Special Analysis Seminar - Princeton University



The Kate & Hans Wedding Conference in Analysis Saturday Fine Hall

December 18

11:00 Coffee, Common Room

11:30 Victor Guillemin "The Strong Szego Limit Theorem"

1:30 Sergiu Klainerman "PDE as a unified subject"

2:30 Chris Sogge "Global estimates for the wave equation"

3:30 Alice Chang "Linking the Zeta functional determinant to problems in PDE"

All are welcome! To help the organizers, please e-mail conf99@math.princeton.edu before December 9, 1999 if you are planning to attend.

Week of December 6 - 10, 1999

Analysis and Applications Seminar Wednesday 12:30 Fine PL

Topic: Random Eigenvalues and Wireless Communications December 8

Presenter: Sergio Verdu, Princeton University, EE and PACM

Abstract: The eigenvalues of certain random matrices play a key role in determining the capacity of various wireless communication channels. We give an introduction to those channels as well as a brief tour of the literature on the asymptotic distribution of the spectrum of large random matrices. The interplay between engineering insights and mathematical results has proven to be fruitful.

Statistical Mechanics Seminar Wednesday 2:00 Jadwin 343

Topic: Smooth dynamics and new theoretical ideas in December 8

nonequilibrium statistical mechancis

Presenter: David Ruelle, I.H.E.S.

Thinking about Mathematics Wednesday 8:00 McDon A02

Topic: Calendrical Conundrums December 8

Presenter: John Conway, Princeton University

Abstract: Why do the months have the lengths they do, and why do we start the year on January 1? Where did someone live who was nearly 68 years old on his first birthday? For the answers to these and many other questions about the calendar, come to this, the seventh lecture in John Conway's series "Thinking about Mathematics."

Princeton Discrete Math Seminar Thursday 1:30 Fine 224

Topic: Packing cycles in graphs December 9

Presenter: Guoli Ding, Louisiana State University

Abstract: The main result to be presented in the talk is a characterization of graphs G=(V,E) that have the following

property:

For any nonnegative integral function w on V,

the maximum number of cycles in G such that each

vertex x is used at most w(x) times

=

the minimum of sum{w(x): x in S}, where the

minimum is taken over all subsets S of V

such that deleting S from G results a forest.

Ergodic Theory & Statistical Mechanics Seminar Thursday 2:30 Fine 110

Topic: Universality in 2D Ising Model December 9

Presenter: Haru Pinson, IAS

Symplectic Geometry Seminar Thursday 2:30 Fine 401

Topic: Transverse intersection of foliations in 3 manifolds December 9

Presenter: Takashi Tsuboi, Tokyo University

Abstract: We are interested in knowing whether the transverse intersection of two foliations is unique. The dynamics of several flows, such as the Anosov flows, give rise to multi-foliations, hence the uniqueness of the intersection of two foliations implies that the flow is determined (up to parametrization) by the associated foliations. We will discuss the uniqueness question for several pairs of foliations. In particular, I will explain a joint work with Shigenori MATSUMOTO that the transverse intersection is unique for the Anosov foliations of the suspensions of hyperbolic toral automorphisms, however, the transverse intersection is not unique for the Anosov foliations of the unit tangent bundles over hyperbolic surfaces.

Topology & Symplectic Geometry Seminar Thursday 4:30 Fine 314

Title: Planar Polygons and Special Lagrangians in Calabi-Yau Manifolds December 9

Presenter: Ciprian S. Borcea, Rider University

Abstract: The possible configurations, up to orintation-preserving isometry, for a planar $n$-gon with prescribed length for each of its edges, make-up a compact space, which is, in general, a smooth, orientable manifold of dimension $(n-3)$.Its topological type varies according a chamber structure for admissible edge-length-vectors, and can be investigated by means of Morse theory, geometric invariant theory, symplectic and toric geometry.

In adequate coordinates, the defining equations are algebraic, and yield families of complex projective varieties whose real points are the above configuration spaces. In particular, a construction used by Darboux for quadrilaterals, leads, in arbitrary dimension, to

alabi-Yau varieties. The singularities of the latter are away from the real locus, and resolutions to Calabi-Yau manifolds will contain identifiable types of special Lagrangians.

A conjecture of Strominger, Yau, and Zaslow suggests that myrror symmetry for pairs of Calabi-Yau manifolds corresponds geometrically to a duality of fibrations in special Lagrangian tori, and indeed, we do find special Lagrangian tori at appropriate points in our family.

A different, yet related complexification, and thus other examples of special Lagrangian tori on Calabi-Yau manifolds, can be obtained from the non-Euclidean scenario. We investigate in more detail the families of K3 surfaces and Calabi-Yau threefolds associated to configuration spaces of pentagons and hexagons.

Graduate Student Seminar Friday 1:30 Fine 314

Topic: Volume-Minimizing Submanifolds via Calibrated Geometry December 10

Presenter: Dan Grossman, Princeton University

Geometry Seminar Friday 3:00 Fine 314

Topic: Analysis of the non-linear $\overline\partial$ operator December 10

Presenter: Igor Rodnianski, Princeton University

Week of December 13 - 17, 1999

PACM Colloquium Monday 4:30 Fine 224

Topic: Unsteady Aerodynamics of Insect Flight December 13

Presenter: Z. Jane Wang, Cornell University

Abstract: The myth `bumble-bees can not fly according to conventional aerodynamics' simply reflects our poor understanding of unsteady viscous fluid dynamics. In particular, we lack a theory of vorticity shedding due to dynamic boundaries at the intermediate Reynolds numbers relevant to insect flight, typically between $10^2$ and $10^4$, where both viscous and inertial effects are important. In our study, we compute unsteady viscous flows, governed by the Navier-Stokes equation, about a two dimensional flapping wing which mimics the motion of an insect wing. I will present two main results: the existence of a prefered frequency in forward flight and its physical origin, and 2) the vortex dynamics and forces in hovering dragonfly flight.

Symplectic Geometry Seminar Tuesday 2:30 Fine 1201

Topic: Introduction to Symplectic Field Theory December 14

Presenter: Yakov Eliashberg, Princeton University

Algebraic Geometry Seminar Tuesday 4:15 Fine 322

Topic: Multiplier ideals and test ideals December 14

Presenter: Karen Smith, University of Michigan

Nonlinear Analysis Joint Seminar IAS / Princeton / Rutgers Thursday 4:00 Rutgers

Topic: Mathematical problems of superfluids December 16

Presenter: Fabrice Bethuel, University of Paris 6

Location: Rutgers, Hill Center, Room 705, tea is available in the 7th floor lounge 3:30 p.m.

Topology & Symplectic Geometry Seminar Thursday 4:30 Fine 314

Title: Monopoles and relations between four-manifold invariants December 16

Presenter: Paul Feehan, Ohio State University

Geometry Seminar Friday 3:00 Fine 314

Topic: An example of points of double concentration: the sonic boom December 17

Presenter: Thierry Aubin, Paris VI

The Kate & Hans Wedding Conference in Analysis Saturday Fine Hall

December 18

11:00 Coffee, Common Room

11:30 Victor Guillemin "The Strong Szego Limit Theorem"

1:30 Sergiu Klainerman "PDE as a unified subject"

2:30 Chris Sogge "Global estimates for the wave equation"

3:30 Alice Chang "Linking the Zeta functional determinant to problems in PDE"

All are welcome! To help the organizers, please e-mail conf99@math.princeton.edu before December 9, 1999 if you are planning to attend.

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