**Current Seminars**

updated 2/27/ 2002

__As
of February____ ____27
- March 1__

*Department
Colloquium*

Topic: On the Monge Ampere equation in periodic media

Presenter: **
****Luis A. Caffarelli**, University of Texas at Austin

Date: Wednesday, February 27, 2002, Time: 4:30 p.m., Location: Fine Hall 314

*Discrete
Mathematics Seminar*

Topic: Bipartite cuts and judicious partitions in graphs without short cycles

Presenter: **
Michael Krivelevich**, Tel Aviv University

Date: Thursday, February 28, 2002, Time: 2:00 p.m., Location: Fine Hall 224

*Ergodic
Theory and Statistical Mechanics Seminar ***
Rescheduled from February 21, 2002*

Topic: Limiting distributions for special last passage percolation models Part I

Presenter: **
****Jinho Baik**, Princeton University and the Institute for Advanced
Study

Date: Thursday, February 28, 2002, Time: 2:00 p.m., Location: Fine Hall 601

Abstract: A few special last passage percolation models have exact determinantal formulas for their distribution functions using ideas from combinatorics. In the first talk, we discuss the algebraic steps to obtain the determinantal formulas. In the second talk, we analyze the determinants asymptotically and obtain the limiting distributions. We also consider their relation to random matrix theory.

*Topology Seminar *

Topic: Mapping class groups, Lefschetz fibrations and Stein fillings

Presenter: **
****Andras Stipsicz**, ELTE/Princeton

Date: Thursday, February 28, 2002, Time: 4:00 p.m., Location: Fine Hall 314

*Princeton
University/IAS Number Theory Seminar *

Topic: Automorphisms of even unimodular lattices

Presenter: **
****Benedict Gross**, Harvard University

Date: Thursday, February 28, 2002, Time: 4:30 p.m., Location: IAS SH-101

*Graduate
Student Seminar *

Topic: Cryptologic Properties of GammaPi Class

Presenter: **
****Seth Patinkin**, Princeton University

Date: Friday, March 1, 2002, Time: 1:00 p.m., Location: Fine Hall 1001

Abstract: I will present a new cryptologic primitive which may be used in a variety of contexts, both symmetric and asymmetric. This method is based on the construction of a class of mappings from the space of real-entry matrices to the space of characteristic functions defined on bounded, finite-dimensional geometric regions. Novelty, computational infeasibility, efficiency, and known attacks shall be addressed.

*Joint
Princeton University/IAS/Rutgers Non-Linear Analysis Seminar ***
Note special day and time and location*

Topic: Constraint methods for nonlinear homogenization in periodic and random media, Part II'

Presenter: **
****Luis A. Caffarelli**, University of Texas at Austin

Date: Friday, March 1, 2002, Time: 4:30 p.m., Location: Hill Center Room 705 , Rutgers University

__March____ ____4
- 8__

*Algebraic
Geometry Seminar *** Please note special date, time,
and location*

Topic: Differential geometry of gerbes, II

Presenter:
**William Messing**, University of
Minnesota

Date: Monday, March 4, 2002, Time: 4:00 p.m., Location: Fine Hall 322

* Analysis Seminar*

Topic: TBA

Presenter: **
****Fabrice Planchon**, Université Pierre et Marie Curie

Date: Monday, March 4, 2002, Time: 4:00 p.m., Location: Fine Hall 314

*PACM
Colloquium*

Topic: Solving Differential Equations Without the Equations

Presenter: **
William Gear**, NEC Research

Date: Monday, March 4, 2002, Time: 4:00 p.m., Location: Fine Hall 214

*Algebraic
Geometry Seminar*

Topic: On the effective cones of moduli spaces

Presenter:
**Brendan Hassett**, Rice University

Date: Tuesday, March 5, 2002, Time: 4:30 p.m., Location: Fine Hall 314

Abstract: The cone of effective divisors on a smooth projective variety has many properties which are analogous to the cone of effective curves. To understand the cone geometrically, it is necessary to classify its `coextremal rays', generating curve classes of the dual cone corresponding to distinguished fibrations on the variety. We compute these rays for several moduli spaces of curves and give applications to the study of rational points.

*CR
Seminar*

Topic: The half-torsion of a Bernstein-Gelfand-Gelfand diagram

Presenter: **
****Tom Branson**, University of Iowa

Date: Tuesday, March 5, 2002, Time: 4:00 p.m., Location: Fine Hall 401

Abstract: Let $D$ be a conformally invariant differential operator with suitable ellipticity properties. A choice of a Riemannian metric on a compact manifold assigns a (pure point) spectrum to $D$. This spectrum, and therefore spectral invariants like the functional determinant det$(D)$, are not {\it conformal} invariants: they move as we move within a conformal class of metrics. However they lead to nice max/min problems which tend to pick out distinguished metrics within a conformal class, since one can write a nice (Polyakov) formula for the quotient of such determinants in conformally related metrics; this has been an important theme in string theory. Though the Laplacians of the de Rham complex are not conformally invariant, a certain combination of their determinants admits a nice Polyakov formula. In even dimension $n=2m$ this is $\prod_{k=0}^{m-1}({\rm det}\Delta_k)^{(-1)^k(m-k)}$. This {\it half-torsion} has considerably less invariance than the Reidemeister-Ray-Singer torsion. This may be viewed as a functional determinant for the Maxwell operator that ``feels'' effect of that operator's gauge (as well as conformal) invariance. We show that the proper setting for the above principle is that of generalized Bernstein-Gelfand-Gelfand (gBGG) sequences, and that each of these has a half-torsion with a Polyakov formula, at least in the locally conformally flat case. (The exponents are now not just $(-1)^k(m-k)$, but are determined by the conformal weights of bundles in the gBGG sequence.) For example, the next most elementary gBGG sequence (after the de Rham complex) is the metric deformation complex, an important construct in quantum gravity.

*Department
Colloquium*

Topic: TBA

Presenter: **
****Ingrid Daubchies**, Princeton University

Date: Wednesday, March 6, 2002, Time: 4:30 p.m., Location: Fine Hall 314

*Discrete
Mathematics Seminar*

Topic: TBA

Presenter: **
****John Conway**, Princeton University

Date: Thursday, March 7, 2002, Time: 2:00 p.m., Location: Fine Hall 224

*Ergodic
Theory and Statistical Mechanics Seminar ***
Rescheduled from February 28, 2002*

Topic: Limiting distributions for special last passage percolation models Part II

Presenter: **
Jinho Baik**, Princeton University and the Institute for Advanced Study

Date: Thursday, March 7, 2002, Time: 2:00 p.m., Location: Fine Hall 601

Abstract: A few special last passage percolation models have exact determinantal formulas for their distribution functions using ideas from combinatorics. In the first talk, we discuss the algebraic steps to obtain the determinantal formulas. In the second talk, we analyze the determinants asymptotically and obtain the limiting distributions. We also consider their relation to random matrix theory.

*Topology Seminar *

Topic: Torsion invariants in symplectic Floer theory

Presenter: **
****Yi-Jen Lee**, Princeton University

Date: Thursday, March 7, 2002, Time: 4:00 p.m., Location: Fine Hall 314

*Princeton
University/IAS Number Theory Seminar *

Topic: New Upper Bounds on Sphere Packing

Presenter: **
****Henry Cohn**, Microsoft and the
American Institute of Mathematics (AIM)

Date:
Thursday, March 7, 2002, Time: 4:30, Location: Fine
Hall 322

Abstract: We develop an analogue for sphere packings of the linear programming bound
for error-correcting codes, and use it to improve the known upper bounds for the density of sphere packings in dimensions 4 through 36. We conjecture
that our approach can be used to solve the sphere packing problem in dimensions 8 and 24; at the very least, the numerical bounds obtained come
very close to equality. (This is joint work with Noam Elkies.)

*Geometric
Analysis Seminar*

Topic: Cohomology ring of crepant resolutions of orbifolds

Presenter: **
****Ruan Yongbin**, University of Wisconsin and Hong Kong University of Science and
Technology

Date: Friday, March 8, 2002, Time: 3:00 p.m., Location: Fine Hall 314

__March____ ____11
- 15__

* Analysis Seminar*

Topic: TBA

Presenter: **
****Alexandru Ionescu**, University of Wisconsin

Date: Monday, March 11, 2002, Time: 4:00 p.m., Location: Fine Hall 314

*PACM
Colloquium*

Topic: Moving Mesh Methods Based on Harmonic Maps

Presenter: **
****Pingwen Zhang**, Peking University and Princeton University

Date: Monday, March 11, 2002, Time: 4:00 p.m., Location: Fine Hall 214

*Algebraic
Geometry Seminar*

Topic: Fukaya categories and deformations

Presenter:
**Paul Seidel**, the Institute for Advanced Study

Date: Tuesday, March 12, 2002, Time: 4:30 p.m., Location: Fine Hall 314

*Mathematical
Physics Seminar*

Topic: Coherent State Path Integrals without Resolutions of Unity

Presenter: **
****John Klauder**, University of Florida, Gainesville

Date: Tuesday, March 12, 2002, Time: 4:30 p.m., Location: Jadwin A06

Abstract: From the very beginning, coherent state path integrals have always relied on a coherent state resolution of unity for their construction. By choosing an inadmissible fiducial vector, a set of ``coherent states'' spans the same space but loses its resolution of unity, and for that reason has been called a set of weak coherent states. Despite having no resolution of unity, it is nevertheless shown how the propagator in such a basis may admit a phase-space path integral representation in essentially the same form as if it had a resolution of unity.

*Discrete
Mathematics Seminar*

Topic: Separating random points

Presenter: **
****Van Vu**, University of California, San Diego

Date: Thursday, March 14, 2002, Time: 2:00 p.m., Location: Fine Hall 224

*Joint
Princeton University/IAS/Rutgers Non-Linear Analysis Seminar *

Topic: Global existence and convergence for a fourth order flow in conformal geometry

Presenter: **
****Simon Brendle**, University of Tuebingnon

Date: Thursday, March 14, 2002, Time: 4:00, Location: Fine Hall 214

*Princeton
University/IAS Number Theory Seminar *

Topic: TBA

Presenter: **
****Florian Pop**, University of Bonn and the Institute for Advanced
Study

Date: Thursday, March 14, 2002, Time: 4:30, Location: IAS SH-101

*Geometric
Analysis Seminar*

Topic: On the Singular Set of J-holomorphic Maps

Presenter: **
****Tristan Riviere**, ETH (Swiss Federal Institute of Technology,
Zurich)

Date: Friday, March 15, 2002, Time: 3:00 p.m., Location: Fine Hall 314

__March____ ____18
- 22__

*PACM
Colloquium*

Topic: Local Discontinuous Galerkin Methods for Partial Differential Equations with Higher Order Derivatives

Presenter: **
Chi-Wang Shu**, Brown University

Date: Monday, March 18, 2002, Time: 4:00 p.m., Location: Fine Hall 214

*Mathematical
Physics Seminar *** Please note change in date
from **February
26, 2002*

Topic: The Cauchy Problem for a Dynamical Euler Elastica

Presenter: **
Almut Burchard**, University of Virginia

Date: Tuesday, March 19, 2002, Time: 4:30 p.m., Location: Jadwin A06

Abstract: We consider the dynamics for a thin, closed loop inextensible Euler's elastica moving in three dimensions. The equations of motion for the elastica include a wave equation involving fourth order spatial derivatives, and a second order elliptic equation for its tension. Local existence and uniqueness of solutions are established for sufficiently regular initial data. This is joint work with L.E. Thomas.

*Joint
Princeton University/IAS/Rutgers Non-Linear Analysis Seminar *

Topic: Interaction functionals for hyperbolic systems of conservation laws

Presenter: **
****Alberto Bressan**, Scuola Internazionale Superiore di Studi
Avanzati (SISSA), Italy

Date: Thursday, March 21, 2002, Time: 4:00, Location: Fine Hall 214

Abstract: For strictly hyperbolic systems of conservation laws in one space dimension, global existence of entropy weak solution was proved in a classical paper of Glimm (1965). The construction of solution is here based on a compactness argument, where the total oscillation (i.e. the BV norm) is controlled by a suitable interaction functional. Very recently, wave interaction functionals have been introduced also in connection with viscous perturbations of hyperbolic systems, not necessarily in conservation form. This allows the construction of unique "viscosity solutions" to nonlinear hyperbolic systems, continuously depending on the initial data. The talk will also discuss the possibility of a-priori BV bounds (in terms of similar interaction functionals) for other types of approximations, such as relaxations or finite-difference numerical schemes.

__March
25 - 29__

* Analysis Seminar*

Topic: TBA

Presenter: **
****Andreas Seeger**, University of Wisconsin

Date: Monday, March 25, 2002, Time: 4:00 p.m., Location: Fine Hall 314

*PACM
Colloquium*

Topic: Flash & Turn: Self-organization and dynamics of fireflies and ants

Presenter: **
****Bard Ermentrout**, University of Pittsburgh

Date: Monday, March 25, 2002, Time: 4:00 p.m., Location: Fine Hall 214

*Algebraic
Geometry Seminar*

Topic: TBA

Presenter:
**Kiran Kedlaya**,
University of California, Berkeley

Date: Tuesday, March 26, 2002, Time: 4:30 p.m., Location: Fine Hall 314

*Discrete
Mathematics Seminar*

Topic: A trace bound for the discrepancy

Presenter: **
****Bernard Chazelle**, Princeton University

Date: Thursday, March 28, 2002, Time: 2:00 p.m., Location: Fine Hall 224

*Princeton
University/IAS Number Theory Seminar *** Please note
special time*

Topic: Ramified Triple Product Identities

Presenter: **
****Thomas Watson**, UCLA

Date: Thursday, March 28, 2002, Time: 4:00 p.m., Location: Fine Hall 322

*Geometric
Analysis Seminar*

Topic: TBA

Presenter: **
Bruce Kleiner**, University of Michigan & Courant Institute of Mathematics

Date: Friday, March 29, 2002, Time: 3:00 p.m., Location: Fine Hall 314

__April
1-5__

*PACM
Colloquium*

Topic: Some themes of feedback control theory, and their relevance to systems molecular biology

Presenter: **
****Eduardo Sontag**, Rutgers University and Princeton University

Date: Monday, April 1, 2002, Time: 4:00 p.m., Location: Fine Hall 214

*Algebraic
Geometry Seminar*

Topic: p-adic Fourier Theory and Lubin-Tate theory

Presenter:
**Jeremy Teitelbaum**, University Illinois at Chicago.

Date: Tuesday, April 2, 2002, Time: 4:30 p.m., Location: Fine Hall 314

Abstract: In this talk I will discuss some new results (joint with Peter Schneider) on p-adic integration that generalize old results of Amice and Lazard. Let $L$ be a finite extension of Qp$. We study the space of locally L-analytic functions on the ring of integers $o=o_L$, and its dual, the ring of locally $L$-analytic distributions. We show that this ring of distributions is isomorphic to the global functions on a rigid space $\hat{o}$ parameterizing $L$-analytic characters of $o$. The space $\hat{o}$ turns out to be quite interesting; if $L$ is not Q_p $\hat{o}$ isomorphic over C_{p}$ to the open unit disk, but is not a disk over any discretely valued extension of $L$. Our methods rely on Lubin-Tate theory and some results from Tate's classic paper on p-divisible groups. I will also explain how these results allow one to construct a p-adic L-function for a CM elliptic curve at a supersingular prime. Such functions have been discussed by Katz and by Boxall, but our results allow one to approach the construction using "Coleman power series" in a manner that is formally identical to that used for ordinary primes as described, for example, in deShalit's book.

*Mathematical
Physics Seminar*

Topic: Tunneling on Quantum Graphs

Presenter: **
****Pavel Exner**, Theor. Physics, Czech Academy of Science, Prague

Date: Tuesday, April 2, 2002, Time: 4:30 p.m., Location: Jadwin A06

*Department
Colloquium*

Topic: Evolution of Language

Presenter: **
****Stephen Smale,** University of California at Berkeley

Date: Wednesday, April 3, 2002, Time: 4:30 p.m., Location: Fine Hall 314

Abstract: A mathematical model is presented which helps to understand how languages are formed. A theorem in this setting is the convergence to a common language under a hypothesis on linguistic encounters.

__April
8 - 12__

*Analysis Seminar*

Topic: TBA

Presenter: **
****Diego Cordoba**, Princeton University

Date: Monday, April 8, 2002, Time: 4:00 p.m., Location: Fine Hall 314

*Algebraic
Geometry Seminar*

Topic: TBA

Presenter:
**Joseph Silverman**, Brown University

Date: Tuesday, April 9, 2002, Time: 4:30 p.m., Location: Fine Hall 314

*Department
Colloquium*

Topic: TBA

Presenter: **
****Michael Rabin,** Harvard University

Date: Wednesday, April 10, 2002, Time: 4:30 p.m., Location: Fine Hall 314

*Joint
Princeton University/IAS/Rutgers Non-Linear Analysis Seminar *

Topic: $L_p$-bounds on curvature and rectifiability of singular setsy

Presenter: **
****Jeff Cheeger**, Courant Instititue, NYU

Date: Thursday, April 11, 2002, Time: 4:00, Location: Fine Hall 214

*Princeton
University/IAS Number Theory Seminar *

Topic: Galois groups and geometry of modular varieties

Presenter: **
****Alexander Goncharov**, Brown University

Date: Thursday, April 11, 2002, Time: 4:30, Location: TBA

*Geometric
Analysis Seminar*

Topic: TBA

Presenter: **
****Rina Rotman**, University of Toronto and the Courant Institute of
Mathematics

Date: Friday, April 12, 2002, Time: 3:00 p.m., Location: Fine Hall 314

__April
15 - 19__

*PACM
Colloquium*

Topic: TBA

Presenter: **
Christodolous Floudas**, Chemical Engineering, Princeton University

Date: Monday, April 15, 2002, Time: 4:00 p.m., Location: Fine Hall 214

*Algebraic
Geometry Seminar*

Topic: TBA

Presenter:
**Alexander Braverman**, Harvard University

Date: Tuesday, April 16, 2002, Time: 4:30 p.m., Location: Fine Hall 314

*Mathematical
Physics Seminar *** Please note change in date from
March 19, 2002*

Topic: TBA

Presenter: **
Jakob Yngvason**, University of Vienna

Date: Tuesday, April 16, 2002, Time: 4:30 p.m., Location: Jadwin A06

*Geometric
Analysis Seminar*

Topic: Bifurcations of $J$-holmorphic maps

Presenter: **
Tom Parker**, Michigan State University and the Institute for Advanced Study

Date: Friday, April 19, 2002, Time: 3:00 p.m., Location: Fine Hall 314

__April
22 - 26__

*Analysis Seminar*

Topic: The lost proof of Loewner's theorem

Presenter: **
****Barry Simon**, Caltech

Date: Monday, April 22, 2002, Time: 4:00 p.m., Location: Fine Hall 314

Abstract: A real-valued function, F, on an interval (a,b) is called matrix monotone if F(A) < F(B) whenever A and B are finite matrices of the same order with eigenvalues in (a,b) and A < B. In 1934, Loewner proved the remarkable theorem that F is matrix monotone if and only if F is real analytic with continuations to the upper and lower half planes so that Im F > 0 in the upper half plane. This deep theorem has evoked enormous interest over the years and a number of alternate proofs. There is a lovely 1954 proof that seems to have been "lost" in that the proof is not mentioned in various books and review article presentations of the subject, and I have found no references to the proof since 1960. The proof uses continued fractions. I'll provide background on the subject and then discuss the lost proof and a variant of that proof which I've found, which avoids the need for estimates, and proves a stronger theorem.

*PACM
Colloquium*

Topic: TBA

Presenter: ** ****Ken Church**,
AT&T Labs - Research

Date: Monday, April 22, 2002, Time: 4:00 p.m., Location: Fine Hall 214

__April
29 -May 3__

*PACM
Colloquium*

Topic: TBA

Presenter: ** ****Herb Keller**,
California Institute of Technology

Date: Monday, April 29, 2002, Time: 4:00 p.m., Location: Fine Hall 214

*Princeton
University/IAS Number Theory Seminar *

Topic: TBA

Presenter: **
****Brooks Roberts**, University of Idaho

Date: Thursday, May 2, 2002, Time: 4:30, Location: TBA