrary gauge group. We shall also explain how this can be viewed as an affine version of the results of Givental-Kim describing the small quantum cohomology ring of flag varieties. If time permits we shall also discuss some questions the above approach raises about Gromov-Witen invariants of 3 dimensional Calabi-Yau manifolds. |
| 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 |
|
| 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 |
|
| 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 |