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OCTOBER 2010 |
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Statistical Mechanics Seminar |
Topic: |
Characterization of Lee-Yang polynomials |
Presenter: |
David Ruelle, IHES, France |
Date: |
Wednesday, October 27, 2010, Time: 2:00 p.m., Location: Jadwin Hall 343 |
Abstract: |
I shall give a characterization of the multi-affine polynomials in n variables that occur in the proof of the Lee-Yang Circle Theorem. In particular, it will be seen that the spin interactions for which the Circle Theorem holds at all temperatures must be the ferromagnetic pair interactions originally considered by Lee and Yang (i.e., for non-pair interactions, the theorem fails at some temperature!). |
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Discrete Mathematics Seminar |
Topic: |
Unbalanced Allocations |
Presenter: |
Amanda Redlich, Rutgers University |
Date: |
Thursday, October 28, 2010, 2010, Time: 2:15 p.m., Location: Fine Hall 224 |
Abstract: |
Recently, there has been much research on processes that are mostly random, but also have a small amount of deterministic choice; e.g., Achlioptas processes on graphs. This talk builds on the balanced allocation algorithm first described by Azar, Broder, Karlin and Upfal. Their algorithm (and its relatives) uses randomness and some choice to distribute balls into bins in a balanced way. Here is a description of the opposite family of algorithms, with an analysis of exactly how unbalanced the distribution can become. |
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Algebraic Topology Seminar |
Topic: |
Algebraic structures from operads and moduli spaces |
Presenter: |
Ralph Kaufmann, IAS |
Date: |
Thursday, October 28, 2010, Time: 3:00 p.m., Location: Fine Hall 322 |
Abstract: |
Some classical algebraic structures like Gerstenhaber's bracket on the Hochschild complex have an operadic origin. We discuss generalizations of these operations coming from different operadic type settings. This includes geometric constructions from moduli spaces and master equations appearing in string topology and in a "pedestrian" version of string field theory. |
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Joint Princeton University and IAS Number Theory Seminar |
Topic: |
Constructing Abelian varieties over Qbar not isogenous to a Jacobian |
Presenter: |
Jacob Tsimerman, Princeton University |
Date: |
Thursday, October 28, 2010, Time: 4:30 p.m., Location: Fine Hall 314 |
Abstract: |
We discuss the following question of Nick Katz and Frans Oort: Given an Algebraically closed field K, is there an Abelian variety over K of dimension g which is not isogenous to a Jacobian? For K the complex numbers its easy to see that the answer is yes for g>3 using measure theory, but over a countable field like Qbar new methods are required. Building on work of Chai-Oort, we show that, as expected, such Abelian varieties exist for K=Qbar and g>3. We will explain the proof as well as its connection to the Andre Oort conjecture. |
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Topology Seminar |
Topic: |
Fox re-embedding and Bing submanifolds |
Presenter: |
Kei Nakamura, Temple University |
Date: |
Thursday, October 28, 2010, Time: 4:30 p.m., Location: Fine Hall 314 |
Abstract: |
Let M be an orientable closed connected 3-manifold, and Y be a connected compact 3-manifold. We show that the following two conditions are equivalent: (i) Y can be embedded in M so that the closure of the complement of the image of Y is a union of handlebodies; and (ii) Y can be embedded in M so that every embedded closed loop in M can be isotoped to lie within the image of Y. Our result can be regarded as a common generalization of Fox's reimbedding theorem (1948) and Bing's characterization of 3-sphere (1958), as well as more recent results of Hass and Thompson (1989) and Kobayashi and Nishi (1994). |
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Differential Geometry and Geometric Analysis Seminar |
Topic: |
TBA |
Presenter: |
Jie Qing, UC Santa Cruz |
Date: |
Friday, October 29, 2010, Time: 3:00 p.m., Location: Fine Hall 314 |
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Ergodic Theory and Statistical Mechanics Seminar *** Please note special date and time*** |
Topic: |
Diffusive or superdiffusive asymtotics for periodic and non-periodic Lorentz processes |
Presenter: |
Domokos Szasz, Budapest University of Technology and Economics |
Date: |
Friday, October 29, 2010, Time: 3:00 p.m., Location: Fine Hall 401 |
Abstract: |
After the first success in establishing the diffusive, Brownian limit of planar, finite-horizon, periodic Lorentz processes, in 1981 Sinai turned the interest toward studying models when periodicity is hurt, in particular, to locally perturbed Lorentz processes. The 1981 solution for a random-walk-model - by Telcs and the speaker - only led in 2009 to that for the locally perturbed, finite-horizon Lorentz process (by Dolgopyat, Varju and the present author). Beside reporting on these results we also analyze the first steps in extending the limits obtained for the periodic Lorentz process to locally perturbed periodic or quasi-periodic ones (results by Nandori, Paulin, Varju and the speaker). |
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NOVEMBER 2010 |
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Analysis Seminar |
Topic: |
TBA |
Presenter: |
Natasa Pavlovic, University of Texas at Austin |
Date: |
Monday, November 8, 2010, Time: 4:00 p.m., Location: Fine Hall 314 |
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PACM Colloquium |
Topic: |
Novel Phenomena and Models of Active Fluids |
Presenter: |
Michael Shelley, Courant Institute |
Date: |
Monday, November 8, 2010, Time: 4:00 p.m., Location: Fine Hall 214 |
Abstract: |
Fluids with suspended microstructure - complex fluids - are common actors in micro- and biofluidics applications and can have fascinating dynamical behaviors. A new area of complex fluid dynamics concerns "active fluids" which are internally driven by having dynamic microstructure such as swimming bacteria. Such motile suspensions are important to biology, and are candidate systems for tasks such as microfluidic mixing and pumping. To understand these systems, we have developed both first-principles particle and continuum kinetic models for studying the collective dynamics of hydrodynamically interacting microswimmers. The kinetic model couples together the dynamics of a Stokesian fluid with that of an evolving "active" stress field. It has a very interesting analytical and dynamical structure, and predicts critical conditions for the emergence of hydrodynamic instabilities and fluid mixing. These predictions are verified in our detailed particle simulations, and are consistent with current experimental observation. |
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Algebraic Geometry Seminar |
Topic: |
4-dimensional symplectic holomorphic contractions |
Presenter: |
Marco Andreatta, Trento |
Date: |
Tuesday, November 9, 2010, Time: 4:30 p.m., Location: Fine Hall 322 |
Abstract: |
In the talk I will consider birational projective morphisms from smooth holomorphic symplectic fourfolds into affine normal varieties. The ultimate goal will be to classify such maps. For the moment I can present special features of them and discuss some important examples. |
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Mathematical Physics Seminar |
Topic: |
TBA |
Presenter: |
Clément Hongler, Columbia University |
Date: |
Tuesday, November 9, 2010, Time: 4:30 p.m., Location: Jadwin 343 |
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Statistical Mechanics Seminar |
Topic: |
Bethe-Ansatz for the two species totally asymmetric diffusion model |
Presenter: |
Birgit Kauffmann, Purdue University |
Date: |
Wednesday, November 10, 2010, Time: 2:00 p.m., Location: Jadwin Hall 343 |
Abstract: |
We study the two species asymmetric diffusion model that describes two species and vacancies diffusing asymmetrically on a one-dimensional lattice. Our method is the algebraic Bethe Ansatz. We will explain this technique which we use to find the finite-size scaling behavior of the lowest lying eigenstates of the quantum Hamiltonian describing the model. This allows us to extract the dynamical critical exponent. |
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Department Colloquium |
Topic: |
Metaphors in systolic geometry |
Presenter: |
Larry Guth, Toronto University |
Date: |
Wednesday, November 10, 2010, Time: 4:30 p.m., Location: Fine Hall 314 |
Abstract: |
The systolic inequality says that any Riemannian metric on an n-dimensional torus with volume 1 contains a non-contractible closed curve with length at most C(n) - a constant depending only on n. One remarkable feature of the inequality is it holds for such a wide class of metrics. It's much more general than an inequality that holds for all metrics obeying a certain curvature condition.
The systolic inequality is a difficult theorem, and each proof is guided by a metaphor that connects the systolic inequality to a different area of geometry or topology. In this talk, I will explain three metaphors. They connect the systolic inequality to minimal surface theory, topological dimension theory, and scalar curvature. |
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Symplectic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Ralph Kaufmann, Perdue University |
Date: |
Thursday, November 11, 2010, Time: 1:30 p.m., Location: Fine Hall 601 |
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Ergodic Theory and Statistical Mechanics Seminar |
Topic: |
TBA |
Presenter: |
Percy Wong, Princeton University |
Date: |
Thursday, November 11, 2010, Time: 2:00 p.m., Location: Fine Hall 401 |
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Discrete Mathematics Seminar |
Topic: |
TBA |
Presenter: |
Oleg Pikhurko, Carnegie Mellon |
Date: |
Thursday, November 11, 2010, Time: 2:15 p.m., Location: Fine Hall 224 |
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Princeton University and IAS Number Theory Seminar |
Topic: |
Periods of special cycles and derivatives of L-series |
Presenter: |
Shou-Wu Zhang, Columbia University |
Date: |
Thursday, November 11, 2010, Time: 4:30 p.m., Location: Fine Hall 214 |
Abstract: |
In this talk, I will state some conjectures and examples concerning the central derivatives of automorphic L-series in terms of heights of special cycles on Shimura varieties. |
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Topology Seminar |
Topic: |
Transverse homology |
Presenter: |
Lenny Ng, Duke University |
Date: |
Thursday, November 11, 2010, Time: 4:30 p.m., Location: Fine Hall 314 |
Abstract: |
Knot contact homology is a combinatorial Floer-theoretic knot invariant derived from Symplectic Field Theory. I'll discuss the geometry behind this invariant and a new filtered version, transverse homology, which turns out to be a fairly effective invariant of transverse knots |
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Differential Geometry and Geometric Analysis Seminar |
Topic: |
TBA |
Presenter: |
Olivaine De Queiroz, Universidade Estadual De Campinas |
Date: |
Friday, November 12, 2010, Time: 3:00 p.m., Location: Fine Hall 314 |
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PACM Colloquium |
Topic: |
A New Formalism for Electromagnetic Scattering in Complex Geometry |
Presenter: |
Leslie Greengard, Courant Institute |
Date: |
Monday, November 15, 2010, Time: 4:00 p.m., Location: Fine Hall 214 |
Abstract: |
We will describe some recent, elementary results in the theory of electromagnetic scattering in R3. There are two classical approaches that we will review - one based on the vector and scalar potential and applicable in arbitrary geometry, and one based on two scalar potentials, due to Lorenz, Debye and Mie, valid only in the exterior (or interior) of a sphere. In extending the Lorenz-Debye-Mie approach to arbitrary geometry, we have encountered some new mathematical questions involving differential geometry, partial differential equations and numerical analysis. This is joint work with Charlie Epstein. |
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Algebraic Geometry Seminar |
Topic: |
Around the Tate conjecture with integral coefficients |
Presenter: |
Tamás Szamuely, Hungarian Academy and University of Pennsylvania |
Date: |
Tuesday, November 16, 2010, Time: 4:30 p.m., Location: Fine Hall 322 |
Abstract: |
Due to the analogy with the Hodge conjecture, it has been known for a long time that the Tate conjecture for algebraic cycles on varieties over finite fields does not hold if one considers the cycle map into \'etale cohomology with Z_\ell-coefficients. Still, some cases may be expected to hold and they have interesting consequences. We shall explain some of the negative and positive results. |
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Statistical Mechanics Seminar |
Topic: |
Critical velocites in rotating Bose gases |
Presenter: |
Jakob Yngvason, University of Vienna |
Date: |
Wednesday, November 17, 2010, Time: 2:00 p.m., Location: Jadwin Hall 343 |
Abstract: |
Some of the remarkable phenomena that emerge when a trapped, ultracold Bose gas is set in rapid rotational motion will be reviewed. In anharmonic traps, where the rotational velocity can in principle be arbitrarily large, one can distinguish three critical velocities at which the flow pattern changes radically. The first is the velocity at which vorticity sets in, eventually leading to a lattice of vortices, at the second a 'hole' is created and the condensate becomes concentrated in an annulus while the vortex lattice persists in the bulk, and at the third a transition to a 'giant vortex' state takes place in which all vorticity disappears from the bulk but a macroscopic circulation around the hole remains.
The mathematical model used for analysis of these phenomena has similarities with Ginzburg-Landau (GL) Theory in superconductivity with the critical velocities in rotating gases playing an analogous role to the critical magnetic fields in GL theory, and techniques originally developed in the context of GL theory have, indeed, been important for understanding rotating gases. There are, however, also important differences, and in particular the theory of the giant vortex transition requires significant modifications of the GL setting. Theses similarities and differences will be discussed. (Joint work with Michele Correggi and Nicoals Rougerie.) |
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Department Colloquium |
Topic: |
Acoustical spacetime geometry and shock formation |
Presenter: |
Demetri Christodoulou, ETH |
Date: |
Wednesday, November 17, 2010, Time: 4:30 p.m., Location: Fine Hall 314 |
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Symplectic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Sean T. Paul, University of Wisconsin Madison |
Date: |
Thursday, November 18, 2010, Time: 1:30 p.m., Location: Fine Hall 601 |
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Ergodic Theory and Statistical Mechanics Seminar |
Topic: |
TBA |
Presenter: |
Percy Wong, Princeton University |
Date: |
Thursday, November 18, 2010, Time: 2:00 p.m., Location: Fine Hall 401 |
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Discrete Mathematics Seminar |
Topic: |
TBA |
Presenter: |
Noga Alon, Tel-Aviv University and IAS |
Date: |
Thursday, November 18, 2010, Time: 2:15 p.m., Location: Fine Hall 224 |
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Princeton University and IAS Number Theory Seminar |
Topic: |
TBA |
Presenter: |
Tasho Kaletha, Princeton University and IAS |
Date: |
Thursday, November 18, 2010, Time: 4:30 p.m., Location: IAS S-101 |
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Topology Seminar |
Topic: |
TBA |
Presenter: |
Igor Rivin, Temple University |
Date: |
Thursday, November 18, 2010, Time: 4:30 p.m., Location: Fine Hall 314 |
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Differential Geometry and Geometric Analysis Seminar |
Topic: |
Laplace eigenvalues via asymptotic separation of variables |
Presenter: |
Chris Judge, Indiana University |
Date: |
Friday, November 19, 2010, Time: 3:00 p.m., Location: Fine Hall 314 |
Abstract: |
We study the behavior of eigenvalues under geometric perturbations using a method that might be called asymptotic separation of variables. In this method, we use quasi-mode approximations to compare the eigenvalues of a warped product and another metric that is asymptotically close to a warped product. As one application, we shoe that the generic Euclidean triangle has simple Laplace spectrum. This is joint work with Luc Hillairet. |
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Analysis Seminar |
Topic: |
TBA |
Presenter: |
Vincent Moncrief, Yale University |
Date: |
Monday, November 22, 2010, Time: 4:00 p.m., Location: Fine Hall 314 |
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PACM Colloquium |
Topic: |
Wavelet Frames and Applications |
Presenter: |
Zuowei Shen, National University of Singapore |
Date: |
Monday, November 22, 2010, Time: 4:00 p.m., Location: Fine Hall 214 |
Abstract: |
This talk focuses on the tight wavelet frames derived from multiresolution analysis and their applications in imaging sciences. One of the major driven forces in the area of applied and computational harmonic analysis over the last two decades is to develop and understand redundant systems that have sparse approximations of different classes of functions. Such redundant systems include wavelet frame, ridgelet, curvelet, shearlet and so on. In this talk, we will first give a brief survey on the development of the unitary extension principle and its generalizations. The unitary extension principle and its extensions give systematical constructions of wavelet frames from multiresolution analysis that can be used in various problems in imaging science. Then we will focus on applications of wavelet frames. Especially, we will discuss frame based image analysis and restorations, which includes image inpainting, image denosing, image deblurring and blind deblurring, image decomposition, and image segmentation. |
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Analysis Seminar |
Topic: |
TBA |
Presenter: |
Colin Guillarmou, Universite de Nice Sophia-Antipolis |
Date: |
Monday, November 29, 2010, Time: 4:00 p.m., Location: Fine Hall 314 |
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DECEMBER 2010 |
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Department Colloquium |
Topic: |
Natural maps old and new |
Presenter: |
Gerard Besson, Grenoble |
Date: |
Wednesday, December 1, 2010, Time: 4:30 p.m., Location: Fine Hall 314 |
Abstract: |
In 1995, G. Courtois, S. Gallot and myself constructed a family of maps with very good properties regarding volume elements between certain manifolds. We used it to give an alternative proof of Mostow's rigidity for rank one closed symmetric spaces as well as a rigidity result for their geodesic flow, conjectured by A. Katok. Various modifications of the original construction have been made since yielding new results in different settings. We shall describe the basic construction, the modifications, some applications and open questions. |
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Ergodic Theory and Statistical Mechanics Seminar |
Topic: |
TBA |
Presenter: |
Zhiren Wang
, Princeton University |
Date: |
Thursday, December 2, 2010, Time: 2:00 p.m., Location: Fine Hall 401 |
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Princeton University and IAS Number Theory Seminar |
Topic: |
TBA |
Presenter: |
Christopher Skinner, Princeton University and IAS |
Date: |
Thursday, December 2, 2010, Time: 4:30 p.m., Location: Fine Hall 214 |
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Topology Seminar |
Topic: |
TBA |
Presenter: |
Sa'ar Hersonsky, University of Georgia |
Date: |
Thursday, December 2, 2010, Time: 4:30 p.m., Location: Fine Hall 314 |
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Differential Geometry and Geometric Analysis Seminar |
Topic: |
TBA |
Presenter: |
Gilles Courtois, École/ Polytechnique/ |
Date: |
Friday, December 3, 2010, Time: 3:00 p.m., Location: Fine Hall 314 |
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PACM Colloquium |
Topic: |
Diffusions Interacting Through Their Ranks, and the Stability of Large Equity Markets |
Presenter: |
Ioannis Karatzas, Columbia University |
Date: |
Monday, December 6, 2010, Time: 4:00 p.m., Location: Fine Hall 214 |
Abstract: |
We introduce and study ergodic multidimensional diusion processes interacting through their ranks. These interactions give rise to invariant measures which are in broad agreement with stability properties observed in large equity markets over long time-periods. The models we develop assign growth rates and variances that depend on both the name (identity) and the rank (according to capitalization) of each individual asset. Such models are able realistically to capture critical features of the observed stability of capital distribution over the past century, all the while being simple enough to allow for rather detailed analytical study. The methodologies used in this study touch upon the question of triple points for systems of interacting diusions; in particular, some choices of parameters may permit triple (or higher-order) collisions to occur. We show, however, that such multiple collisions have no eect on any of the stability properties of the resulting system. This is accomplished through a detailed analysis of intersection local times. The theory we develop has connections with the analysis of Queueing Networks in heavy traffic, as well as with models of competing particle systems in Statistical Mechanics, such as the Sherrington-Kirkpatrick model for spin-glasses. |
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Princeton University and IAS Number Theory Seminar |
Topic: |
TBA |
Presenter: |
Benedict Gross, Harvard University |
Date: |
Thursday, December 9, 2010, Time: 4:30 p.m., Location: IAS S-101 |
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Algebraic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Izzet Coskun, UIC |
Date: |
Tuesday, December 14, 2010, Time: 4:30 p.m., Location: Fine Hall 322 |
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Joint Princeton University and IAS Number Theory Seminar |
Topic: |
TBA |
Presenter: |
Henryk Iwaniec, Rutgers University |
Date: |
Thursday, December 16, 2010, Time: 4:30 p.m., Location: Fine Hall 214 |
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Topology Seminar |
Topic: |
TBA |
Presenter: |
Andy Cotton-Clay, Harvard University |
Date: |
Thursday, December 16, 2010, Time: 4:30 p.m., Location: Fine Hall 314 |
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