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NOVEMBER 2010 |
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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: |
Guanbo Xu, Princeton 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: |
A survey of results in universality of Wigner matrices, Part I |
Presenter: |
Percy Wong, Princeton University |
Date: |
Thursday, November 11, 2010, Time: 2:00 p.m., Location: Fine Hall 401 |
Abstract: |
In the 1950's, Wigner proved the famous semicircle laws for Wigner matrices and started the study of universality results in random matrices. In these two talks, this will serve as our starting point as we surveyed the historical developments in this field. We will end with a discussion of the proof of the local semicircle law of Erdos, Schlein and Yau and the four moment theorem by Tao and Vu. We will also discuss some of the open problems in the study of random matrices if time permits. |
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Discrete Mathematics Seminar |
Topic: |
Hypergraph Turan Problem |
Presenter: |
Oleg Pikhurko, Carnegie Mellon |
Date: |
Thursday, November 11, 2010, Time: 2:15 p.m., Location: Fine Hall 224 |
Abstract: |
The Turan function ex(n,F) of a k-graph F is the maximum number of edges in an F-free k-graph on n vertices. This problem goes back to the fundamental paper of Turan from 1941 that solved it for complete graphs (k=2). Unfortunately, very few non-trivial instances of the problem have been solved when we consider hypergraphs (k>2).
We survey some recent results and methods on the hypergraph Turan function. In particular, we discuss the so-called stability approach that greatly helps in obtaining exact results from asymptotic computations (for example, those that use flag algebras or graph limits). |
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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: |
Sharp gradient estimates for a class of elliptic equations |
Presenter: |
Olivaine De Queiroz, Universidade Estadual De Campinas |
Date: |
Friday, November 12, 2010, Time: 3:00 p.m., Location: Fine Hall 314 |
Abstract: |
I will present some results related with existence and sharp regularity for solutions to a class of singular elliptic equations with gradient dependence for which solutions may exhibit a free boundary. Once we have obtained sharp regularity, further analysis of the free boundary may be carried out with nondegeneracy and refined gradient estimates. I will also show how to employ an asymptotic analysis obtaining some known results for the obstacle and cavity problems. Work done in collaboration with M. Montenegro and E. Teixeira. |
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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 |
Abstract: |
In 2007 I published a monograph which treated the relativistic Euler equations in three space dimensions for a perfect fluid with an arbitrary equation of state. In this monograph I considered initial data which outside a sphere coincide with the data corresponding to a constant state. Under a suitable restriction on the size of the initial departure from the constant state, I established theorems which gave a complete description of the maximal classical development.. In particular, I showed that the boundary of the domain of the maximal classical development has a singular part where the inverse density of the wave fronts vanishes, signaling shock formation. In fact, the theorems which I established give a complete picture of shock formation in three-dimensional irrotational fluids . In my talk I shall give a simplified presentation of these results and of their proof. The approach is geometric, the central concept being that of the acoustical space time manifold. |
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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: |
A survey of results in universality of Wigner matrices, Part II |
Presenter: |
Percy Wong, Princeton University |
Date: |
Thursday, November 18, 2010, Time: 2:00 p.m., Location: Fine Hall 401 |
Abstract: |
In the 1950's, Wigner proved the famous semicircle laws for Wigner matrices and started the study of universality results in random matrices. In these two talks, this will serve as our starting point as we surveyed the historical developments in this field. We will end with a discussion of the proof of the local semicircle law of Erdos, Schlein and Yau and the four moment theorem by Tao and Vu. We will also discuss some of the open problems in the study of random matrices if time permits. |
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Discrete Mathematics Seminar |
Topic: |
Hypergraph list coloring and Euclidean Ramsey Theory |
Presenter: |
Noga Alon, Tel-Aviv University and IAS |
Date: |
Thursday, November 18, 2010, Time: 2:15 p.m., Location: Fine Hall 224 |
Abstract: |
A hypergraph is simple if it has no two edges sharing more than a single vertex. It is s-list colorable if for any assignment of a list of s colors to each of its vertices, there is a vertex coloring assigning to each vertex a color from its list, so that no edge is monochromatic. I will discuss a recent result, obtained jointly with A. Kostochka, that asserts that for any r and s there is a finite d=d(r,s) so that any r-uniform simple hypergraph with average degree at least d(r,s) is not s-list-colorable. This extends a similar result for graphs, and has some geometric Ramsey-type consequences. |
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Princeton University and IAS Number Theory Seminar |
Topic: |
Endoscopic transfer of depth-zero supercuspidal L-packets |
Presenter: |
Tasho Kaletha, Princeton University and IAS |
Date: |
Thursday, November 18, 2010, Time: 4:30 p.m., Location: IAS S-101 |
Abstract: |
In a recent paper, DeBacker and Reeder have constructed a piece of the local Langlands correspondence for pure inner forms of unramified p-adic groups and have shown that the corresponding L-packets are stable. In this talk we are going to discuss the endoscopic transfer of these L-packets: the theory of endoscopy -- an instance of the broad principle of functoriality -- predicts precise relationships between the L-packets on a group G and its endoscopic groups H. This relationship is encoded in the so called endoscopic character identities. We will motivate and state these identities, paying attention to the precise normalization of all objects involved. If time permits, we will then discuss their proof and the extension of the correspondence to non-pure inner forms via the theory of isocrystals with additional structure. |
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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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Differential Geometry and Geometric Analysis Seminar *** Please note special time |
Topic: |
Rigidity of critical metrics in dimension four |
Presenter: |
Jeff Viaclovsky, University of Wisconsin |
Date: |
Friday, November 19, 2010, Time: 4:00 p.m., Location: Fine Hall 314 |
Abstract: |
The general quadratic curvature functional is considered in dimension four. It is possible to "gauge" the Euler-Lagrange equations, in a self-adjoint fashion, to become elliptic. Fredholm theory may then be used to describe local properties of the moduli space of critical metrics. I'll show that a number of compact examples are infinitesimally rigid, and are therefore isolated as critical metrics. I'll also discuss solutions of the gauged linearized equation on several noncompact examples which are asymptotically locally Euclidean. This is joint work with Matt Gursky. |
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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: |
Linear PDEs in critical regularity spaces: Hierarchical construction of their nonlinear solutions |
Presenter: |
Eitan Tadmor, University of Maryland |
Date: |
Monday, November 29, 2010, Time: 4:00 p.m., Location: Fine Hall 314 |
Abstract: |
We construct uniformly bounded solutions of the equations div(U)=f and curl(U)=f, for general f's in the critical regularity spaces L^d(R^d) and, respectively, L3(R3). The study of these equations was motivated by recent results of Bourgain & Brezis. The equations are linear but construction of their solutions is not. Our constructions are, in fact, special cases of a rather general framework for solving linear equations, L(U)=f, covered by the closed range theorem. The solutions are realized in terms of nonlinear hierarchical representations, U=sum(u_j), which we introduced earlier in the context of image processing. The u_j's are constructed recursively as proper minimizers, yielding a multi-scale decomposition of the solutions U. |
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Analysis Seminar *** Please note special time |
Topic: |
TBA |
Presenter: |
Colin Guillarmou, Universite de Nice Sophia-Antipolis |
Date: |
Monday, November 29, 2010, Time: 5:00 p.m., Location: Fine Hall 314 |
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Algebraic Geometry Seminar |
Topic: |
The tautological ring of M_g |
Presenter: |
Rahul Pandharipande, Princeton University |
Date: |
Tuesday, November 30, 2010, Time: 4:30 p.m., Location: Fine Hall 322 |
Abstract: |
I will talk about an approach to the ring generated by the kappa classes via the moduli space of stable quotients. The main new result (with A. Pixton) is a proof of a conjecture by Faber and Zagier of an elegant set of relations. Whether these are all the relations is an interesting question. I will discuss the data on both sides. |
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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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Symplectic Geometry Seminar |
Topic: |
A conjecture of Arnold |
Presenter: |
Heather Macbeth, Princeton University |
Date: |
Thursday, December 2, 2010, Time: 1:30 p.m., Location: Fine Hall 601 |
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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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Symplectic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Ralph Kaufmann, Perdue University |
Date: |
Thursday, December 9, 2010, Time: 1:30 p.m., Location: Fine Hall 601 |
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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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