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| OCTOBER 2009 |
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| Graduate Student Seminar |
| Topic: |
Differential equations arising from group actions on manifolds |
| Presenter: |
Mohammad Farajzadeh Tehrani, Princeton University |
| Date: |
Thursday, October 1, 2009, Time: 12:30 p.m., Location: Fine Hall 314 |
| Abstract: |
We consider ODE's arising from the action of Lie groups on manifolds and discuss how solvability of corresponding lie algebra helps to find explicit solution |
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| Topology Seminar ***Please note special time and location |
| Topic: |
Topologically minimal surfaces in 3-manifolds |
| Presenter: |
David Bachman, Pitzer College |
| Date: |
Thursday, October 1, 2009 Time: 2:00 p.m., Location: Fine Hall 322 |
| Abstract: |
Topologically minimal surfaces are the topological analogue of geometrically minimal surfaces. Such surfaces generalize well known classes, such as incompressible, strongly irreducible (or weakly incompressible), and critical surfaces. Applications include problems dealing with stabilization, amalgamation, and isotopy of Heegaard splittings and bridge spheres for knots. In this talk we will review the basic definitions and discuss both existing and potential applications of this new theory. |
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| Ergodic Theory and Statistical Mechanics Seminar |
| Topic: |
The decay of Fourier modes in solutions of Navier-Stokes systems |
| Presenter: |
Yakov Sinai, Princeton University |
| Date: |
Thursday, October 1, 2009, Time: 2:00 p.m., Location: Fine Hall 401 |
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| Discrete Mathematics Seminar |
| Topic: |
Claw-free graphs with strongly perfect complements. Fractional and integral version |
| Presenter: |
Yori Zwols, Columbia University |
| Date: |
Thursday, October 1, 2009, Time: 2:15 p.m., Location: Fine Hall 224 |
| Abstract: |
Strongly perfect graphs have been studied by several authors (e.g. Berge, Duchet, Ravindra, Wang). This paper deals with a fractional relaxation of strong perfection. Motivated by a wireless networking problem, we consider claw-free graphs that are fractionally strongly perfect in the complement. We obtain a forbidden induced subgraph characterization and display graph-theoretic properties of such graphs. It turns out that the forbidden induced subgraphs that characterize claw-free fractionally co-strongly perfect graphs are precisely the cycle of length 6, all cycles of length 8 and longer, four particular graphs, and a collection of graphs that are constructed by taking two graphs, each a copy of one of three particular graphs, and joining them by a path of arbitrary length in a certain way. Wang gave a characterization of strongly perfect claw-free graphs. As a corollary of the results in this paper, we obtain a characterization of claw-free graphs whose complements are strongly perfect. |
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| Joint IAS/Princeton University Number Theory Seminar |
| Topic: |
Even Galois Representations and the Fontaine-Mazur Conjecture |
| Presenter: |
Frank Calegari, Northwestern |
| Date: |
Thursday, October 1, 2009, Time: 4:30 p.m., Location: Fine Hall 214 |
| Abstract: |
We prove, under mild hypotheses, there are no irreducible two-dimensional ordinary even Galois representations of the Galois group of Q with distinct Hodge-Tate weights, in accordance with the Fontaine-Mazur conjecture. We also show how this method can be applied to a related circle of problems. |
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| Topology Seminar |
| Topic: |
Persistence of Essential Surfaces after Dehn filling |
| Presenter: |
David Bachman, Pitzer College |
| Date: |
Thursday, October 1, 2009 Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: |
We show that the set of closed, essential, 2-sided surfaces (considered up to isotopy) in a 3-manifold with a torus boundary component survives unchanged in all suitably generic Dehn fillings. Furthermore, for all but finitely many non-generic fillings, we show that two essential surfaces can only become isotopic in a very constrained way. If time permits, we will also sketch future work on the persistence of the set of Heegaard surfaces after generic Dehn filling. This is joint work with Ryan Derby-Talbot and Eric Sedgwick. |
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| Differential Geometry and Geometric Analysis Seminar |
| Topic: |
Hamiltonian Stationary Tori in Kahler Manifolds |
| Presenter: |
Justin Corvino, Lafayette |
| Date: |
Friday, October 2, 2009, Time: 3:00 p.m., Location: Fine Hall 314 |
| Abstract: |
A solution of the Hamitonian stationary variational problem is a Lagrangian submanifold (of a symplectic manifold with compatible Riemannian metric) whose volume is stationary under Hamiltonian variations. In joint work with Adrian Butscher, we construct families of small Hamiltonian stationary Lagrangian tori near a point in a Kahler four-manifold, under a non-degeneracy condition on the complex curvature tensor at the point. |
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| Analysis Seminar |
| Topic: |
TBA |
| Presenter: |
Tristan Roy, IAS |
| Date: |
Monday, October 5, 2009, Time: 4:00 p.m., Location: Fine Hall 110 |
| Abstract: |
In this talk I will discuss the global existence of H^{2} solutions of a barely energy supercritical equation, namely a loglog defocusing quitic wave equation. The first step is to control the $L_{t}^{4} L_{x}^{12}$ norm of the solution on an arbitrary long-time interval [0,T] by an a priori bound of its $L_{t}^{\infty} H^{2}([0,T])$ norm. To do that we divide the interval into subintervals on which the $L_{t}^{4} L_{x}^{12}$ norm of the solution is substantial. We prove that the length of these subintervals is also substantial. Then, by using a variant of a Morawetz-type estimate from Shatah-Struwe (the variant we use is due to Bahouri-Gerard), we can control the length of large sequences of these subintervals. Eventually we can estimate their number. The second estimate is to estimate a posteriori the $L_{t}^{\infty} H^{2}([0,T])$ norm of the solution. This is done by a connectedness-in-time argument, using the Strichartz estimates and the control of the $L_{t}^{4} L_{x}^{12}$ norm. |
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| Geometry, Representation Theory, and Moduli Seminar |
| Topic: |
TBA |
| Presenter: |
A. Okounkov, Princeton University |
| Date: |
Monday, October 5, 2009, Time: 4:00 p.m., Location: Fine Hall 314 |
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| PACM Colloquium |
| Topic: |
Self-organized selectivity in Calcium and Sodium Channels: important biology ready for mathematical analysis |
| Presenter: |
Robert Eisenberg, Rush Medical Center/Chicago and Argonne National Labs |
| Date: |
Monday, October 5, 2009, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: |
Ion channels are irresistible objects for biological study because they are the [nano] valves of life controlling an enormous range of biological function, much as transistors control computers. Ion channels are appealing objects for physical investigation because conformation changes are not involved in channel function, once the channel is open. Open channels are interesting objects for chemical study because they effectively select among chemically similar ions, under unfavorable circumstances. Channels are interesting objects for physical study because they contain an enormous density of charge, fixed, mobile, and induced. Direct simulation of channel behavior in atomic detail is difficult if not impossible, because ion transit takes ~ 10-8 sec compared to a simulation calculation time step of 10-16 sec and a biological time scale beginning at 10-4 sec. Direct simulation must deal with concentrations of 10-7 to 55 M in a single calculation, and macroscopic electric fields and concentration gradients produce substantial flows which are the function of the channel, making equilibrium analysis unhelpful. |
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| Junior Faculty Seminar |
| Topic: |
Why should you care about graph theory? |
| Presenter: |
Sergey Norin, Princeton University |
| Date: |
Tuesday, October 6, 2009, Time: 12:00 p.m., Location: Fine Hall 601 |
| Abstract: |
The Four Color problem has long been a poster child for graph theory and has inspired much of its development over the years. I will mention a few, perhaps surprising, equivalent formulations of the problem, outline the main ideas of its proof and discuss some of the related open questions. |
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| Algebraic Geometry Seminar |
| Topic: |
Homotopy Theoretic methods on Chow varieties |
| Presenter: |
Wenchuan Hu, IAS |
| Date: |
Tuesday, October 6, 2009, Time: 4:30 p.m., Location: Fine Hall 322 |
| Abstract: |
The homotopy theoretic method has been applied to the algebraic cycle theory for a long period of time. In particular, it can be applied to compute topological invariants of Chow varieties. In this talk I will discuss this method in calculating the Euler Characteristic of Chow varieties. The calculation in a direct and simple way (this result has been obtained by Blaine Lawson and Stephen Yau in a different way). This technique also can be applied to Chow varieties with certain group actions and other cases. Furthermore, I will also talk about the application of the method on l-adic Euler-Poincare Characteristic of Chow varieties over arbitrary algebraic closed field. |
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| Ergodic Theory and Statistical Mechanics Seminar |
| Topic: |
Nearest neighbor distances for several rotations |
| Presenter: |
Ilya Vinogradov, Princeton University |
| Date: |
Thursday, October 8, 2009, Time: 2:00 p.m., Location: Fine Hall 401 |
| Abstract: |
We will discuss results of Marklof on distributions of nearest neighbor distances. We will look at the Poisson scaling and at CLT scaling. Another point of view is to look at the number of distinct gap lengths in this scenario. Here we will explain unpublished results of Boshernitzan and Dyson. |
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| Discrete Mathematics Seminar |
| Topic: |
TBA |
| Presenter: |
Hamed Hatami, Princeton University |
| Date: |
Thursday, October 8, 2009, Time: 2:15 p.m., Location: Fine Hall 224 |
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| Algebraic Topology Seminar |
| Topic: |
Projective product spaces |
| Presenter: |
Don Davis, Lehigh University |
| Date: |
Thursday, October 8, 2009, Time: 3:00 p.m., Location: Fine Hall 1201 |
| Abstract: |
A projective product space is a space obtained from a product of spheres by modding out by the antipodal action in all factors. We discuss cohomology, splittings, span, parallelizability, and immersion dimension of these spaces. |
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| Joint IAS/Princeton University Number Theory Seminar |
| Topic: |
An arithmetic fundamental lemma for unitary group of three variable |
| Presenter: |
Wei Zhang, Harvard |
| Date: |
Thursday, October 8, 2009, Time: 4:30 p.m., Location: Fine Hall 214 |
| Abstract: |
In this talk I'll present a relative trace formula approach to the Gross-Zagier formula and its high dimensional generalization (a derivative version of the global Gross-Prasad conjecture) for unitary group. In particular, an arithmetic fundamental lemma (AFL) is proposed. Some results proved recently will be presented, including the AFL for unitary group of three variable. |
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| Topology Seminar |
| Topic: |
Rational homology disks and symplectic topology |
| Presenter: |
Andras Stipsicz, Renyi Institute, Hungary |
| Date: |
Thursday, October 8, 2009, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: |
Surface singularities admitting a smoothing with the homology of the 4--disk (a so-called rational homology disk, QHD) play central role in the construction of exotic 4-manifolds through the 'rational blow down process'. Applying various forms of gauge theory we derive obstructions for a singularity to admit such smoothings. Using symplectic topology we classify all starshaped resolution graphs with QHD smoothings. |
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| Differential Geometry and Geometric Analysis Seminar |
| Topic: |
Calibrated geometry of optimal transportation |
| Presenter: |
Micah Warren, Princeton University |
| Date: |
Friday, October 9, 2009, Time: 3:00 p.m., Location: Fine Hall 314 |
| Abstract: |
Given a manifold M, there is a naturally occurring pseudo-Riemannian metric and K\"ahler form on the product M x M. The graph of the solution to the optimal transportation problem for given densities on M is then a calibrated maximal surface in a manifold conformal to M x M. These calibrations are pseudo-Riemannian analogues of the special Lagrangian calibrations for Calabi-Yau manifolds. Like in the Calabi-Yau case, these manifold have a moduli space of dimension b_1(M). They also define solutions to a generalization of the optimal transportation problem which arises when the manifold has nontrivial topology. This is joint work with Young-Heon Kim and Robert McCann. |
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| Geometry, Representation Theory, and Moduli Seminar |
| Topic: |
TBA |
| Presenter: |
A. Okounkov, Princeton University |
| Date: |
Monday, October 12, 2009, Time: 4:00 p.m., Location: Fine Hall 314 |
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| PACM Colloquium (Joint with Analysis Seminar) |
| Topic: |
Harmonic Analysis and Geometries of Digital Data Bases |
| Presenter: |
Raphy Coifman, Yale University |
| Date: |
Monday, October 12, 2009, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: |
Given a matrix (of Data) we describe methodologies to build two multiscale (inference) Geometries/Harmonic Analysis one on the rows , the other on the columns . The geometries are designed to simplify the representation of the data base . We will provide a number of examples including; matrices of operators , psychological questionnaires, vector valued images, scientific articles, etc. In all these cases tensor Haar orthogonal bases play a crucial role in organizing the data base viewed as a function of two variables (row, column) in the case of potential operators we relate to Calderon Zugmund decompositions , while for other data this is a "data agnostic analytic learning tool" For the example of the matrix of eigenfunctions of a discretized Laplace operator ( say, on a compact manifold) we obtain both the Geometry of the domain of the Laplace operator as well as a dual multiscale Geometry of the eigenvectors... |
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| Algebraic Geometry Seminar |
| Topic: |
TBA |
| Presenter: |
Jong Hae Keum, KIAS |
| Date: |
Tuesday, October 13, 2009, Time: 4:30 p.m., Location: Fine Hall 322 |
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| Department Colloquium |
| Topic: |
Entropy in Measurable Dynamics |
| Presenter: |
Lewis Bowen, Texas A & M |
| Date: |
Wednesday, October 14, 2009, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: |
In 1958, Kolmogorov defined the entropy of a probability measure preserving transformation. Entropy has since been central to the classification theory of measurable dynamics. In the 70s and 80s researchers extended entropy theory to measure preserving actions of amenable groups (Kieffer, Ornstein-Weiss). My recent work generalizes the entropy concept to actions of sofic groups; a class of groups that contains for example, all subgroups of GL(n,C). Applications include the classification of Bernoulli shifts over a free group, answering a question of Ornstein and Weiss. |
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| Ergodic Theory and Statistical Mechanics Seminar |
| Topic: |
A priori bounds for bounded-primitive renormalization |
| Presenter: |
Jeremy Kahn, SUNY Stony Brook |
| Date: |
Thursday, October 15, 2009, Time: 2:00 p.m., Location: Fine Hall 401 |
| Abstract: |
We say that an infinitely renormalizable quadratic polynomial has bounded-primitive type if we can find an infinite sequence of primitive renormalization times, such that the ratio between consecutive terms of the sequence is bounded. We prove that any such polynomial has the a priori bounds: there is a lower bound on the modulus of all renormalizations. This implies that the Mandelbrot set is locally connected at the associated parameter values. |
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| Discrete Mathematics Seminar |
| Topic: |
TBA |
| Presenter: |
Matt DeVos, Simon Fraser |
| Date: |
Thursday, October 15, 2009, Time: 2:15 p.m., Location: Fine Hall 224 |
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| Joint IAS/Princeton University Number Theory Seminar |
| Topic: |
Volume estimates in analytic and adelic geometry |
| Presenter: |
Antoine Chambert-Loir, IAS |
| Date: |
Thursday, October 15, 2009, Time: 4:30 p.m., Location: IAS S-101 |
| Abstract: |
The solution to many classical counting asymptotics problems in number theory goes by comparison with an analogous volume asumptotics. In a general setting, we establish asymptotic formulae for volumes of height balls in analytic varieties over local fields and in adelic points of algebraic varieties over number fields, relating the Mellin transforms of height functions to Igusa integrals and to global geometric invariants of the underlying variety. In the adelic setting, this involves the construction of general Tamagawa measures. This is joint work with Yuri Tschinkel (Courant). |
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| Topology Seminar |
| Topic: |
Immersed surfaces in closed hyperbolic 3-manifolds |
| Presenter: |
Jeremy Kahn, SUNY Stony Brook |
| Date: |
Thursday, October 15, 2009, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: |
Given any closed hyperbolic 3-manifold $M$ and $\epsilon > 0$, we find a closed hyperbolic surface $S$ and a map $f\from S \to M$ such that $f$ lifts to a $1+\epsilon$-quasi-isometry from the universal cover of $S$ to the universal cover of $M$. This is joint work with Vladimir Markovic. |
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| Extra Topology Seminar ***Please note special date, time, and location |
| Topic: |
More on immersed surfaces in closed hyperbolic 3-manifolds |
| Presenter: |
Jeremy Kahn, SUNY Stony Brook |
| Date: |
Friday, October 16, 2009, Time: 1:30 p.m., Location: Fine Hall 401 |
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| Differential Geometry and Geometric Analysis Seminar |
| Topic: |
TBA |
| Presenter: |
Marcus Khuri, SUNY Stony Brook |
| Date: |
Friday, October 16, 2009, Time: 3:00 p.m., Location: Fine Hall 314 |
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| Analysis Seminar |
| Topic: |
Counterexamples to the Strichartz estimates for the wave equation in domains |
| Presenter: |
Oana Ivanovici, Johns Hopkins University |
| Date: |
Monday, October 18, 2009, Time: 4:00 p.m., Location: Fine Hall 110 |
| Abstract: |
We prove that the Strichartz estimates for the wave equation inside a strictly convex domain \Omega of dimension 2 suffer losses when compared to the usual case \mathbb{R}2, (at least for a subset of the usual range of indices) and this is due to microlocal phenomena such as caustics generated in arbitrariIly small time near the boundary. |
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| Geometry, Representation Theory, and Moduli Seminar |
| Topic: |
TBA |
| Presenter: |
I. Setayesh, Princeton University |
| Date: |
Monday, October 19, 2009, Time: 4:00 p.m., Location: Fine Hall 314 |
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| Algebraic Geometry Seminar |
| Topic: |
Algebraic curves with CM |
| Presenter: |
Frans Oort, University of Utrecht |
| Date: |
Tuesday, October 20, 2009, Time: 4:30 p.m., Location: Fine Hall 322 |
| Abstract: |
Is every abelian variety isogenous with the Jacobian of an algebraic curve? We will study also several other questions in arithmetic geometry and show various implications. We will mention some solutions to these problems. |
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| Department Colloquium |
| Topic: |
Symplectic Embeddings and Continued Fractions |
| Presenter: |
Dusa McDuff, Columbia University |
| Date: |
Wednesday, October 21, 2009, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: |
It has been known since the time of Gromov that questions about symplectic embeddings lie at the heart of symplectic geometry. This talk will mostly be about some recent work with Schlenk in which we work out precisely when a four dimensional ellipsoid embeds symplectically in a ball. This problem turns out to have unexpected relations with the properties of continued fractions and of exceptional curves in blow ups of the complex projective plane. It is also related to questions of lattice packing of planar triangles. |
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| Ergodic Theory and Statistical Mechanics Seminar |
| Topic: |
A pair correlation bound implies the Central Limit Theorem for Sinai Billiards |
| Presenter: |
Mikko Stenlund, Courant Institute, NYU |
| Date: |
Thursday, October 22, 2009, Time: 2:00 p.m., Location: Fine Hall 401 |
| Abstract: |
It is an open problem in the study of dynamical systems whether fast decay of correlations alone is sufficient for the Central Limit Theorem (CLT) to hold. On the one hand, there are no examples of dynamical systems for which correlations decay quickly but the CLT fails. On the other, existing CLT proofs rely on statistical properties much stronger than correlation decay. In the talk I will discuss a prime class of physically relevant systems, called Sinai Billiards, and show that a single bound on correlations indeed implies the CLT directly. As a byproduct, the CLT is obtained for observables possessing remarkably little regularity. |
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| Discrete Mathematics Seminar |
| Topic: |
TBA |
| Presenter: |
Wesley Pegden, Rutgers University |
| Date: |
Thursday, October 22, 2009, Time: 2:15 p.m., Location: Fine Hall 224 |
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| Joint IAS/Princeton University Number Theory Seminar |
| Topic: |
Torsion in the homology of arithmetic groups |
| Presenter: |
Akshay Venkatesh, Stanford University |
| Date: |
Thursday, October 22, 2009, Time: 4:30 p.m., Location: IAS S-101 |
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| Differential Geometry and Geometric Analysis Seminar |
| Topic: |
TBA |
| Presenter: |
Sophie Chen, IAS |
| Date: |
Friday, October 23, 2009, Time: 3:00 p.m., Location: Fine Hall 314 |
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| Analysis Seminar |
| Topic: |
Cocompact imbeddings and critical nonlinearity revisited |
| Presenter: |
Kyril Tintarev, Uppsala University |
| Date: |
Monday, October 26, 2009, Time: 4:00 p.m., Location: Fine Hall 110 |
| Abstract: |
We introduce a notion of cocompact imbeddings relative to a group of linear isometries.We discuss the notion of critical Sobolev nonlinearity in connection with the usual dilation actions that make the (non-compact) limit Sobolev imbedding co-compact and yield solutions of Talenti type for semilinear elliptic equations with self-similar autonomous nonlinearities of critical growth.
We then consider similar dilation and translations groups for $H_01(B)$, where $B$ is a unit disk on a plane, which preserve the Sobolev norm, but do not preserve the Trudinger-Moser functional $\int e^{4\pi u2}$. We give then two examples of invariant critical nonlineairites that are stronger than Trudinger-Moser nonlinearity and lack the weakly continuity properties of the latter.
We give further examples of cocompactness in Sobolev spaces over manifolds, including subelliptic spaces over nilpotent Lie groups, as well as some interpolation results that lead to cocompactness of imbeddings of Besov spaces. This work is partially done in collaboration with Adimurthi, M. Cwikel and J.M. do O. |
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| Geometry, Representation Theory, and Moduli Seminar |
| Topic: |
TBA |
| Presenter: |
V. Shende, Princeton University |
| Date: |
Monday, October 26, 2009, Time: 4:00 p.m., Location: Fine Hall 314 |
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| Analysis Seminar *** Please note special time |
| Topic: |
TBA |
| Presenter: |
Jared Speck, University of Cambridge |
| Date: |
Monday, October 26, 2009, Time: 5:00 p.m., Location: Fine Hall 110 |
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| Algebraic Geometry Seminar |
| Topic: |
BGG correspondence and the cohomology of compact Kaehler manifolds |
| Presenter: |
Mihnea Popa, UIC |
| Date: |
Tuesday, October 27, 2009, Time: 4:30 p.m., Location: Fine Hall 322 |
| Abstract: |
The cohomology algebra of the sheaf of holomorphic functions on a compact Kaehler manifold can be naturally viewed as a module over the exterior algebra of a vector space. A well-known result of Bernstein-Gel'fand-Gel'fand gives a correspondence between such "exterior" modules and linear complexes of modules over the symmetric algebra, i. e. the polynomial ring. I will explain how one can use a modern view on this correspondence, together with the Generic Vanishing theory developed by Green and Lazarsfeld via Hodge-theoretic methods, in order to understand subtle algebraic structures of the cohomology algebra. As a bonus, homological and commutative algebra tools can be applied on the polynomial ring side to obtain new inequalities for the holomorphic Euler characteristic and the Hodge numbers of compact Kaehler manifolds. This is joint work with R. Lazarsfeld. |
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| Discrete Mathematics Seminar |
| Topic: |
TBA |
| Presenter: |
Julia Wolf, Rutgers University |
| Date: |
Thursday, October 29, 2009, Time: 2:15 p.m., Location: Fine Hall 224 |
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| Joint IAS/Princeton University Number Theory Seminar |
| Topic: |
TBA |
| Presenter: |
David Geraghty, Harvard |
| Date: |
Thursday, October 29, 2009, Time: 4:30 p.m., Location: Fine Hall 214 |
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| Joint IAS/Princeton University Number Theory Seminar ***Please note special date, time, and location |
| Topic: |
TBA |
| Presenter: |
David Geraghty, Harvard |
| Date: |
Friday, October 30, 2009, Time: 4:00 p.m., Location: Fine Hall 322 |
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| NOVEMBER 2009 |
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| PACM Colloquium |
| Topic: |
Geometry and Analysis of point sets in high dimensions |
| Presenter: |
Mauro Maggioni, Duke University |
| Date: |
Monday, November 9, 2009, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: |
The analysis of high dimensional data sets is useful in a large variety of applications, from machine learning to dynamical systems: data sets are often modeled as low-dimensional, noisy data sets embedded in high-dimensional spaces; dynamical systems often have very high-dimensional state spaces but sometimes interesting dynamics occurs on low-dimensional sets. We discuss several problems associated with the analysis of the geometry of such sets, and with the approximation of functions on such sets, together with some solutions: in particular we discuss how to construct random walks on such data sets and perform multiscale analysis of them and their applications (especially to machine learning); how to construct robust coordinate systems for data sets; how to estimate reliably the intrinsic dimensionality of the data when only few noisy samples are available. |
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| Algebraic Geometry Seminar |
| Topic: |
TBA |
| Presenter: |
Matt DeLand, Stony Brook University |
| Date: |
Tuesday, November 10, 2009, Time: 4:30 p.m., Location: Fine Hall 322 |
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| Discrete Mathematics Seminar |
| Topic: |
TBA |
| Presenter: |
Andrew King, Columbia University |
| Date: |
Thursday, November 12, 2009, Time: 2:15 p.m., Location: Fine Hall 224 |
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| Joint Columbia-Courant-PrincetonUniversity Algebraic Geometry Seminar |
| Topic: |
TBA |
| Presenter: |
Vikraman Balaji, Chennai Mathematical Institute
Tony Pantev, University of Pennsylvania |
| Date: |
Friday, November 13, 2009, Time: 4:30 p.m., Location: Fine Hall 322 |
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| Differential Geometry and Geometric Analysis Seminar |
| Topic: |
TBA |
| Presenter: |
Rick Schoen, Stanford University |
| Date: |
Friday, November 13, 2009, Time: 3:00 p.m., Location: Fine Hall 314 |
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| Analysis Seminar |
| Topic: |
Astala's conjecture on Hausdorff measure distortion under planar quasiconformal mappings and related removability problems |
| Presenter: |
Ignacio Uriarte-Tuero, Michigan State University |
| Date: |
Monday, November 16, 2009, Time: 4:00 p.m., Location: Fine Hall 110 |
| Abstract: |
In his celebrated paper on area distortion under planar quasiconformal mappings (Acta 1994) (for which he received the Salem prize), Astala proved that if $E$ is a compact set of Hausdorff dimension $d$ and $f$ is $K$-quasiconformal, then $fE$ has Hausdorff dimension at most $d' = \frac{2Kd}{2+(K-1)d}$, and that this result is sharp. He conjectured (Question 4.4) that if the Hausdorff measure $\mathcal{H}^d (E)=0$, then $\mathcal{H}^{d'} (fE)=0$. This conjecture was known to be true if $d'=0$ (obvious), $d'=2$ (Ahlfors), and $d'=1$ (Astala, Clop, Mateu, Orobitg and UT, Duke 2008.) The approach in the last mentioned paper does not generalize to other dimensions. UT showed that Astala's conjecture is sharp in the class of all Hausdorff gauge functions (IMRN, 2008). Lacey, Sawyer and UT jointly proved completely Astala's conjecture in all dimensions (Acta, 2009?) The proof uses Astala's 1994 approach, geometric measure theory, and new weighted norm inequalities for Calder\'{o}n-Zygmund singular integral operators which cannot be deduced from the classical Muckenhoupt $A_p$ theory. These results are intimately related to removability problems for various classes of quasiregular maps. I will particularly mention sharp removability results for bounded $K$-quasiregular maps recently obtained in joint work of Tolsa and UT. The talk will be self-contained. |
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| PACM Colloquium |
| Topic: |
Testable New Theory about Early-Universe Density Fluctuations and Origins of Solar Systems: Applied-Probability and Quantum-Physics Aspects |
| Presenter: |
Erik Vanmarcke, Civil and Environmental Engineering |
| Date: |
Monday, November 16, 2009, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: |
The talk will summarize, with a focus on applied-probability aspects, the main findings, testable predictions and research opportunities stemming from a new probabilistic model of how complex patterns of energy-density fluctuations may have arisen during the inflation phase of the Big Bang. Based on first (quantum-physical) principles and requiring a minimum number of (observationally-accessible) parameters, the "embryonic inflation model" yields a coherent set of testable (hence falsifiable) hypotheses about the formation, evolution, composition, internal structure and cosmic environment of galaxies, stars and planets, and is consistent with key findings from observations of the Cosmic Microwave Background (CMB). Implying a robust alternative (and challenge) to the dual paradigm of spatially-uniform light-element primordial nucleosynthesis and stellar "recycling" of matter as the sole mechanism of heavy-element production, the theory holds the promise of integrating astrophysical and planetary sciences with cosmology and galaxy formation in a coherent evolutionary framework. Observations indicating overall cosmic flatness, the existence of an accelerating component, dark matter and dark energy all fit, in quantifiable and testable ways, into the framework of the theory. |
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| Algebraic Geometry Seminar |
| Topic: |
TBA |
| Presenter: |
Paul Hacking, University of Massachusetts Amherst |
| Date: |
Tuesday, November 17, 2009, Time: 4:30 p.m., Location: Fine Hall 322 |
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| Discrete Mathematics Seminar |
| Topic: |
TBA |
| Presenter: |
Peter Winkler, Dartmouth College |
| Date: |
Thursday, November 19, 2009, Time: 2:15 p.m., Location: Fine Hall 224 |
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| Algebraic Geometry Seminar |
| Topic: |
TBA |
| Presenter: |
Tommase deFernex, University of Utah |
| Date: |
Tuesday, November 24, 2009, Time: 4:30 p.m., Location: Fine Hall 322 |
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| PACM Colloquium |
| Topic: |
TBA |
| Presenter: |
Joris Dik, Delft University of Technology, Netherlands |
| Date: |
Monday, November 30, 2009, Time: 4:00 p.m., Location: Fine Hall 214 |
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DECEMBER 2009 |
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| Algebraic Geometry Seminar |
| Topic: |
TBA |
| Presenter: |
Ekaterina Amerik, IAS |
| Date: |
Tuesday, December 1, 2009, Time: 4:30 p.m., Location: Fine Hall 322 |
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| Discrete Mathematics Seminar *** Please note special day |
| Topic: |
TBA |
| Presenter: |
Maria Chudnovsky, Columbia University |
| Date: |
Wednesday, December 2, 2009, Time: 2:15 p.m., Location: Fine Hall 224 |
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| Ergodic Theory and Statistical Mechanics Seminar |
| Topic: |
TBA |
| Presenter: |
Boris Rozovsky, Lefschetz Center for Dynamical Systems, Brown University |
| Date: |
Thursday, December 3, 2009, Time: 2:00 p.m., Location: Fine Hall 401 |
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| Differential Geometry and Geometric Analysis Seminar |
| Topic: |
TBA |
| Presenter: |
Christine Breiner, MIT |
| Date: |
Friday, December 4, 2009, Time: 3:00 p.m., Location: Fine Hall 314 |
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| PACM Colloquium |
| Topic: |
Imaging Techniques and the Rejuvenation of Artwork |
| Presenter: |
Roy S. Berns, Munsell Color Science Laboratory, Chester F. Carlson Center for Imaging Science, Rochester Institute of Technology, USA |
| Date: |
Monday, December 7, 2009, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: |
Advances in digital imaging within the visible spectrum enable the accurate color rendering of artwork. It is possible to generate a colorimetric image with high spatial resolution and high image quality (appropriate sharpness and low noise). When the number of sensor channels exceeds three, it is also possible to generate spectral images. Spectral images can be used to calculate colorimetric images for any illuminant and observer pair, to evaluate color inconstancy, as an aid in retouching (i.e., restorative inpainting), for pigment mapping, and to improve printed reproductions. These digital images, of course, record the color and spectra of the artwork in its current condition. Depending on how the artwork has aged, its color may bear little resemblance to its appearance when first executed. This can dramatically affect the analysis of the painting in terms of its historical context and understanding the artist's working methods. A variety of techniques can be used to determine such color changes including analysing cross-sections, finding protected areas and identical materials that retain their color, early photographic records, and descriptions by art critics and connoisseurs at the time of creation. Having determined that a color change has occurred, it is possible to rejuvenate the colors of a digital image by using the principles of instrumental-based color matching. These principles are used to determine pigments and their concentrations that when mixed, match a particular color. This is equivalent to pigment mapping. The digital rejuvenation is performed by either replacing the spectral properties of the changed pigment with one that hasn't changed or increasing the concentration of a pigment that has faded. These rejuvenated images, while speculative, provide important and interesting new insights. This presentation will review research by the author in digital rejuvenation using examples by Vincent Van Gogh and Georges Seurat. |
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| Algebraic Geometry Seminar |
| Topic: |
TBA |
| Presenter: |
Roya Beheshti Zavareh, Washington University in St. Louis |
| Date: |
Tuesday, December 8, 2009, Time: 4:30 p.m., Location: Fine Hall 322 |
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| Ergodic Theory and Statistical Mechanics Seminar |
| Topic: |
TBA |
| Presenter: |
Michael Boshernitzan, Rice University |
| Date: |
Thursday, December 10, 2009, Time: 2:00 p.m., Location: Fine Hall 401 |
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| Differential Geometry and Geometric Analysis Seminar |
| Topic: |
TBA |
| Presenter: |
Song Sun, Wisconsin |
| Date: |
Friday, December 11, 2009, Time: 3:00 p.m., Location: Fine Hall 314 |
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| Discrete Mathematics Seminar |
| Topic: |
TBA |
| Presenter: |
Alexandra Ovetsky Fradkin, Princeton University |
| Date: |
Thursday, December 17, 2009, Time: 2:15 p.m., Location: Fine Hall 224 |
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