SEMINARS
Updated: 10-21-2009

   
OCTOBER 2009
   
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.
   
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.
   
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.
   
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
   
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.
   
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
   
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.

   
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.
   
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.
   
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.
   
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.
   
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.
   
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.
   
Discrete Mathematics Seminar
Topic: TBA
Presenter: Julia Wolf, Rutgers University
Date:  Thursday, October 29, 2009, Time: 2:15 p.m., Location: Fine Hall 224
   
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.
   
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.
   
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.
   
NOVEMBER 2009
   
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
   
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
   
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.
   
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
   
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
   
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).
   
Discrete Mathematics Seminar
Topic: TBA
Presenter: Andrew King, Columbia University
Date:  Thursday, November 12, 2009, Time: 2:15 p.m., Location: Fine Hall 224
   
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
   
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.
   
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
   
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.
   
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.
   
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
   
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
   
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
   
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.
   
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
   
Discrete Mathematics Seminar
Topic: TBA
Presenter: Peter Winkler, Dartmouth College
Date:  Thursday, November 19, 2009, Time: 2:15 p.m., Location: Fine Hall 224
   
PACM Colloquium
Topic: TBA
Presenter: Warren Powell, ORFE
Date:  Monday, November 23, 2009, Time: 4:00 p.m., Location: Fine Hall 214
   
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
   
Group Actions Seminar
Topic: TBA
Presenter: Zhiren Wang, Princeton University
Date:  Tuesday, November 24, 2009, Time: 12:30 p.m., Location: Fine Hall 322
   
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
   
Mathematical Physics Seminar
Topic: TBA
Presenter: Alexander Sodin, Tel Aviv University
Date:  Tuesday, November 24, 2009, Time: 4:30 p.m., Location: Jadwin 343
   
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
   

DECEMBER 2009

   
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
   
Algebraic Geometry Seminar
Topic: TBA
Presenter: Ekaterina Amerik, IAS
Date:  Tuesday, December 1, 2009, Time: 4:30 p.m., Location: Fine Hall 322
   
Mathematical Physics Seminar
Topic: TBA
Presenter: Vieri Mastropietro, Univ. Rome II
Date:  Tuesday, December 1, 2009, Time: 4:30 p.m., Location: Jadwin 343
   
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
   
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.
   
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
   
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.
   
Group Actions Seminar
Topic: TBA
Presenter: Uri Shapira, Hebrew University
Date:  Tuesday, December 8, 2009, Time: 12:30 p.m., Location: Fine Hall 322
   
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
   
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
   
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
   
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
   
Topology Seminar
Topic: TBA
Presenter: Peter Ozsvath, Columbia University
Date:  Thursday, December 17, 2009, Time: 4:30 p.m., Location: Fine Hall 314