As
of March 6
- 8
Department Colloquium **** COLLOQUIUM HAS BEEN POSTPONED ****
Topic: TBA
Presenter: Ingrid Daubchies, Princeton University
Date:
Wednesday, March 6, 2002, Time: 4:30 p.m., Location: Fine Hall 314
Discrete Mathematics Seminar *** Please note change in speaker
Topic: Counting Sumfree Sets
Presenter: Ben Green, Cambridge 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.)
Graduate Student Seminar
Topic: Interval exchange transformations and the Teichmueller flow
Presenter: Alexander I. Bufetov, Princeton University
Date: Friday, March 8, 2002, Time: 1:00 p.m., Location: Fine Hall 1001
Abstract:
Assume we take an interval, cut it into a finite number of subintervals,
perhaps of different lengths, then permute these subintervals. We obtain
in this fashion a map of the original interval into itself, called an interval
exchange transformation; it clearly preserves the Lebesgue measure; for
example, an exchange of two intervals is a circle rotation. First
results on ergodic behaviour of interval exchange transformations were
obtained by V. I. Oseledets (finite multiplicity of the spectrum - 1966).
In 1982 H. Masur and W. Veech, proved (independently and simultaneously)
that almost all interval exchange transformations admit of no invariant
probability measure other than Lebesgue (unique ergodicity; conjectured
by Keane in 1975). In that study, H. Masur discovered a beautiful relationship
between the behaviour of interval exchanges and the Teichmueller flow,
that is, the geodesic flow on the moduli space of closed surfaces. In the
talk, I shall give the main ideas of the papers of Masur and Veech.
More recently, A. Zorich, A. Zoriuch and M. Kontsevich, and G. Forni have
studied the Lyapunov spectrum of the Teichmueller flow and its relationship
to the decay of correaltions for interval exchanges; if time permits, I
shall speak about these results as well. The talk would strive to
be elementary, self-contained and accessible to undergraduate students;
it would presuppose no knowledge of either ergodic or Teichmueller theory.
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
CR Seminar
Topic: Stanton's paper on the heat equation and pseudo-conformal invariants
Presenter: Howard Jacobowitz, Rutgers University
Date:
Tuesday, March 12, 2002, Time: 4:00 p.m., Location: Fine Hall 401
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
Ergodic Theory and Statistical Analysis Seminar
Topic: Topological shocks and Lagrangian minimizers
Presenter: Konstantin Khanin, Newton Institute, Cambridge
Date:
Thursday, March 14, 2002, Time: 2:00 p.m., Location: Fine Hall 601
Joint Princeton University/IAS/Rutgers University 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
Joint Princeton University/Rutgers University Topology Seminar
Topic: Aspects of rigidity for mapping class groups and automorphism groups of free groups
Presenter: Martin Bridson, Imperial College London/Columbia
Date:
Thursday, March 14, 2002, Time: 4:00 p.m.,
Location: Fine Hall 314
Princeton University/IAS Number Theory Seminar
Topic: Pro-l birational anabelian geometry
Presenter: Florian Pop, University of Bonn and the Institute for Advanced Study
Date: Thursday, March 14, 2002, Time: 4:30, Location: IAS SH-101
Abstract:
The ``yoga'' of anabelian geometry is that under certain ``anabelian hypothesis''
arithmetic and geometry are encoded in Galois theory. There are mainly
two points of view: The functorial one and the constructive one. We will
explain how an infinite finitely generated field is ``encoded'' in its
pro-l Galois theory; hence, how it can be reconstructed from its pro-l
Galois theory (where l is a prime different from the characteristic).
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 University 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
Ergodic Theory and Statistical Analysis Seminar
Topic: Strange nonchaotic attractors
Presenter: Arkady Pikovsky, Universitat Potsdam
Date: Thursday, March 28, 2002, Time: 2:00 p.m., Location: Fine Hall 601
Abstract:
I discuss states that appear in nonlinear quasiperiodically forced systems
and are from one hand non-chaotic (the largest Lyapunov exponent is negative)
and from another hand are fractal objects. Two approaches to characterize
these sets are discussed: one is based on the rational approximations of
the quasiperiodic forcing, another is based on the calculation of finite-time
Lyapunov exponents. I show that in some cases the strange nonchaotic attractors
have singular continuous spectra. Several situations are described,
where the onset of strange nonchaotic attractors can be characterized vie
the renormalization group method.
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.
Ergodic Theory and Statistical Analysis Seminar
Topic: Bernoulli diffeomorphisms with non-zero exponents on any manifold
Presenter: Yakov Pesin, Penn State University
Date: Thursday, April 4, 2002, Time: 2:00 p.m., Location: Fine Hall 601
Abstract:
In the talk I will describe a solution of a long-standing problem to construct
a Bernoulli diffeomorphism with nonzero Lyapunox exponents on any compact
smooth Riemannian manifold.
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 University 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
Mathematical Physics Seminar
Topic: Sum Rules and Spectral Properties of Jacobi Matrices
Presenter: Barry Simon, Caltech
Date:
Tuesday, April 23, 2002, Time: 4:30 p.m., Location: Jadwin A06
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