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SEPTEMBER 2006 |
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Discrete Mathematics Seminar |
Topic: |
On the minimal density of triangles in graphs |
Presenter: |
Alexander Razborov, IAS |
Date: |
Wednesday, September 27, 2006, Time: 2:15 p.m., Location: Fine 224 |
Abstract: |
http://www.math.princeton.edu/~bsudakov/razborov2006-fall.pdf |
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Geometry, Representation Theory, and Moduli Seminar |
Topic: |
Quantizing deep water waves: quantum hydrodynamics in one dimension |
Presenter: |
A. Abanov, Stony Brook |
Date: |
Wednesday, September 27, 2006, Time: 3:00 p.m., Location: Fine 214 |
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Department Colloquium |
Topic: |
The Sato-Tate conjecture |
Presenter: |
Richard Taylor, Harvard University |
Date: |
Wednesday, September 27, 2006, Time: 4:30 p.m., Location: Fine 314 |
Abstract: |
A fixed elliptic curve over the rational numbers is known to have approximately p points modulo p for any prime number p. In about 1960 Sato and Tate gave a conjectural distribution for the error term. Laurent Clozel, Michael Harris, Nick Shepherd-Barron and I recently proved this conjecture in the case that the elliptic curve has somewhere multiplicative reduction. In this talk I will describe the Sato-Tate conjecture and the ideas Tate and Serre had for proving it. I will also sketch how we were able to prove sufficient higher dimensional modularity results to complete the proof. |
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Topology Seminar |
Topic: |
A combinatorial description of some Heegaard Floer homologies |
Presenter: |
Sucharit Sarkar,Princeton University |
Date: |
Thursday, September 28, 2006, Time: 4:30 p.m., Location: Fine 314 |
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Differential Geometry and Geometric Analysis Seminar |
Topic: |
Ancient solutions for mean curvature flow |
Presenter: |
Maria Calle, Courant Institute |
Date: |
Friday, September 29, 2006, Time: 3:00 p.m., Location: Fine 314 |
Abstract: |
In the first part of the talk, I'll introduce mean curvature flow. A family of surfaces in R3 (or, in general, k- submanifolds in Rn) is said to move by mean curvature flow if its movement satisfies a particular parabolic PDE. This evolution follows the steepest descent direction for the area, that is, the surfaces decrease their area at the fastest possible rate. I present some basic facts about mean curvature flow solutions, such as a mean value inequality and the definition of density at a point.
After that, I'll present a result about ancient solutions. An ancient solution for mean curvature flow is a solution defined for all times t<0. I give a bound on the dimension of the ambient space of an ancient solution, depending on a bound on the density of the evolving submanifold. |
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Differential Geometry and Geometric Analysis Seminar *** Note special time |
Topic: |
A Geometric Evolution Equation on Principal Bundles |
Presenter: |
Jeff Streets, Duke University |
Date: |
Friday, September 29, 2006, Time: 4:00 p.m., Location: Fine 314 |
Abstract: |
In this talk I will motivate and define a natural geometric evolution equation on principal bundles. This flow is a non-trivial coupling of the usual Ricci flow for a metric and the Yang-Mills flow for a connection. I will describe various basic analytic aspects of this flow, and show a stability-type convergence result on four- manifolds, the targets of primary interest. Also I will present some plausible (and powerful) conjectures about the long-time behaviour of this flow. If there is time I will describe a related flow coupling the usual Ricci flow for a metric and a Yang-Mills type flow for gerbes (local 2-form field strength potentials). |
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OCTOBER 2006 |
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Analysis Seminar |
Topic: |
The mass-critical NLS |
Presenter: |
Monica Visan, IAS |
Date: |
Monday, October 2, 2006, Time: 4:00 p.m., Location: Fine 110 |
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Algebraic Geometry Seminar |
Topic: |
Preconceptions and misconceptions on singularly relative stable maps |
Presenter: |
Dan Abramovich, Brown University |
Date: |
Tuesday, October 3, 2006, Time: 4:30 p.m., Location: Fine 322 |
Abstract: |
Joint work in progress with Barabra Fantechi, with closely related symplectic counterpart by Joshua Davis. A key tool in Gromov-Witten theory is the degeneration method, in which a variety is allowed to degenerate into two smooth components meeting transversally. Additional flexibility is obtained from more singular degenerations, which are the topic of this work. I'll review the old and discuss the new, emphasizing the surprises one meets on every turn. |
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Mathematical Physics Seminar |
Topic: |
Circular beta Ensembles |
Presenter: |
Rowan Killip, UCLA |
Date: |
Tuesday, October 3, 2006, Time: 4:30 p.m., Location: Jadwin 343 |
Abstract: |
I will describe two results concerning Dyson's circular ensembles (i.e., the Coulomb gas on the unit circle) at arbitrary temperature: (i) their appearance as the eigenvalue distribution of a Schroedinger-like model with random decaying potential; and (ii) Gaussian fluctuations for the number of particles in an interval. |
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Discrete Mathematics Seminar |
Topic: |
Cycles in graphs |
Presenter: |
Jacques Verstraete, McGill University |
Date: |
Wednesday, October 4, 2006, Time: 2:15 p.m., Location: Fine 224 |
Abstract: |
http://www.math.princeton.edu/~bsudakov/verstraete2006-fall.pdf |
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Analysis Seminar ***Please note special date and time |
Topic: |
Geometrization of Probability |
Presenter: |
Vitali Milman, Tel-Aviv University |
Date: |
Wednesday, October 4, 2006, Time: 3:00 p.m., Location: TBA |
Abstract: |
It was recently observed that asymptotic theory of high dimensional convexity is naturally extended to the much larger category of log-concave measures. The main goal of the talk is to show how some important geometric inequalities are interpreted and extended for log-concave measures. Also, some typical probabilistic results are interpreted and proved in a geometric framework. Moreover, this extension of the geometric approach to the log-concave category is needed to solve some central problems of purely geometric nature. |
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Geometry, Representation Theory, and Moduli Seminar |
Topic: |
Weighted Gromov-Witten theory |
Presenter: |
V. Alexeev, Georgia |
Date: |
Wednesday, October 4, 2006, Time: 3:00 p.m., Location: Fine 214 |
Abstract: |
I will describe moduli spaces of weighted stable maps (C,P1...Pn)->V, a version in which to each point P_i one assigns a weight between zero and one; I will then describe the corresponding weighted Gromov-Witten and descendent invariants (based on a joint work with Michael Guy). Time permitting, I will also explain some of the "higher-dimensional" theory, with stable curves replaced by higher-dimensional varieties. |
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Department Colloquium |
Topic: |
TBA |
Presenter: |
Luis Caffarelli, University of Texas at Austin |
Date: |
Wednesday, October 4, 2006, Time: 4:30 p.m., Location: Fine 314 |
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Ergodic Theory and Statistical Mechanics Seminar |
Topic: |
TBA |
Presenter: |
Corinna Ulcigrai, Princeton University |
Date: |
Thursday, October 5, 2006, Time: 2:00 p.m., Location: Fine 401 |
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Topology Seminar |
Topic: |
Stable decompositions of complements of complex coordinate subspace arrangements and generalized moment angle complexes |
Presenter: |
Tony Bahri, Rider University |
Date: |
Thursday, October 5, 2006, Time: 4:30 p.m., Location: Fine 314 |
Abstract: |
A report of joint work with Martin Bendersky, Fred Cohen and Sam Gitler. We investigate a splitting, after one suspension, of a generalized moment angle complex into pieces related directly to the underlying simplicial complex defining it. In the particular case of the complements of complex coordinate subspace arrangements, our result implies a well known homology result of Goresky and MacPherson. |
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Differential Geometry and Geometric Analysis Seminar |
Topic: |
TBA |
Presenter: |
Kate Okikiolu, University of Pennsylvania and USCD |
Date: |
Friday, October 6, 2006, Time: 3:00 p.m., Location: Fine 314 |
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Analysis Seminar |
Topic: |
Blow up of the critical norm for some L^2 super critical nonlinear Schrodinger equations |
Presenter: |
Pierre Raphael, Princeton University |
Date: |
Monday, October 9, 2006, Time: 4:00 p.m., Location: TBA |
Abstract: |
Let the focusing (NLS) $iu_t+\Delta u+u|u|^{2}=0$ in dimension $N\geq 1$ with initial data in the energy space $H1$. For $N=1$, the problem is $L2$ subcritical and all $H1$ solutions are global. On the contrary, in dimensions $N=2,3$, there exist finite time blow up solutions but the understanding of the blow up dynamics is still very poor. In dimension $N=2$, the equation is $L2$ critical and thus the critical -that is scaling invariant- $L2$ norm is bounded because it is conserved. In dimension $N=3$, the problem is $H^{1/2}$ critical and numerics suggest that this norm should blow up if the solution blows up in finite time. We prove this result for radially symmetric initial data together with a lower bound $|u(t)|_{H^{1/2}}\geq |log(T-t)|^{\alpha}$. This is joint work with Frank Merle. |
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PACM Colloquium |
Topic: |
Vincent Van Gogh and Imitators in Greyscale: An Experiment in Cross-Disciplinary Stimulation |
Presenter: |
C. Richard Johnson, Jr., Electrical and Computer Engineering, Cornell University |
Date: |
Monday, October 9, 2006, Time: 4:00 p.m., Location: Fine 214 |
Abstract: |
This seminar describes a recently initiated project intended to accelerate the interaction of art historians and image processors in artist identification. The collection of digital images of artwork has been underway for over twenty years. Subsequently, in the last ten years image processors have initiated projects to process digitized images of paintings and drawings to assist art historians in artist identification. A key issue in the advance of this emerging technology, which is poised to expand rapidly over the next ten years, is bridging the gap between the two cultures of image processor system developers and art historian users. Four teams presently creating image processing schemes to assist the art historian in artist identification have agreed to prepare a daylong program for art historians to introduce them to the potential of this technology. The Van Gogh Museum in Amsterdam and the Kroller-Muller Museum in Otterloo have agreed to provide these four teams access to a common database of digitized paintings by Vincent Van Gogh and his imitators. The Van Gogh Museum plans to host a workshop on May 18, 2007, to be attended by art historians to whom the four teams will make presentations on brushstroke analysis in assistance of artist identification. The genesis of this pioneering experiment in cross-disciplinary stimulation raises a number of interesting issues about research between one field suffused with mathematics, models, and algorithms and another where such intellectual tools are practically absent and conceivably considered intellectually inappropriate. |
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Analysis Seminar |
Topic: |
TBA |
Presenter: |
Pierre Raphael, Princeton University |
Date: |
Monday, October 9, 2006, Time: 4:00 p.m., Location: TBA |
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Mathematical Physics Seminar |
Topic: |
Self-avoiding loop correlations and loop erasure |
Presenter: |
David Brydges, Univ of British Columbia, IAS |
Date: |
Tuesday, October 10, 2006, Time: 4:30 p.m., Location: Jadwin 343 |
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Operations Research and Financial Engineering Seminar |
Topic: |
Tikhonov regularisation for functional minimum distance estimators |
Presenter: |
Olivier Scaillet, University of Geneva |
Date: |
Tuesday, October 10, 2006, Time: 4:30 p.m., Location: E-219, E-Quad |
Abstract: |
We study the asymptotic properties of a Tikhonov regularised (TiR) estimator of a functional parameter based on a minimum distance principle for nonparametric conditional moment restrictions. The estimator is computationally tractable and even takes a closed form in the linear case. We derive its asymptotic Mean Integrated Squared Error (MISE), its rate of convergence and its pointwise asymptotic normality under a regularisation para- meter depending on the sample size. The optimal value of the regularisation parameter is characterised. We illustrate our theoretical findings and the small sample properties with simulation results for two numerical examples. We also discuss two data driven selection procedures of the regularisation parameter via a spectral representation and a subsampling approximation of the MISE. Finally, we provide an empirical application to nonparametric estimation of an Engel curve. |
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Discrete Mathematics Seminar |
Topic: |
The rank of random graphs |
Presenter: |
Kevin Costello, Rutgers University |
Date: |
Wednesday, October 11, 2006, Time: 2:15 p.m., Location: Fine 224 |
Abstract: |
http://www.math.princeton.edu/~bsudakov/costello2006-fall.pdf |
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Geometry, Representation Theory, and Moduli Seminar |
Topic: |
TBA |
Presenter: |
I. Smith, Cambridge |
Date: |
Wednesday, October 11, 2006, Time: 3:00 p.m., Location: Fine 214 |
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Department Colloquium |
Topic: |
TBA |
Presenter: |
Klaus Schmidt, University of Vienna / Schrodinger Institute |
Date: |
Wednesday, October 11, 2006, Time: 4:30 p.m., Location: Fine 314 |
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Differential Geometry and Geometric Analysis Seminar |
Topic: |
TBA |
Presenter: |
Andrea Malchiodi, SISSA, Trieste |
Date: |
Friday, October 13, 2006, Time: 3:00 p.m., Location: Fine 314 |
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PACM Colloquium |
Topic: |
One sketch for all: a sublinear approximation scheme for heavy hitters |
Presenter: |
Anna Gilbert, Mathematics, University of Michigan |
Date: |
Monday, October 16, 2006, Time: 4:00 p.m., Location: Fine 214 |
Abstract: |
The heavy hitters problem elicits a list of the m largest-magnitude components in a signal of length d. Although this problem is easy when the signal is presented explicitly, it becomes much more challenging in the setting of streaming data, where the signal is presented implicitly as a sequence of additive updates. One approach maintains a small sketch of the data that can be used to approximate the heavy hitters quickly. In previous work, this sketch is essentially a random linear projection of the data that fails with small probability for each signal. It is often desirable that the sketch succeed simultaneously for ALL signals from a given class, a requirement that may be called uniform heavy hitters. It arises, for example, when the signal is queried a large number of times or when the signal updates are stochastically dependent.
This talk describes a random linear sketch for uniform heavy hitters that succeeds with high probability. The recovery algorithm produces a list of heavy hitters that approximates the input signal with an l2 error that is optimal, except for an additive term that depends on the optimal l1 error and a controllable parameter e. The recovery algorithm requires space m*poly(log(d)/e) and time m2*poly(log(d)/e) to produce the list of heavy hitters. Up to logarithmic factors, the performance of this algorithm is the best possible with respect to several resources.
Joint work with Martin Strauss, Joel Tropp, and Roman Vershynin.
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Algebraic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Sándor Kovács, University of Washington |
Date: |
Tuesday, October 17, 2006, Time: 4:30 p.m., Location: Fine 322 |
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Mathematical Physics Seminar |
Topic: |
TBA |
Presenter: |
Alessandro Giuliani, Princeton University |
Date: |
Tuesday, October 17, 2006, Time: 4:30 p.m., Location: Jadwin 343 |
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Operations Research and Financial Engineering Seminar |
Topic: |
TBA |
Presenter: |
Jonathan Eckstein, Rutgers University |
Date: |
Wednesday, October 18, 2006, Time: 4:30 p.m., Location: E-219, E-Quad |
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Differential Geometry and Geometric Analysis Seminar |
Topic: |
TBA |
Presenter: |
Tristan Riviere, ETHZ, Zurich |
Date: |
Friday, October 20, 2006, Time: 3:00 p.m., Location: Fine 314 |
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PACM Colloquium |
Topic: |
Solving Nasty Optimization Problems in Science and Engineering |
Presenter: |
Margaret Wright, Computer Science Department, CIMS, New York University |
Date: |
Monday, October 23, 2006, Time: 4:00 p.m., Location: E-Fine 214 |
Abstract: |
Many important optimization problems in science and engineering involve functions that can fairly be described as "nasty", which can mean any or all of wildly nonlinear, nonsmooth, noisy, and defined through complex black-box simulation or error-prone experimental data. Because it is often impossible or impractical to calculate derivatives of these functions, non-derivative methods are the only feasible choice. These methods are in the midst of a renaissance involving research on their theoretical and computational properties, as well as investigation of which methods are best suited for which applications. This talk will include examples of challenging problems along with the speaker's assessment of the state of the art in non-derivative optimization methods.
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Operations Research and Financial Engineering Seminar |
Topic: |
TBA |
Presenter: |
Robert Smith, University of Michigan |
Date: |
Tuesday, October 24, 2006, Time: 4:30 p.m., Location: E-219, E-Quad |
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Discrete Mathematics Seminar |
Topic: |
Packing Hamilton cycles in random graphs |
Presenter: |
Michael Krivelevich, Tel Aviv University |
Date: |
Wednesday, October 25, 2006, Time: 2:15 p.m., Location: Fine 224 |
Abstract: |
See http://www.math.princeton.edu/~sudakov/krivelevich2006-fall.pdf |
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Differential Geometry and Geometric Analysis Seminar |
Topic: |
TBA |
Presenter: |
Gaoyong Zhang, Polytechnic University, NY |
Date: |
Friday, October 27, 2006, Time: 3:00 p.m., Location: Fine 314 |
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NOVEMBER 2006 |
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PACM Colloquium |
Topic: |
Information Theory and Probability Estimation: From Shannon to Shakespeare via Laplace, Good, Turing, Hardy, Ramanujan, and Fisher |
Presenter: |
Alon Orlitsky, ECE and CSE, University of California, San Diego |
Date: |
Monday, November 6, 2006, Time: 4:00 p.m., Location: Fine 214 |
Abstract: |
Standard information-theoretic results show that data over small, typically binary, alphabets can be compressed to Shannon's entropy limit. Yet most practical sources, such as text, audio, or video, have essentially infinite support. Compressing such sources requires estimating probabilities of unlikely, even unseen, events, a problem considered by Laplace. Of existing estimators, an ingenious if cryptic one derived by Good and Turing while deciphering the Enigma code works best yet not optimally. Hardy and Ramanujan's celebrated results on the number of integer partitions yield an asymptotically optimal estimator that compresses arbitrary-alphabet data patterns to their entropy. The same approach generalizes Fisher's seminal work estimating the number of butterfly species and its extension authenticating a poem purportedly written by The Bard. The talk covers these topics and is self contained.
Joint work with Prasad Santhanam, Krishna Viswanathan, and Junan Zhang
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Algebraic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Aaron Bertram, University of Utah |
Date: |
Tuesday, November 7, 2006, Time: 4:30 p.m., Location: Fine 322 |
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Operations Research and Financial Engineering Seminar |
Topic: |
TBA |
Presenter: |
Dilip Madan, University of Maryland |
Date: |
Tuesday, November 7, 2006, Time: 4:30 p.m., Location: E-219, E-Quad |
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Department Colloquium |
Topic: |
TBA |
Presenter: |
Richard Schwartz, Brown University |
Date: |
Wednesday, November 8, 2006, Time: 4:30 p.m., Location: Fine 314 |
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PACM Colloquium |
Topic: |
Denoising Color Images |
Presenter: |
Yang Wang, Mathematics, Georgia Institute of Technology |
Date: |
Monday, November 13, 2006, Time: 4:00 p.m., Location: Fine 214 |
Abstract: |
Natural color images captured by digital cameras often exhibit noticeable noise, particularly when the pictures are taken under low lighting or artificial lighting conditions. Traditional denoising techniques, which are often tested for removing artificial noise in monochromatic images, often do not work well for noisy color images.
In this talk, we present an overview of some of the traditional methods for denoising. We discuss a new strategy, which we call the cross-channel principle, that can be applied for very effective denoising of color images. In particular we show how this principle can be applied to the total variation denoising scheme and an ENO type denoising scheme.
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Algebraic Geometry Seminar |
Topic: |
Toric vector bundles and the resolution property |
Presenter: |
Sam Payne, Stanford University; Clay Institute |
Date: |
Tuesday, November 14, 2006, Time: 4:30 p.m., Location: Fine 322 |
Abstract: |
Is every coherent sheaf on an algebraic variety the quotient of a locally free sheaf of finite rank? I will discuss an investigation of this question via equivariant vector bundles on toric varieties, and will give examples of complete (singular, nonprojective) toric threefolds with no nontrivial equivariant vector bundles of rank less than or equal to 3. It is not known whether these varieties have any nontrivial vector bundles at all. |
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Mathematical Physics Seminar |
Topic: |
Many Bosons |
Presenter: |
E. Trubowitz, ETH, Zurich |
Date: |
Tuesday, November 14, 2006, Time: 4:30 p.m., Location: Jadwin 343 |
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Department Colloquium |
Topic: |
TBA |
Presenter: |
Mircea Mustaţă, University of Michigan; IAS |
Date: |
Wednesday, November 15, 2006, Time: 4:30 p.m., Location: Fine 314 |
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Topology Seminar |
Topic: |
TBA |
Presenter: |
William Jaco, IAS and Oklahoma State University |
Date: |
Thursday, November 16, 2006, Time: 4:30 p.m., Location: Fine 314 |
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Algebraic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Mircea Mustaţă, University of Michigan; IAS |
Date: |
Tuesday, November 21, 2006, Time: 4:30 p.m., Location: Fine 322 |
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Mathematical Physics Seminar |
Topic: |
Mean-Field and Classical Limit of Many-body Schroedinger Dynamics for Bosons (joint work with J.Froehlich and S.Schwarz) |
Presenter: |
Sandro Graffi, Univ. of Bologna |
Date: |
Tuesday, November 21, 2006, Time: 4:30 p.m., Location: Jadwin 343 |
Abstract: |
A new proof of the convergence of the N-particle Schroedinger dynamics for bosons towards the dynamics generated by the Hartree equation in the mean-field limit. For a restricted class of two-body interactions, we obtain convergence estimates uniform in h- bar, up to an exponentially small remainder. For h-bar = 0, the classical dynamics in the mean-field limit is given by the Vlasov equation. |
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PACM Colloquium |
Topic: |
Inverse scattering in nuclear magnetic resonance |
Presenter: |
Charles Epstein, Mathematics, University of Pennsylvania |
Date: |
Monday, November 27, 2006, Time: 4:00 p.m., Location: Fine 214 |
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Operations Research and Financial Engineering Seminar |
Topic: |
TBA |
Presenter: |
Marcel Rindisbacher, University of Toronto |
Date: |
Tuesday, November 28, 2006, Time: 4:30 p.m., Location: E-219, E-Quad |
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DECEMBER 2006 |
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PACM Colloquium - Distinguished Lecture Series |
Topic: |
TBA |
Presenter: |
Eric S. Lander, Broad Institute, Massachusetts Institute of Technology |
Date: |
Friday, December 1, 2006, Time: 8:00 p.m., Location:A02 McDonnell Hall |
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Algebraic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Günter Harder, Max Planck Institut für Mathematik; IAS |
Date: |
Tuesday, December 5, 2006, Time: 4:30 p.m., Location: Fine 322 |
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Operations Research and Financial Engineering Seminar |
Topic: |
TBA |
Presenter: |
Gordan Zitkovic, University of Texas |
Date: |
Tuesday, December 5, 2006, Time: 4:30 p.m., Location: E-219, E-Quad |
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Discrete Mathematics Seminar |
Topic: |
TBA |
Presenter: |
Tom Bohman, Carnegie Mellon University |
Date: |
Wednesday, December 6, 2006, Time: 2:15 p.m., Location: Fine 224 |
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Department Colloquium |
Topic: |
TBA |
Presenter: |
Yakov Sinai, Princeton University |
Date: |
Wednesday, December 6, 2006, Time: 4:30 p.m., Location: Fine 314 |
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Algebraic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Brendan Hassett, Rice University |
Date: |
Tuesday, December 12, 2006, Time: 4:30 p.m., Location: Fine 322 |
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