APRIL 21 - APRIL 23, 2004 |
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| Joint Institute for Advanced Study and Princeton University Complex Geometry Seminar | |
| Topic: | Crepant Resolutions of Calabi-Yau Orbifolds |
| Presenter: | Anda Degeratu, Duke University and MSRI |
| Date: | Wednesday, April 21, 2004, Time: 2:00 p.m., Location: Fine Hall 322 |
| Discrete Mathematics Seminar | |
| Topic: | Lower Bounds for Degeneracy Testing |
| Presenter: | Bernard Chazelle, Princeton University |
| Date: | Wednesday, April 21, 2004, Time: 3:00 p.m., Location: Fine Hall 224 |
| Abstract: | I will discuss how to prove lower bounds in a decision tree model for the problem of testing whether out of n numbers k of them sum up to 0. This is joint work with Nir Ailon. |
| Department Colloquium | |
| Topic: | Arnold Diffusion |
| Presenter: | John Mather, Princeton University |
| Date: | Wednesday, April 21, 2004, Time: 4:30 p.m., Location: Fine Hall 314 |
| Ergodic Theory and Statistical Mechanics Seminar | |
| Topic: | Universality in Random Matrix Theory for Orthogonal and Symplectic Ensembles (joint work with P.Deift) |
| Presenter: | Dimitri Gioev, University of Pennsylvania and Courant Institute |
| Date: | Thursday, April 22, 2004, Time: 2:00 p.m., Location: Fine Hall 322 |
| Abstract: | We give a proof of the Universality Conjecture in Random Matrix Theory for orthogonal (beta=1) and symplectic (beta=4) ensembles in the scaling limit for a class of weights w(x)=exp(-V(x)) on the line where V(x) is a polynomial. (For such weights the associated equilibrium measure is supported on a single interval.) Our starting point is Widom's representation of the correlation kernels for the beta=1,4 cases in terms of the unitary (beta=2) correlation kernel plus a correction. In the asymptotic analysis of the correction terms we use amongst other things differential equations for the derivatives of orthogonal polynomials (OP's) due to Tracy-Widom, and uniform Plancherel-Rotach type asymptotics for OP's due to Deift-Kriecherbauer-McLaughlin-Venakides-Zhou. The problem reduces to a small norm problem for a certain matrix of a fixed size that is equal to the degree of the polynomial potential. |
| Topology Seminar | |
| Topic: | Small volume cusped hyperbolic three-manifolds |
| Presenter: | Peter Milley , Princeton University |
| Date: | Thursday, April 22, 2004, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: | This talk will discuss a project of myself, David Gabai, and Robert Meyerhoff to develop a unifying theory to reveal the structure of low volume cusped and closed hyperbolic 3-manifolds. We will detail preliminary results in the cusped case. |
| Geometric Analysis Seminar | |
| Topic: | Critical points of holomorphic sections and string/M theory vacua |
| Presenter: | Steve Zelditch, Johns Hopkins University |
| Date: | Friday, April 23, 2004, Time: 3:00 p.m., Location: Fine Hall 314 |
| Abstract: | This talk is about joint work with M. R. Douglas and B. Shiffman on statistics of supersymmetric vacua in string theory. Mathematically, it is about the number and location of critical points of holomorphic sections of a hermitian line bundle. The average number of critical points of a random holomorphic section depends on the metric. In the case of a positive line bundle, Calabi extremal metrics are extremals for the asymptotics of the average number of critical points. |
APRIL 26 - APRIL 30, 2004 |
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| Joint Princeton University/Institute for Advanced Study Number Theory Seminar | |
| Topic: | Metaplectic Eisenstein Series and Analytic
Continuations of Dirichlet Series |
| Presenter: | Ben Brubaker, Stanford University |
| Date: | Monday, April 26, 2004, Time: 4:00 p.m., Location: Fine Hall 322 |
| Abstract: | We will review the definition of Eisenstein series on the metaplectic group and show how they led to the notion of "multiple Dirichlet series," Dirichlet series whose numerator is again a Dirichlet series. We'll look at some interesting examples and new results using the methods of multiple Dirichlet series will be surveyed. Finally, we discuss the broader context of these examples as a result of very recent joint work with Daniel Bump. |
| PACM Colloquium | |
| Topic: | PlanetLab: Introducing Disruptive Technology into the Internet |
| Presenter: | Larry Peterson, Computer Science, Princeton University |
| Date: | Monday, April 26, 2004, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: | A new class of geographically distributed network services is emerging, and the most effective way to design, evaluate, and deploy these services is by using an overlay-based testbed. Unlike conventional network testbeds, however, we advocate an approach that supports both researchers that want to develop new services, and clients that want to use them. This dual use, in turn, suggests four design principles that are not widely supported in existing testbeds: services should be able to run continuously and access a slice of the overlay's resources, control over resources should be distributed, overlay management services should be unbundled and run in their own slices, and APIs should be designed to promote application development. This talk describes this high-level vision, and reports the status and plan for the realization of the vision in PlanetLab. |
| Algebraic Geometry Seminar | |
| Topic: | TBA |
| Presenter: | Jaroslaw Wisniewski, Purdue University and Warsaw |
| Date: | Tuesday, April 27, 2004, Time: 4:30 p.m., Location: Fine Hall 322 |
| Mathematical Physics Seminar | |
| Topic: | Limit shapes for dimers and complex Burgers equation |
| Presenter: | Andrei Okounkov, Princeton University |
| Date: | Tuesday, April 27, 2004, Time: 4:30 p.m., Location: Jadwin A06 |
| 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 |
| 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. |
MAY 3 - MAY 7, 2004 |
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| 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 |