SEPTEMBER 2009 |
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| Graduate Student Seminar |
| Topic: |
Nonlinear Waves |
| Presenter: |
Jonathan Luk, Princeton University |
| Date: |
Thursday, September 24, 2009, Time: 12:30 p.m., Location: Fine Hall 314 |
| Abstract: |
Given a nonlinear wave equation whose nonlinearity contains derivatives of the unknown function: $-\partial_t^2\phi+\sum_{i=1}^ 3 \partial_{x_i}^2\phi=N(\partial\phi)$ in $3+1$ dimensions, what can we say about the global existence of solutions? What if the initial conditions are small and compactly supported? If time permits, I will discuss the case of a wave map. |
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| Discrete Mathematics Seminar |
| Topic: |
Counting flags in digraph |
| Presenter: |
Sergey Norin, Princeton University |
| Date: |
Thursday, September 24, 2009, Time: 2:15 p.m., Location: Fine Hall 224 |
| Abstract: |
Many results in asymptotic extremal combinatorics are obtained using just a handful of instruments, such as induction and Cauchy-Schwarz inequality. The ingenuity lies in combining these tools in just the right way. Recently, Razborov developed a flag calculus which captures many of the available techniques in pure form, and allows one, in particular, to computerize the search for the right combination.
In this talk we outline the general approach and describe its application to two problems in extremal digraph theory. We show that an n vertex digraph with minimum outdegree 0.3465n contains a directed triangle, obtaining a new bound in an important special case of the Caccetta-Haggkvist conjecture. We also show that the maximum number of induced directed two-edge paths in an n vertex digraph is n3/15 + o(n3), resolving a conjecture of Thomasse.
Based on joint work with Jan Hladky and Daniel Kral. |
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| Differential Geometry and Geometric Analysis Seminar |
| Topic: |
A parabolic flow of Hermitian metrics |
| Presenter: |
Jeff Streets, Princeton University |
| Date: |
Friday, September 25, 2009, Time: 3:00 p.m., Location: Fine Hall 314 |
| Abstract: |
I will introduce a parabolic flow of Hermitian metrics which is a generalization of Kahler-Ricci flow. This flow preserves the pluriclosed condition, and its existence and convergence properties are closely related to the underlying topology of the given complex manifold. I will discuss a stability result for the flow near Kahler-Einstein metrics. Further, I will classify static solutions to the flow on various classes of complex surfaces, and show that no static solutions exist on Class VII surfaces. Finally I will discuss possible applications of this flow to understanding the topology of nonKahler surfaces. Joint with G. Tian. |
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| Algebraic Geometry Seminar |
| Topic: |
TBA |
| Presenter: |
Radu Laza, Stony Brook University |
| Date: |
Tuesday, September 29, 2009, Time: 4:30 p.m., Location: Fine Hall 322 |
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| OCTOBER 2009 |
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| Topology Seminar ***Please note special time and location |
| Topic: |
Topologically minimal surfaces in 3-manifolds |
| Presenter: |
David Bachman, Pitzer College |
| Date: |
Thursday, October 1, 2009 Time: 2:00 p.m., Location: Fine Hall 322 |
| Abstract: |
Topologically minimal surfaces are the topological analogue of geometrically minimal surfaces. Such surfaces generalize well known classes, such as incompressible, strongly irreducible (or weakly incompressible), and critical surfaces. Applications include problems dealing with stabilization, amalgamation, and isotopy of Heegaard splittings and bridge spheres for knots. In this talk we will review the basic definitions and discuss both existing and potential applications of this new theory. |
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| Ergodic Theory and Statistical Mechanics Seminar |
| Topic: |
The decay of Fourier modes in solutions of Navier-Stokes systems |
| Presenter: |
Yakov Sinai, Princeton University |
| Date: |
Thursday, October 1, 2009, Time: 2:00 p.m., Location: Fine Hall 401 |
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| Discrete Mathematics Seminar |
| Topic: |
TBA |
| Presenter: |
Yori Zwols, Columbia University |
| Date: |
Thursday, October 1, 2009, Time: 2:15 p.m., Location: Fine Hall 224 |
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| Topology Seminar |
| Topic: |
Persistence of Essential Surfaces after Dehn filling |
| Presenter: |
David Bachman, Pitzer College |
| Date: |
Thursday, October 1, 2009 Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: |
We show that the set of closed, essential, 2-sided surfaces (considered up to isotopy) in a 3-manifold with a torus boundary component survives unchanged in all suitably generic Dehn fillings. Furthermore, for all but finitely many non-generic fillings, we show that two essential surfaces can only become isotopic in a very constrained way. If time permits, we will also sketch future work on the persistence of the set of Heegaard surfaces after generic Dehn filling. This is joint work with Ryan Derby-Talbot and Eric Sedgwick. |
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| Differential Geometry and Geometric Analysis Seminar |
| Topic: |
TBA |
| Presenter: |
Justin Corvino, Lafayette |
| Date: |
Friday, October 2, 2009, Time: 3:00 p.m., Location: Fine Hall 314 |
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| Geometry, Representation Theory, and Moduli Seminar |
| Topic: |
TBA |
| Presenter: |
A. Okounkov, Princeton University |
| Date: |
Monday, October 5, 2009, Time: 4:00 p.m., Location: Fine Hall 314 |
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| PACM Colloquium |
| Topic: |
Self-organized selectivity in Calcium and Sodium Channels: important biology ready for mathematical analysis |
| Presenter: |
Robert Eisenberg, Rush Medical Center/Chicago and Argonne National Labs |
| Date: |
Monday, October 5, 2009, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: |
Ion channels are irresistible objects for biological study because they are the [nano] valves of life controlling an enormous range of biological function, much as transistors control computers. Ion channels are appealing objects for physical investigation because conformation changes are not involved in channel function, once the channel is open. Open channels are interesting objects for chemical study because they effectively select among chemically similar ions, under unfavorable circumstances. Channels are interesting objects for physical study because they contain an enormous density of charge, fixed, mobile, and induced. Direct simulation of channel behavior in atomic detail is difficult if not impossible, because ion transit takes ~ 10-8 sec compared to a simulation calculation time step of 10-16 sec and a biological time scale beginning at 10-4 sec. Direct simulation must deal with concentrations of 10-7 to 55 M in a single calculation, and macroscopic electric fields and concentration gradients produce substantial flows which are the function of the channel, making equilibrium analysis unhelpful. |
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| Algebraic Geometry Seminar |
| Topic: |
Homotopy Theoretic methods on Chow varieties |
| Presenter: |
Wenchuan Hu, IAS |
| Date: |
Tuesday, October 6, 2009, Time: 4:30 p.m., Location: Fine Hall 322 |
| Abstract: |
The homotopy theoretic method has been applied to the algebraic cycle theory for a long period of time. In particular, it can be applied to compute topological invariants of Chow varieties. In this talk I will discuss this method in calculating the Euler Characteristic of Chow varieties. The calculation in a direct and simple way (this result has been obtained by Blaine Lawson and Stephen Yau in a different way). This technique also can be applied to Chow varieties with certain group actions and other cases. Furthermore, I will also talk about the application of the method on l-adic Euler-Poincare Characteristic of Chow varieties over arbitrary algebraic closed field. |
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| Ergodic Theory and Statistical Mechanics Seminar |
| Topic: |
TBA |
| Presenter: |
Ilya Vinogradov, Princeton University |
| Date: |
Thursday, October 8, 2009, Time: 2:00 p.m., Location: Fine Hall 401 |
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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: |
TBA |
| Presenter: |
Andras Stipsicz, Renyi Institute, Hungary |
| Date: |
Thursday, October 8, 2009, Time: 4:30 p.m., Location: Fine Hall 314 |
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| Differential Geometry and Geometric Analysis Seminar |
| Topic: |
TBA |
| Presenter: |
Micah Warren, Princeton University |
| Date: |
Friday, October 9, 2009, Time: 3:00 p.m., Location: Fine Hall 314 |
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| Geometry, Representation Theory, and Moduli Seminar |
| Topic: |
TBA |
| Presenter: |
A. Okounkov, Princeton University |
| Date: |
Monday, October 12, 2009, Time: 4:00 p.m., Location: Fine Hall 314 |
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| PACM Colloquium (Joint with Analysis Seminar) |
| Topic: |
Harmonic Analysis and Geometries of Digital Data Bases |
| Presenter: |
Raphy Coifman, Yale University |
| Date: |
Monday, October 12, 2009, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: |
Given a matrix (of Data) we describe methodologies to build two multiscale (inference) Geometries/Harmonic Analysis one on the rows , the other on the columns . The geometries are designed to simplify the representation of the data base . We will provide a number of examples including; matrices of operators , psychological questionnaires, vector valued images, scientific articles, etc. In all these cases tensor Haar orthogonal bases play a crucial role in organizing the data base viewed as a function of two variables (row, column) in the case of potential operators we relate to Calderon Zugmund decompositions , while for other data this is a "data agnostic analytic learning tool" For the example of the matrix of eigenfunctions of a discretized Laplace operator ( say, on a compact manifold) we obtain both the Geometry of the domain of the Laplace operator as well as a dual multiscale Geometry of the eigenvectors... |
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| Algebraic Geometry Seminar |
| Topic: |
TBA |
| Presenter: |
Jong Hae Keum, KIAS |
| Date: |
Tuesday, October 13, 2009, Time: 4:30 p.m., Location: Fine Hall 322 |
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| 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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| Differential Geometry and Geometric Analysis Seminar |
| Topic: |
TBA |
| Presenter: |
Marcus Khuri, SUNY Stony Brook |
| Date: |
Friday, October 16, 2009, Time: 3:00 p.m., Location: Fine Hall 314 |
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| 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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| Ergodic Theory and Statistical Mechanics Seminar |
| Topic: |
TBA |
| Presenter: |
Mikko Stenlund, Courant Institute, NYU |
| Date: |
Thursday, October 22, 2009, Time: 2:00 p.m., Location: Fine Hall 401 |
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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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| 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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| Algebraic Geometry Seminar |
| Topic: |
BGG correspondence and the cohomology of compact Kaehler manifolds |
| Presenter: |
Mihnea Popa, UIC |
| Date: |
Tuesday, October 27, 2009, Time: 4:30 p.m., Location: Fine Hall 322 |
| Abstract: |
The cohomology algebra of the sheaf of holomorphic functions on a compact Kaehler manifold can be naturally viewed as a module over the exterior algebra of a vector space. A well-known result of Bernstein-Gel'fand-Gel'fand gives a correspondence between such "exterior" modules and linear complexes of modules over the symmetric algebra, i. e. the polynomial ring. I will explain how one can use a modern view on this correspondence, together with the Generic Vanishing theory developed by Green and Lazarsfeld via Hodge-theoretic methods, in order to understand subtle algebraic structures of the cohomology algebra. As a bonus, homological and commutative algebra tools can be applied on the polynomial ring side to obtain new inequalities for the holomorphic Euler characteristic and the Hodge numbers of compact Kaehler manifolds. This is joint work with R. Lazarsfeld. |
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| Discrete Mathematics Seminar |
| Topic: |
TBA |
| Presenter: |
Julia Wolf, Rutgers University |
| Date: |
Thursday, October 29, 2009, Time: 2:15 p.m., Location: Fine Hall 224 |
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| Joint IAS/Princeton University Number Theory Seminar |
| Topic: |
TBA |
| Presenter: |
David Geraghty, Harvard |
| Date: |
Thursday, October 29, 2009, Time: 4:30 p.m., Location: Fine Hall 214 |
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| Joint IAS/Princeton University Number Theory Seminar ***Please note special date, time, and location |
| Topic: |
TBA |
| Presenter: |
David Geraghty, Harvard |
| Date: |
Friday, October 30, 2009, Time: 4:00 p.m., Location: Fine Hall 322 |
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| NOVEMBER 2009 |
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| PACM Colloquium |
| Topic: |
Geometry and Analysis of point sets in high dimensions |
| Presenter: |
Mauro Maggioni, Duke University |
| Date: |
Monday, November 9, 2009, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: |
The analysis of high dimensional data sets is useful in a large variety of applications, from machine learning to dynamical systems: data sets are often modeled as low-dimensional, noisy data sets embedded in high-dimensional spaces; dynamical systems often have very high-dimensional state spaces but sometimes interesting dynamics occurs on low-dimensional sets. We discuss several problems associated with the analysis of the geometry of such sets, and with the approximation of functions on such sets, together with some solutions: in particular we discuss how to construct random walks on such data sets and perform multiscale analysis of them and their applications (especially to machine learning); how to construct robust coordinate systems for data sets; how to estimate reliably the intrinsic dimensionality of the data when only few noisy samples are available. |
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| Algebraic Geometry Seminar |
| Topic: |
TBA |
| Presenter: |
Matt DeLand, Stony Brook University |
| Date: |
Tuesday, November 10, 2009, Time: 4:30 p.m., Location: Fine Hall 322 |
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| Discrete Mathematics Seminar |
| Topic: |
TBA |
| Presenter: |
Andrew King, Columbia University |
| Date: |
Thursday, November 12, 2009, Time: 2:15 p.m., Location: Fine Hall 224 |
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| Joint Columbia-Courant-PrincetonUniversity Algebraic Geometry Seminar |
| Topic: |
TBA |
| Presenter: |
Vikraman Balaji, Chennai Mathematical Institute
Tony Pantev, University of Pennsylvania |
| Date: |
Friday, November 13, 2009, Time: 4:30 p.m., Location: Fine Hall 322 |
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| Differential Geometry and Geometric Analysis Seminar |
| Topic: |
TBA |
| Presenter: |
Rick Schoen, Stanford University |
| Date: |
Friday, November 13, 2009, Time: 3:00 p.m., Location: Fine Hall 314 |
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| PACM Colloquium |
| Topic: |
Testable New Theory about Early-Universe Density Fluctuations and Origins of Solar Systems: Applied-Probability and Quantum-Physics Aspects |
| Presenter: |
Erik Vanmarcke, Civil and Environmental Engineering |
| Date: |
Monday, November 16, 2009, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: |
The talk will summarize, with a focus on applied-probability aspects, the main findings, testable predictions and research opportunities stemming from a new probabilistic model of how complex patterns of energy-density fluctuations may have arisen during the inflation phase of the Big Bang. Based on first (quantum-physical) principles and requiring a minimum number of (observationally-accessible) parameters, the "embryonic inflation model" yields a coherent set of testable (hence falsifiable) hypotheses about the formation, evolution, composition, internal structure and cosmic environment of galaxies, stars and planets, and is consistent with key findings from observations of the Cosmic Microwave Background (CMB). Implying a robust alternative (and challenge) to the dual paradigm of spatially-uniform light-element primordial nucleosynthesis and stellar "recycling" of matter as the sole mechanism of heavy-element production, the theory holds the promise of integrating astrophysical and planetary sciences with cosmology and galaxy formation in a coherent evolutionary framework. Observations indicating overall cosmic flatness, the existence of an accelerating component, dark matter and dark energy all fit, in quantifiable and testable ways, into the framework of the theory. |
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| Algebraic Geometry Seminar |
| Topic: |
TBA |
| Presenter: |
Paul Hacking, University of Massachusetts Amherst |
| Date: |
Tuesday, November 17, 2009, Time: 4:30 p.m., Location: Fine Hall 322 |
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| Discrete Mathematics Seminar |
| Topic: |
TBA |
| Presenter: |
Peter Winkler, Dartmouth College |
| Date: |
Thursday, November 19, 2009, Time: 2:15 p.m., Location: Fine Hall 224 |
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| Differential Geometry and Geometric Analysis Seminar |
| Topic: |
TBA |
| Presenter: |
Martin Li, Courant Institute |
| Date: |
Friday, November 20, 2009, Time: 3:00 p.m., Location: Fine Hall 314 |
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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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| Discrete Mathematics Seminar *** Please note special day |
| Topic: |
TBA |
| Presenter: |
Maria Chudnovsky, Columbia University |
| Date: |
Wednesday, December 2, 2009, Time: 2:15 p.m., Location: Fine Hall 224 |
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| Ergodic Theory and Statistical Mechanics Seminar |
| Topic: |
TBA |
| Presenter: |
Boris Rozovsky, Lefschetz Center for Dynamical Systems, Brown University |
| Date: |
Thursday, December 3, 2009, Time: 2:00 p.m., Location: Fine Hall 401 |
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| Differential Geometry and Geometric Analysis Seminar |
| Topic: |
TBA |
| Presenter: |
Christine Breiner, MIT |
| Date: |
Friday, December 4, 2009, Time: 3:00 p.m., Location: Fine Hall 314 |
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| PACM Colloquium |
| Topic: |
Imaging Techniques and the Rejuvenation of Artwork |
| Presenter: |
Roy S. Berns, Munsell Color Science Laboratory, Chester F. Carlson Center for Imaging Science, Rochester Institute of Technology, USA |
| Date: |
Monday, December 7, 2009, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: |
Advances in digital imaging within the visible spectrum enable the accurate color rendering of artwork. It is possible to generate a colorimetric image with high spatial resolution and high image quality (appropriate sharpness and low noise). When the number of sensor channels exceeds three, it is also possible to generate spectral images. Spectral images can be used to calculate colorimetric images for any illuminant and observer pair, to evaluate color inconstancy, as an aid in retouching (i.e., restorative inpainting), for pigment mapping, and to improve printed reproductions. These digital images, of course, record the color and spectra of the artwork in its current condition. Depending on how the artwork has aged, its color may bear little resemblance to its appearance when first executed. This can dramatically affect the analysis of the painting in terms of its historical context and understanding the artist's working methods. A variety of techniques can be used to determine such color changes including analysing cross-sections, finding protected areas and identical materials that retain their color, early photographic records, and descriptions by art critics and connoisseurs at the time of creation. Having determined that a color change has occurred, it is possible to rejuvenate the colors of a digital image by using the principles of instrumental-based color matching. These principles are used to determine pigments and their concentrations that when mixed, match a particular color. This is equivalent to pigment mapping. The digital rejuvenation is performed by either replacing the spectral properties of the changed pigment with one that hasn't changed or increasing the concentration of a pigment that has faded. These rejuvenated images, while speculative, provide important and interesting new insights. This presentation will review research by the author in digital rejuvenation using examples by Vincent Van Gogh and Georges Seurat. |
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| Algebraic Geometry Seminar |
| Topic: |
TBA |
| Presenter: |
Roya Beheshti Zavareh, Washington University in St. Louis |
| Date: |
Tuesday, December 8, 2009, Time: 4:30 p.m., Location: Fine Hall 322 |
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| Ergodic Theory and Statistical Mechanics Seminar |
| Topic: |
TBA |
| Presenter: |
Michael Boshernitzan, Rice University |
| Date: |
Thursday, December 10, 2009, Time: 2:00 p.m., Location: Fine Hall 401 |
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| Differential Geometry and Geometric Analysis Seminar |
| Topic: |
TBA |
| Presenter: |
Song Sun, Wisconsin |
| Date: |
Friday, December 11, 2009, Time: 3:00 p.m., Location: Fine Hall 314 |
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