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| OCTOBER 2009 |
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| Graduate Student Seminar |
| Topic: |
Strong multiplicity one and l-adic Galois representations |
| Presenter: |
Stefan Patrikis, Princeton University |
| Date: |
Thursday, October 8, 2009, Time: 12:30 p.m., Location: Fine Hall 314 |
| Abstract: |
The strong multiplicity one theorem and its refinements amount to a local-to-global principle in the theory of automorphic representations of GL(N). I will discuss a Galois-theoretic analogue with a surprisingly elementary proof, along with some related questions about the images of l-adic Galois representations. |
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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 Here we will explain unpublished results of Boshernitzan and Dyson.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: |
Graph norms and Erdos-Simonovits-Sidorenko's conjecture |
| Presenter: |
Hamed Hatami, Princeton University |
| Date: |
Thursday, October 8, 2009, Time: 2:15 p.m., Location: Fine Hall 224 |
| Abstract: |
I will prove some results in the direction of answering a question of Lovasz about the norms defined by certain combinatorial structures. Inspired by the similarity of the definitions of $L_p$ norms, trace norms, and Gowers norms, we introduce and study a wide class of norms containing these, as well as many other norms. It will be proven that every norm in this class must satisfy a Cauchy-Schwarz-Gowers type inequality. I will show an application of this inequality to a conjecture of Erdos-Simonovits and Sidorenko about subgraph densities. |
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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: |
Pseudo-Riemannian Calibrated Geometry and 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 smooth densities on M is then a calibrated maximal Lagrangian submanifold in M x M, with respect to a conformal metric on M x M. Thus the graph of the optimal map is special Lagrangian in the sense of Hitchin. This variational characterization of optimal transportation is different from the traditional one. The calibrations which detect these special Lagrangians are pseudo-Riemannian analogues of the special Lagrangian calibrations for Calabi-Yau manifolds. Like in the Calabi-Yau case, the moduli space of such submanifolds is itself a manifold of dimension b_1(M). The calibrated submanifolds that are not the graph of the optimal map are graphs of Lie solutions (see recent work of Delanoe) which are maps which locally satisfy the elliptic equation but do not globally minimize the cost integral. This is joint work with Young-Heon Kim and Robert McCann. |
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| Geometry, Representation Theory, and Moduli Seminar |
| Topic: |
Quantum cohomology of symplectic resolutions II |
| Presenter: |
A. Okounkov, Princeton University |
| Date: |
Monday, October 12, 2009, Time: 4:00 p.m., Location: Fine Hall 314 |
| Abstract: |
Certain holomorphic symplectic varieties of interest, such as Hilbert scheme of points on C^2 and more general moduli of sheaves on surfaces have a singular affine Poisson blowdown X_0 (which for Hilbert schemes is the symmetric power of the surface). Even more classically, such blowdowns exist for cotangent bundles to homogeneous varieties G/P. Equivariant quantum cohomology of such symplectic resolutions show a particularly close connections to classical structures in representation theory. There is an ongoing project to better understand them pursued by several groups from several directions. I will explain the general shape of this program and some of the more interesting examples worked out so far. |
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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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| Analysis Seminar ***Please note special time |
| Topic: |
Ground states of the L^2-critical boson star equation |
| Presenter: |
Rupert Frank, Princeton University |
| Date: |
Monday, October 12, 2009, Time: 5:00 p.m., Location: Fine Hall 110 |
| Abstract: |
The boson star equation $\sqrt{-\Delta} u - (|x|^{-1} * |u|^2) u = -u$ in $\R3$ involves both a non-local kinetic and potential energy and is $L2$-critical. We establish uniqueness, radial symmetry (up to translations) and analyticity of non-negative solutions. We also prove the nondegeneracy of the linearization. Our proof of uniqueness blends variational arguments with the harmonic extension, and our proof of radial symmetry extends the moving planes method to our non-local setting. This is joint work with E. Lenzmann. |
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| Algebraic Geometry Seminar |
| Topic: |
Analogue of the Narasimhan-Seshadri theorem in higher dimensions and holonomy |
| Presenter: |
Jong Hae Keum, KIAS |
| Date: |
Tuesday, October 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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| Operations Research and Financial Engineering Seminar |
| Topic: |
Ergodicity of Markov Processes: A marriage of topology and measure theory |
| Presenter: |
Martin Hairer, Courant Institute |
| Date: |
Tuesday, October 13, 2009, Time: 4:30 p.m., Location: Sherrerd Hall 101 |
| Abstract: |
One very widely used criterion in the theory of Markov chains states that if a Markov operator has the strong Feller property and is topologically irreducible, then it can have at most one invariant measure. While this criterion is very useful in finite-dimensional situations, it fails for many infinite-dimensional problems. In this talk, we will present two different generalisations of the strong Feller property that can be applied to a much larger class of problems. These include semilinear parabolic stochastic PDEs, stochastic delay equations, and diffusions driven by fractional noise. |
| 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: |
The Static Extension Problem in General Relativity |
| Presenter: |
Marcus Khuri, SUNY Stony Brook |
| Date: |
Friday, October 16, 2009, Time: 3:00 p.m., Location: Fine Hall 314 |
| Abstract: |
There are several competing definitions of quasi-local mass in General Relativity. A very promising and natural candidate, proposed by Bartnik, seeks to localize the ADM or total mass. Fundamental to understanding Bartnik's construction, is the question of existence for a canonical geometric boundary value problem associated with the static vacuum Einstein equations. In this talk we report on joint work with M. Anderson, which answers this question affirmatively under the hypothesis of a certain nondegeneracy condition. We also show that uniqueness fails. |
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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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| 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: |
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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| Ergodic Theory and Statistical Mechanics Seminar |
| Topic: |
TBA |
| Presenter: |
Elon Lindenstrauss, Princeton University |
| Date: |
Thursday, October 29, 2009, Time: 2:00 p.m., Location: Fine Hall 401 |
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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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| Geometry, Representation Theory, and Moduli Seminar |
| Topic: |
TBA |
| Presenter: |
L. Borisov, Rutgers University |
| Date: |
Monday, November 2, 2009, Time: 4:00 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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| 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: |
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-PrincetonUniversity 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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| 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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| Geometry, Representation Theory, and Moduli Seminar |
| Topic: |
TBA |
| Presenter: |
Z. Yun, IAS |
| Date: |
Monday, November 16, 2009, Time: 4:00 p.m., Location: Fine Hall 314 |
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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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| 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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|
| 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: |
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: |
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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