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APRIL 29 - MAY 2, 2003
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| Special
Topology Seminar *** Please note special time, date, and location |
| Topic: |
Report on Andrew Casson's Arkansas
Lectures |
| Presenter: |
Baris Coskunuzer, Princeton
University & Ken Baker, University of Texas at Austin |
| Date: |
Tuesday,
April 29, 2003, Time: 4:00 p.m., Location:
Fine
Hall 110 |
| Abstract: |
We will present Casson's reformulations
of the Andrews - Curtis and Poincaré Conjectures. |
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| Algebraic
Geometry Seminar |
| Topic: |
Near by fundamental group of
Mumford Tate curves |
| Presenter: |
Tomohide
Terasoma, Institute for Advanced Study |
| Date: |
Tuesday, April 29, 2003, Time:
4:30 p.m., Location: Fine Hall 322 |
| Abstract: |
We will study a problem of R.Hain.
The main result says that the period of the arithmetic mapping class group
can be written using multiple zeta values. A similar Galois theoretic result
was obtained by Ihara-Nakamura. |
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| Discrete Mathematics
Seminar |
| Topic: |
The exact Turan number of the
Fano plane |
| Presenter: |
Peter Keevash, Princeton
University |
| Date: |
Wednesday, April 30, 2003, Time:
2:15 p.m., Location: Fine Hall 314 |
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| Department
Colloquium |
| Topic: |
Random walks in a random environment |
| Presenter: |
S.R.Srinivasa Varadhan,
New York University |
| Date: |
Wednesday, April 30, 2003, Time:
4:30 p.m., Location: Fine Hall 314 |
| Abstract: |
We will discuss results on the
large deviation behavior of Random Walks in a Random Environment. These
concern the quenched walk that have an almost sure large deviation
behavior and the averaged walk that exhibits a large deviation behavior
that could be partly due to large deviations in the environment itself.
The quenched case has connections to homogenization of random Hamilton
Jacobi equations with small viscosity. |
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| Joint
Institute for Advanced Study /Princeton University/ Rutgers University
Number Theory Seminar |
| Topic: |
Counting number fields of bounded
discrminant |
| Presenter: |
Jordan Ellenberg, Princeton
University |
| Date: |
Thursday, May 1, 2003, Time:
4:15 p.m., Location: Fine Hall 322 |
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| Topology Seminar
*** Please note - rescheduled from April 3, 2003 |
| Topic: |
One parameter families of Calabi-Yau
threefolds |
| Presenter: |
John Morgan, Columbia
University |
| Date: |
Thursday, May 1, 2003, Time:
4:30 p.m., Location: Fine Hall 314 |
| Abstract: |
There are lots of examples of
one-parameter families of Calabi-Yau threefolds occurring as hypersurfaces
or complete intersections in toric varieties. We study the resulting variations
of Hodge structure from these families and compare the results to all possible
variations and to various conjectures arising out of mirror symmetry conjectures. |
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MAY 5 - MAY 9, 2003
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| Joint
Institute for Advanced Study /Princeton University/ Rutgers University
Number Theory Seminar |
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Please note special day and time *** |
| Topic: |
Non tempered A packets of G_2 |
| Presenter: |
Nadya Gurevich, Princeton
University |
| Date: |
Monday,
May 5, 2003, Time: 3:00 p.m., Location:
Fine Hall 322 |
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| Analysis
Seminar |
| Topic: |
Combinatorics of distance sets
and applications |
| Presenter: |
Alex Iosevich, University
of Missouri at Columbia |
| Date: |
Monday, May 5, 2003, Time: 4:00
p.m., Location: Fine Hall 314 |
| Abstract: |
Let $E$ be a subset of ${\Bbb
R}^d$ and let $\Delta(E)=\{|x-y|: x,y \in E\}$, the distance set. It is
well-known that information about $E$ can be used to deduce estimates on
$\Delta(E)$, and vice-versa, in both the discrete and continious settings.
We will discuss some recent results of this type and applications to problems
in harmonic analysis and geometric combinatorics. |
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| Joint
Institute for Advanced Study /Princeton University/ Rutgers University
Number Theory Seminar |
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Please note special day and time *** |
| Topic: |
Horocycles and equidistribution |
| Presenter: |
Andreas Strombergsson,
Princeton University |
| Date: |
Monday,
May 5, 2003, Time: 4:15 p.m., Location:
Fine Hall 322 |
| Abstract: |
I will discuss some questions
regarding equidistribution and rates of convergence of ergodic averages
in the setting of the horocycle flow on the unit tangent bundle of a non-compact
hyperbolic surface of finite area. One of the problems which I will
discuss is related to the pair correlation density of the sequence
$n^2 a$ modulo one. (Joint work with Jens Marklof.) |
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| Special
Joint Institute for Advanced Study/Princeton University/Rutgers University
Number Theory Seminar |
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Please note special day, time, and location *** |
| Topic: |
Maximal p-extensions of Q with
restricted ramification |
| Presenter: |
Helmut Koch, Humboldt
University, Berlin |
| Date: |
Tuesday,
May 6, 2003, Time: 2:00 p.m., Location:
Fine
Hall 110 |
| Abstract: |
Let p be a prime, K an algebraic
number field and S a finite set of places of K. Then K_S denotes
the maximal p-extension unramified outside S. The Galois group G_S
of K_S/K is a pro-p-group with finitely many generators and relations.
Subject of the talk is the finer structure of G_S mostly in the case of
K=\mathbb{Q}. After an historical introdution, we explain recent
results of Boston, Leedham-Green, Eick and the speaker. |
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| Department
Colloquium |
| Topic: |
The lost proof of Loewner's theorem |
| Presenter: |
Barry Simon, Caltech |
| Date: |
Wednesday, May 7, 2003, Time:
4:30 p.m., Location: Fine Hall 314 |
| Abstract:
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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. |
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| Ergodic
Theory and Statistical Analysis Seminar |
| Topic: |
Aggregation of inertial particles
in turbulent flows |
| Presenter: |
Jérémie Bec,
Institute
for Advanced Study |
| Date: |
Thursday, May 8, 2003, Time:
2:30 p.m., Location: Fine Hall 214 |
| Abstract: |
The clustering properties of
inertial (finite-size) particle suspensions in an incompressible turbulent
flow play an essential role in the understanding of many natural and industrial
problems, such as optimization of combustion processes, the growth of rain
droplets in turbulent clouds, the formation of planetesimals of the Solar
System, co-existence between several species of plankton. We consider
the motion of collisionless inertial particles embedded in a d-dimensional
smooth incompressible flow. This system is governed by a 2d-dimensional
dissipative dynamical system in the position-velocity phase space, so that
the phase-space density becomes singular in the statistical steady state.
I will demonstrate that there exists a threshold in Stokes number (non-dimensional
viscous friction time) for the condensation of the particles onto dynamical
fractal clusters in the physical space. This result was confirmed by numerical
studies which gave also some hints on the scaling properties of the multifractal
distribution for the mass of particles. Finally, I will show how these
properties can be related to the large deviations of the finite-time Lyapunov
exponents. |
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| Mathematical
Physics Seminar *** Please note special
date and time |
| Topic: |
A Canonical Factorization for
Meromorphic Herglotz Functions on the Disk and a Proof of the Jacobi Matrix
P2 Sum Rule on One Foot |
| Presenter: |
Barry Simon, Caltech |
| Date: |
Thursday,
May 8, 2003, Time: 1:30 p.m., Location:
Jadwin A06 |
| Abstract: |
Last year Killip and Simon provided a complete
description of the spectral measure associated to Jacobi matrices with
L2 potentials. I will present a simple proof of their result that
relies on two elements: an analysis of the general form of meromorphic
Herglotz functions on the disk and the upper semicontinuity of the entropy.
I'll begin by describing the general issue of the spectral and inverse
spectral problems for Jacobi matrices, the significance of the P2 sum rule,
then the canonical factorization and then the proof of the P2 sum rule. |
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| Joint
Institute for Advanced Study /Princeton University/ Rutgers University
Number Theory Seminar |
| Topic: |
Small gaps between primes |
| Presenter: |
Dan Goldston, San Jose
State University |
| Date: |
CANCELLEDThursday,
May 8, 2003, Time: 4:15 p.m., Location: Fine Hall 322 |
| Abstract: |
This talk will discuss
the main new idea behind the proof that there are infinitely many primes
much closer together than the average spacing between primes, and how this
idea was discovered. A sketch of the proof will be given. This is joint
work with C. Yalcin Yildirim. |
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| Joint
Institute for Advanced Study /Princeton University/ Rutgers University
Number Theory Seminar |
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Please note special day and time *** |
| Topic: |
Recent Developments Related to
Prime Gaps |
| Presenter: |
Dan Goldston, San Jose
State University |
| Date: |
CANCELLED
Friday, May 9, 2003, Time: 2:00 p.m.,
Location: Fine Hall 322 |
| Abstract: |
This talk will discuss
improvements in the method for detecting small gaps between primes made
by a number of people in the last two months, and problems that still need
to be examined. |
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MAY 12 - MAY 16, 2003
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| Algebraic
Geometry Seminar |
| Topic: |
TBA |
| Presenter: |
B.
Guralnick |
| Date: |
Tuesday, May 13, 2003, Time:
4:30 p.m., Location: Fine Hall 322 |
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