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OCTOBER 2009 |
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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: |
Applying a Local Lemma to Thue games |
Presenter: |
Wesley Pegden, Rutgers University |
Date: |
Thursday, October 22, 2009, Time: 2:15 p.m., Location: Fine Hall 224 |
Abstract: |
In this talk, I will discuss probabilistic proofs for the existence of winning strategies in sequence games where the goal is nonrepetitiveness. The technique involves a `one-sided' generalization of the Local Lemma, which allows us to ignore the dependencies on `future' events which would normally prevent this kind of proof from working. I will also discuss the extension of these results to graphs. Although many proofs about games are motivated by a probabilistic intuition, these results appear to represent the first successful applications of a Local Lemma to games. |
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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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Topology Seminar |
Topic: |
Cusp volume of fibered 3-manifolds |
Presenter: |
David Futer, Temple |
Date: |
Thursday, October 22, 2009, Time: 4:30 p.m., Location: Fine Hall 314 |
Abstract: |
Consider a 3-manifold M that fibers over the circle, with fiber a punctured surface F. I will explain how the volume of a maximal cusp of M (in the hyperbolic metric) is determined up to a bounded constant by combinatorial properties of the arc complex of the fiber surface F. This is joint work with Saul Schleimer. |
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Differential Geometry and Geometric Analysis Seminar |
Topic: |
The Yamabe problem on manifolds with boundary |
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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PACM Colloquium |
Topic: |
Some variants on the flows of suspensions: Diffusion, dispersion, and biofilms |
Presenter: |
Howard Stone, Mechanical and Aerospace Engineering |
Date: |
Monday, October 26, 2009, Time: 4:00 p.m., Location: Fine Hall 214 |
Abstract: |
In this talk I will present several fluid mechanics problems that concern the flow of particles and suspensions. This topic has many variants, which I will introduce to provide breadth and perspective for the listener (most of you) who has not studied the topic. After the introduction I will highlight (i) shear-enhanced diffusion, as studied in a microfluidic device, (ii) axial dispersion due to shear-enhanced diffusion, and (iii) unusual structures formed when bacteria flow, and biofilms grow, in curved channels. Some answers will be given and pen questions will be indicated. |
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Geometry, Representation Theory, and Moduli Seminar |
Topic: |
The HOMFLY polynomial of algebraic links via Euler characteristics of Hilbert schemes |
Presenter: |
V. Shende, Princeton University |
Date: |
Monday, October 26, 2009, Time: 4:30 p.m., Location: Fine Hall 314 |
Abstract: |
We consider the generating function of Euler characteristics of stratified Hilbert schemes of a locally planar curve. We show that it is a rational function, which, at least in the case of unibranch singularities, depends only on the topology near the singular points. It is well known that the topology may be characterized by the knot (or, in general, link) obtained by intersecting the curve with the three-sphere bounding a small neighborhood of a point; we conjecture that in fact our generating function is the HOMFLY polynomial of this link. For singularities which are topologically equivalent to x^m = y^n, for m,n relatively prime -- i.e., corresponding to torus knots, we verify the conjecture by explicit calculation. A certain specialization of our generating function gives the so-called BPS contributions of an isolated Gorenstein curve in Pandharipande-Thomas theory. These have been shown to vanish in genera below the geometric genus and above the arithmetic genus. It follows from our conjecture that these are positive in this range. This talk presents joint work with Alexei Oblomkov. |
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Analysis Seminar *** Please note special time |
Topic: |
The stability of the irrotational Euler-Einstein system with a positive cosmological constant |
Presenter: |
Jared Speck, University of Cambridge |
Date: |
Monday, October 26, 2009, Time: 5:00 p.m., Location: Fine Hall 110 |
Abstract: |
The irrotational Euler-Einstein system models the evolution of a dynamic spacetime containing a perfect fluid with vanishing vorticity. In this talk, which is a summary of recent joint work with Igor Rodnianski, I will discuss the stability of a family of background cosmological solutions to the irrotational Euler-Einstein system in 1 + 3 dimensions with a positive cosmological constant Lambda. The background solutions describe an initially uniform quiet fluid of positive energy density evolving in a spacetime undergoing accelerated expansion. Our main result is a proof that under the equation of state p = c^2_s\rho, 0 < c^2_s < 1/3; the background solutions are globally future-stable under small irrotational perturbations. In particular, the perturbed spacetimes, which have the topological structure [0;inf) xT^3;,are future causally geodesically complete. It is of special interest to note that the behavior of the fluid in an exponentially expanding spacetime differs drastically from the case of flat spacetime. More specifically, Christodoulou has recently shown that on the Minkowski space background, irrotational data arbitrarily close to that of an initially quiet uniform fluid can lead to solutions that form shocks. In view of this fact, we remark that the proof of our main result can be used to show the following: exponentially expanding spacetime backgrounds can stabilize irrotational fluids. This work is an extension of recent work by Ringstrom. |
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Group Actions Seminar |
Topic: |
Domains of Discontinuity with compact quotients |
Presenter: |
Anna Wienhard, Princeton University |
Date: |
Tuesday, October 27, 2009, Time: 12:30 p.m., Location: Fine Hall 322 |
Abstract: |
Given a discrete subgroup in a semisimple Lie group G, it is natural to ask on which homogeneous spaces this subgroup acts properly discontinuous and with compact quotient. In this talk I will discuss a large class of examples of such subgroups and explain a construction of open subsets in G/P where P is a parabolic subgroup, on which these groups act properly discontinuous with compact quotient. The class of examples I am going to discuss includes subgroups arising from higher Teichmueller spaces, and finding geometric structures parametrized by higher Teichmueller spaces is an important motivation for this work. This is joint work with O. Guichard. |
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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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Ergodic Theory and Statistical Mechanics Seminar |
Topic: |
A brief survey of effective equidistribution results in Gamma\G |
Presenter: |
Elon Lindenstrauss, Princeton University |
Date: |
Thursday, October 29, 2009, Time: 2:00 p.m., Location: Fine Hall 401 |
Abstract: |
Equidistribution results for orbits and more general configurations in Gamma\G are a central focus of the theory of flows on homogeneous spaces. A notable example that comes to mind is Ratner's equidistribution theorem. I will survey some old and new quantitive equidistribution results of this flavor by several authors. |
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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: |
Generalizations of the Sato-Tate conjecture |
Presenter: |
David Geraghty, Harvard |
Date: |
Thursday, October 29, 2009, Time: 4:30 p.m., Location: Fine Hall 214 |
Abstract: |
I will discuss a recent joint work with Thomas Barnet-Lamb and Toby Gee in which we prove the Sato-Tate conjecture for non-CM regular algebraic cuspidal automorphic representations of GL_2 over a totally real field. |
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Differential Geometry and Geometric Analysis Seminar |
Topic: |
Center of mass and constant mean curvature foliations in general relativity |
Presenter: |
Lan-Hsuan Huang, Columbia University |
Date: |
Friday, October 30, 2009, Time: 3:00 p.m., Location: Fine Hall 314 |
Abstract: |
We will discuss the existence and uniqueness of the foliation by stable spheres with constant mean curvature for asymptotically flat manifolds satisfying the Regge-Teitelboim condition at infinity. We will first introduce the background and then discuss how the foliation relates to the concept of center of mass in general relativity. |
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Joint IAS/Princeton University Number Theory Seminar ***Please note special date, time, and location |
Topic: |
Modularity lifting for n-dimensional ordinary Galois representations |
Presenter: |
David Geraghty, Harvard |
Date: |
Friday, October 30, 2009, Time: 4:00 p.m., Location: Fine Hall 322 |
Abstract: |
I will discuss a generalization of the modularity lifting theorems of Clozel, Harris and Taylor to the case of ordinary Galois representations. The result is obtained by applying the Taylor-Wiles method (with innovations due to Kisin and Taylor) over a Hida family. A key step is to construct an appropriate ordinary lifting ring and determine its irreducible components. |
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NOVEMBER 2009 |
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Geometry, Representation Theory, and Moduli Seminar |
Topic: |
TBA |
Presenter: |
L. Borisov, Rutgers University |
Date: |
Monday, November 2, 2009, Time: 4:30 p.m., Location: Fine Hall 314 |
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Joint IAS/Princeton University Number Theory Seminar |
Topic: |
Mean values with GL(2) times GL(3) functions |
Presenter: |
M. Young, TAMU |
Date: |
Thursday, November 5, 2009, Time: 4:30 p.m., Location: IAS S-101 |
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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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Group Actions Seminar |
Topic: |
TBA |
Presenter: |
Nimish Shah, Ohio State University |
Date: |
Tuesday, November 10, 2009, Time: 12:30 p.m., Location: Fine Hall 322 |
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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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Mathematical Physics Seminar |
Topic: |
A variational model for crystals with defects |
Presenter: |
Mathieu Lewin, Université de Cergy-Pontoise |
Date: |
Tuesday, November 10, 2009, Time: 4:30 p.m., Location: Jadwin 343 |
Abstract: |
This talk will be devoted to the reduced Hartree-Fock model for crystals with defects.
The main idea is to describe at the same time the electrons bound by the defect and the (nonlinear) behavior of the infinite crystal. This leads to a bounded-below nonlinear functional whose variable is however an operator of infinite-rank.
I will provide the correct functional setting for this functional, state the existence of global-in-time solutions to the associated time-dependent Schrödinger equation, and discuss the existence, the properties and the stability of bound states. In particular I will define the dielectric permittivity of the perfect crystal and relate this to some properties of ground states. This is a review of joint works with Eric Cancès and Amélie Deleurence (Ecoledes Ponts, Paris). |
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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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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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Joint Columbia-Courant-Princeton University Algebraic Geometry Seminar |
Topic: |
Analogue of the Narasimhan-Seshadri theorem in higher dimensions and holonomy |
Presenter: |
Vikraman Balaji, Chennai Mathematical Institute |
Date: |
Friday, November 13, 2009, Time: 4:30 p.m., Location: Fine Hall 322 |
Abstract: |
We will discuss some recent work on natural analogues of the Narasimhan-Seshadri theorem on higher dimensional varieties with some applications to stable bundles on surfaces. The classical result related stability of bundles on projective smooth curves with irreducible unitary representations of the fundamental group. Analogues of holonomy groups and their representations play the corresponding role. |
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Joint Columbia-Courant-Princeton University Algebraic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Tony Pantev, University of Pennsylvania |
Date: |
Friday, November 13, 2009, Time: 4:30 p.m., Location: Fine Hall 322 |
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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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Geometry, Representation Theory, and Moduli Seminar |
Topic: |
TBA |
Presenter: |
Z. Yun, IAS |
Date: |
Monday, November 16, 2009, Time: 4:30 p.m., Location: Fine Hall 314 |
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Group Actions Seminar |
Topic: |
TBA |
Presenter: |
Amir Mohammadi, University of Chicago |
Date: |
Tuesday, November 17, 2009, Time: 12:30 p.m., Location: Fine Hall 322 |
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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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Mathematical Physics Seminar |
Topic: |
The emergence of a giant vortex in a fast rotating Bose gas. |
Presenter: |
Jakob Yngvason, University of Vienna |
Date: |
Tuesday, November 17, 2009, Time: 4:30 p.m., Location: Jadwin 343 |
Abstract: |
A Bose gas in fast rotation normally exhibits a growing number of vortices of unit strength if the angular velocity is increased. In an anharmonic trap at sufficiently high velocity, however, a phase transition is expected: Vortices in the bulk should disappear and all vorticity become concentrated in a region where the density is very low. Moreover, the critical velocity for the transition is expected to increase with on the interaction strength in a definite manner. In the lecture rigorous results on this behavior within two-dimensional Gross-Pitaevskii theory will be presented. This is joint work with Michele Correggi and Nicolas Rougerie. |
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Ergodic Theory and Statistical Mechanics Seminar |
Topic: |
TBA |
Presenter: |
Lai-Sang Young, Courant Institute |
Date: |
Thursday, November 19, 2009, Time: 2:00 p.m., Location: Fine Hall 401 |
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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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PACM Colloquium |
Topic: |
TBA |
Presenter: |
Warren Powell, ORFE |
Date: |
Monday, November 23, 2009, Time: 4:00 p.m., Location: Fine Hall 214 |
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Geometry, Representation Theory, and Moduli Seminar |
Topic: |
TBA |
Presenter: |
D. Zakharov, Columbia University |
Date: |
Monday, November 23, 2009, Time: 4:30 p.m., Location: Fine Hall 314 |
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Group Actions Seminar |
Topic: |
TBA |
Presenter: |
Zhiren Wang, Princeton University |
Date: |
Tuesday, November 24, 2009, Time: 12:30 p.m., Location: Fine Hall 322 |
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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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Mathematical Physics Seminar |
Topic: |
TBA |
Presenter: |
Alexander Sodin, Tel Aviv University |
Date: |
Tuesday, November 24, 2009, Time: 4:30 p.m., Location: Jadwin 343 |
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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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Group Actions Seminar |
Topic: |
TBA |
Presenter: |
Martin Kassabov, Cornell University and IAS |
Date: |
Tuesday, December 1, 2009, Time: 12:30 p.m., Location: Fine Hall 322 |
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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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Mathematical Physics Seminar |
Topic: |
TBA |
Presenter: |
Vieri Mastropietro, Univ. Rome II |
Date: |
Tuesday, December 1, 2009, Time: 4:30 p.m., Location: Jadwin 343 |
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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: |
Unbiased Random Perturbations of Navier-Stokes Equation |
Presenter: |
Boris Rozovsky, Lefschetz Center for Dynamical Systems, Brown University |
Date: |
Thursday, December 3, 2009, Time: 2:00 p.m., Location: Fine Hall 401 |
Abstract: |
A random perturbation of a deterministic Navier-Stokes equation is considered in the form of an Stochastic PDE with Wick product in the nonlinear term. The equation is solved in the space of generalized stochastic processes using the Cameron-Martin version of the Wiener chaos expansion. The generalized solution is obtained as an inverse of solutions to corresponding quantized equations.
An interesting feature of this type of perturbation is that it preserves the mean dynam- ics: the expectation of the solution of the perturbed equation solves the underlying deterministic Navier-Stokes equation. From the stand point of a statistician it means that the perturbed model is unbiased. The talk is based on a joint work with R. Mikulevicius. |
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Differential Geometry and Geometric Analysis Seminar |
Topic: |
Conformal Structure of Minimal Surfaces with Finite Topology |
Presenter: |
Christine Breiner, MIT |
Date: |
Friday, December 4, 2009, Time: 3:00 p.m., Location: Fine Hall 314 |
Abstract: |
The recent construction of a genus-one helicoid verified the existence of a second example of a complete, embedded minimal surface with finite topology and infinite total curvature in $\mathbb{R}3$. We determine the conformal structure and asymptotic Weierstrass data of all surfaces with these properties. Using this structure and the asymptotics, in the case $g=1$ we establish the existence of an orientation preserving isometry. This is joint work with Jacob Bernstein |
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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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Group Actions Seminar |
Topic: |
TBA |
Presenter: |
Uri Shapira, Hebrew University |
Date: |
Tuesday, December 8, 2009, Time: 12:30 p.m., Location: Fine Hall 322 |
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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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Topology Seminar |
Topic: |
TBA |
Presenter: |
Peter Ozsvath, Columbia University |
Date: |
Thursday, December 17, 2009, Time: 4:30 p.m., Location: Fine Hall 314 |
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