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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. | |
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. | |
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 | |
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. | |
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 | |
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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Joint Institute for Advanced Study /Princeton University/ Rutgers University Number Theory Seminar | ||
*** 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 | |
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. | |
Joint Institute for Advanced Study /Princeton University/ Rutgers University Number Theory Seminar | ||
*** 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.) | |
Special Joint Institute for Advanced Study/Princeton University/Rutgers University Number Theory Seminar | ||
** 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. | |
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. | |
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. | |
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. | |
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. | |
Joint Institute for Advanced Study /Princeton University/ Rutgers University Number Theory Seminar | ||
*** 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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Algebraic Geometry Seminar | ||
Topic: | TBA | |
Presenter: | B. Guralnick | |
Date: | Tuesday, May 13, 2003, Time: 4:30 p.m., Location: Fine Hall 322 | |