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FEBRUARY 2010 |
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Department Colloquium |
Topic: |
Mathematical Theory of Cryo-Electron Microscopy |
Presenter: |
Amit Singer, Princeton University |
Date: |
Wednesday, February 3, 2010, Time: 4:30 p.m., Location: Fine Hall 314 |
Abstract: |
The importance of determining three dimensional macromolecular structures for large biological molecules was recognized by the Nobel Prize in Chemistry awarded this year to V. Ramakrishnan, T. Steitz and A. Yonath for studies of the structure and function of the ribosome. The standard procedure for structure determination of large molecules is X-ray crystallography, where the challenge is often more in the crystallization itself than in the interpretation of the X-ray results, since many large proteins have so far withstood all attempts to crystallize them.
In cryo-EM, an alternative to X-ray crystallography, the sample of macromolecules is rapidly frozen in an ice layer so thin that their tomographic projections taken by the electron microscope are typically disjoint. The cryo-EM imaging process produces a large collection of tomographic projections of the same molecule, corresponding to different and unknown projection orientations. The goal is to reconstruct the 3D structure of the molecule from such unlabeled 2D projection images, where data sets typically range from 104 to 105 projection images whose size is roughly 100 x 100 pixels.
I will present a new algorithm for finding the unknown imaging directions of all projections. Compared with existing algorithms, the advantages of the algorithm are five-fold: first, it has a small estimation error even for images of very low signal-to-noise ratio (SNR); second, the algorithm is extremely fast, as it involves only the computation of a few top eigenvectors of a specially designed symmetric matrix; third, it is non-sequential and uses the information in all images at once; fourth, it is amenable to rigorous mathematical analysis using representation theory of the rotation group SO(3) and random matrix theory; finally, the algorithm is optimal in the sense that it reaches the information theoretic Shannon bound up to a constant.
Time permitting, I will discuss generalizations of the algorithm and its mathematical analysis to other applications in computer vision, structural biology and dimensionality reduction. |
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Ergodic Theory and Statistical Mechanics Seminar |
Topic: |
The spectral dichotomy for one-frequency Schrodinger operators |
Presenter: |
Artur Avila, CNRS and IMPA |
Date: |
Thursday, February 4, 2010, Time: 2:00 p.m., Location: Fine Hall 401 |
Abstract: |
In the theory of one-frequency Schrodinger operators, the best understood potentials have been those that can be somehow considered either small or large. Roughly, small potentials tend to inherit the behavior of the Laplacian and present absolutely continuous spectral measures (leading to good transport properties), while for large potentials it is Anderson localization that prevails.
Dynamically, those two distinct local theories correspond to a good understanding of cocycles near constant (``the domain of KAM''), and nonuniformly hyperbolic cocycles. We have proposed to build a global theory by focusing on the description of the phase-transition, from KAM to non-uniform hyperbolicity, in the infinite-dimensional space of cocycles. Its goal was to prove the Spectral Dichotomy: typically, an operator is the direct sum of a ``small-like'' and a ``big-like'' operators, with disjoint spectra.
We will describe the structure of the proof of the Spectral Dichotomy, which has two main parts. The firt one describes the locus of criticality from the point of view of Lyapunov exponents, i.e., the boundary of nonuniform hyperbolicity. The second one relates zero Lyapunov exponents and KAM. |
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Joint Princeton University and Institute for Advanced Study Number Theory Seminar |
Topic: |
Generalized modular functions |
Presenter: |
W. Kohnen, Heidelberg |
Date: |
Thursday, February 4, 2010, Time: 4:30 p.m., Location: IAS S-101 |
Abstract: |
Generalized modular functions are holomorphic functions on the complex upper half-plane, meromorphic at the cusps that satisfy the usual defintion of a modular function, however with the important exception that the character need not be unitary. The theory is partly motivated from conformal field theory in physics. In my talk I will report on recent joint work with G. Mason on properties of their Fourier coefficients and characters. |
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Topology Seminar |
Topic: |
Quasigeodesic pseudo-Anosov flows |
Presenter: |
Sergio Fenley, Princeton University |
Date: |
Thursday, February 4, 2010, Time: 4:30 p.m., Location: Fine Hall 314 |
Abstract: |
A quasigeodesic is a curve which is uniformly efficient in measuring distance in relative homotopy classes or equivalently efficient up to a bounded multiplicative distortion in measuring distance when lifted to the universal cover. A flow is quasigeodesic if all flow lines are quasigeodesics. The talk will explore quasigeodesic pseudo-Anosov flows in atoroidal 3-manifolds, of which there are several infinite families of examples. By geometrization and irreducibility the manifolds are hyperbolic. In such manifolds quasigeodesics are extremely important as for instance they are a bounded distance from minimal geodesics (in the universal cover). One important result is that such flows induce ideal maps from the ideal boundary of the stable/unstable leaves to the boundary of hyperbolic 3-space. The talk will also explore properties of these maps and in particular identification of ideal points. This is connected with the property of the stable/unstable foliations being quasi-isometric foliations. The tools are the dynamics of the flow and also the large scale geometry of the universal cover. |
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Special Group Actions Seminar *** Please note special date, time, and location |
Topic: |
On Ulam stability |
Presenter: |
Marc Burger, ETH |
Date: |
Friday, February 5, 2010, Time: 12:30 p.m., Location: Fine Hall PL |
Abstract: |
We report on recent progress concerning the Ulam stability problem, namely to determine under which conditions an-epsilon-homomorphism with values in a group with a distance, is uniformly close to an actual homomorphism. This is joint work with A.Thom and N.Ozawa. |
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Differential Geometry and Geometric Analysis Seminar |
Topic: |
On m-Quasi Einstein metrics |
Presenter: |
Will Wylie, University of Pennsylvania |
Date: |
Friday, February 5, 2010, Time: 3:00 p.m., Location: Fine Hall 314 |
Abstract: |
We say an n-dimensional Riemannian manifold is an m-Quasi Einstein metric if it is the base of an (n+m)-dimensional warped product Einstein manifold. We view the m-Quasi Einstein equation as a generalization of the Einstein equation (since an Einstein manifold is the base of a trivial product Einstein manifold). The m-Quasi Einstein equation is also closely related to the gradient Ricci soliton equation. In this talk I will give an overview of some earlier results about the classification of m-quasi Einstein metrics and prove a new classification of m-Quasi Einstein metrics with harmonic curvature. This is joint work with Peter Petersen and Chenxu He. |
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Analysis Seminar *** Please note special time |
Topic: |
Generalized principal eigenvalue of elliptic operators in unbounded domains and applications |
Presenter: |
H. Berestycki, EHESS, Paris and University of Chicago |
Date: |
Monday, February 8, 2010, Time: 3:00 p.m., Location: Fine Hall 110 |
Abstract: |
In this talk, I will discuss several notions that are extensions of the principal eigenvalue of a linear elliptic operator to the framework of unbounded domains along with some of their properties. I will describe applications to semi-linear elliptic equations and to propagation in reaction-diffusion equations of the KPP type. These equations are considered in unbounded domains and for general heterogeneous settings. I report here on joint works with Luca Rossi, with François Hamel and with Grégoire Nadin. |
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PACM Colloquium |
Topic: |
Dynamics of renormalization operators |
Presenter: |
Artur Avila, Director of Research, IMPA |
Date: |
Monday, February 8, 2010, Time: 4:00 p.m., Location: Fine Hall 214 |
Abstract: |
It is a remarkable characteristic of some classes of low-dimensional dynamical systems that their long time behavior at a short spatial scale is described by an induced dynamical system in the same class. The renormalization operator that relates the original and the induced transformations can then be iterated. We will discuss how features (such as hyperbolicity) of this "dynamics in parameter space" impact the underlying systems, especially in the case of typical parameters. |
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Algebraic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Maksym Fedorchuk, Columbia University |
Date: |
Tuesday, February 9, 2010, Time: 4:30 p.m., Location: Fine Hall 322 |
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Mathematical Physics Seminar |
Topic: |
Disconnection and Random Interlacements |
Presenter: |
Alain-Sol Sznitman, ETH, Zurich |
Date: |
Tuesday, February 9, 2010, Time: 4:30 p.m., Location: Jadwin 343 |
Abstract: |
The general theme of the talk pertains to the question of understanding how paths of random walks can create large separating interfaces. This question has in particular been investigated in the context of random walk on a discrete cylinder with a large connected base, and when discussing the presence or absence of a giant component in the complement of the trajectory of a random walk on a large discrete torus. We will present an overview of some of the results, and paradigms, which have now emerged and explain how the above problems are related to questions of ercolation and to the model of random interlacements. |
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Special Seminar |
Topic: |
History of the Kervaire invariant problem |
Presenter: |
Bill Browder, Princeton University |
Date: |
Wednesday, February 10, 2010, Time: 3:00 p.m., Location: Fine Hall 110 |
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Department Colloquium |
Topic: |
The Kervaire invariant problem |
Presenter: |
Mike Hopkins, Harvard University |
Date: |
Wednesday, February 10, 2010, Time: 4:30 p.m., Location: Fine Hall 314 |
Abstract: |
The of existence of framed manifolds of Kervaire invariant one
is one of the oldest unresolved problems in algebraic topology.
Important questions about smooth structures on spheres and on the
homotopy groups of spheres depend on its solution. In this talk I
will describe joint work with Mike Hill and Doug Ravenel which solves
this problem in all dimensions except 126. |
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Topology Seminar ***Please note special time and location |
Topic: |
Grothendieck's problem for 3-manifold groups |
Presenter: |
Alan Reid, UT Austin |
Date: |
Thursday, February 11, 2010, Time: 11:00 a.m., Location: Fine Hall 110 |
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Algebraic Topology Seminar |
Topic: |
Equivariant Computations and the Gap Theorem |
Presenter: |
Mike Hill, University of Virginia |
Date: |
Thursday, February 11, 2010, Time: 2:30 p.m., Location: Fine Hall 110 |
Abstract: |
I'll show how elementary computations with equivariant chain complexes and homology can be used to prove the vanishing of certain homotopy groups. Together with the detection theorem, this shows that the group in which the Kervaire classes would be detected is the zero group. |
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Joint Princeton University and Institute for Advanced Study Number Theory Seminar |
Topic: |
TBA |
Presenter: |
Vinayak Vatsal, University of British Columbia, Vancouver |
Date: |
Thursday, February 11, 2010, Time: 4:30 p.m., Location: Fine Hall 214 |
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Topology Seminar |
Topic: |
The proof of the Periodicity Theorem |
Presenter: |
Douglas C. Ravenel, University of Rochester |
Date: |
Thursday, February 11, 2010, Time: 4:30 p.m., Location: Fine Hall 314 |
Abstract: |
The Periodicity Theorem is one of the key steps in the proof of the Kervaire Invariant Theorem. Its proof involves methods from equivariant stable homotopy theory including computations with $RO(G)$-graded homotopy groups. |
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Differential Geometry and Geometric Analysis Seminar |
Topic: |
Optimal conditions for the extension of the mean curvature flow |
Presenter: |
Nam Le, Columbia University |
Date: |
Friday, February 12, 2010, Time: 3:00 p.m., Location: Fine Hall 314 |
Abstract: |
In this talk, we will discuss several optimal (global) conditions for the existence of a smooth solution to the mean curvature flow. Our focus will be on quantities involving only the mean curvature. We will also discuss several applications of a local curvature estimate which is a parabolic analogue of Choi-Schoen estimate for minimal submanifolds. This is joint work with Natasa Sesum. |
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PACM Colloquium |
Topic: |
A Database Schema for the Global Dynamics of Multiparameter Nonlinear Systems |
Presenter: |
Konstantin Mischaikow, Mathematics and BioMaPS Institute, Rutgers University |
Date: |
Monday, February 15, 2010, Time: 4:00 p.m., Location: Fine Hall 214 |
Abstract: |
Prof. Mischaikow will discuss new computational tools based on topological methods that extracts coarse, but rigorous, combinatorial descriptions of global dynamics of multiparameter nonlinear systems. This techniques are motivated by several observations which we claim can, at least in part, be addressed:
1. In many applications there are models for the dynamics, but specific parameters are unknown or not directly computable. To identify the parameters one needs to be able to match dynamics produced by the model against that which is observed experimentally.
2. It is well established that nonlinear dynamical systems can produce extremely complicated dynamics, e.g. chaos, however experimental measurements are often too crude to identify such fine structure.
3. Often the models themselves are based on heuristics as opposed to being derived from first principles and thus the fine structure of the dynamics produced by the models may be of little interest for the applications in mind. To make the above mentioned comments concrete, Prof. Mischaikow will describe the techniques in the context of a simple model arising in population biology. |
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Algebraic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Chenyang Xu, MIT |
Date: |
Tuesday, February 16, 2010, Time: 4:30 p.m., Location: Fine Hall 322 |
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Ergodic Theory and Statistical Mechanics Seminar |
Topic: |
TBA |
Presenter: |
Zeev Rudnick, Tel Aviv University and IAS |
Date: |
Thursday, February 18, 2010, Time: 2:00 p.m., Location: Fine Hall 401 |
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Joint Princeton University and Institute for Advanced Study Number Theory Seminar |
Topic: |
TBA |
Presenter: |
W. Duke, UCLA |
Date: |
Thursday, February 18, 2010, Time: 4:30 p.m., Location: IAS S-101 |
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Differential Geometry and Geometric Analysis Seminar |
Topic: |
TBA |
Presenter: |
Hans-Joachim Hein, Princeton University |
Date: |
Friday, February 19, 2010, Time: 3:00 p.m., Location: Fine Hall 314 |
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PACM Colloquium |
Topic: |
Detection of Faint Edges in Noisy Images |
Presenter: |
Ronen Basri, Weizmann Institute of Science in Israel, Computer Science & Applied Math Dept. |
Date: |
Monday, February 22, 2010, Time: 4:00 p.m., Location: Fine Hall 214 |
Abstract: |
One of the most intensively studied problems in image processing concerns how to detect edges in images. Edges are important since they mark the locations of discontinuities in depth, surface orientation, or reflectance, and their detection can facilitate a variety of applications including image segmentation and object recognition. Accurate detection of faint, low-**contrast edges in noisy images is challenging. Optimal detection of such edges can potentially be achieved if we use filters that match the shapes, lengths, and orientations of the sought edges. This however requires search in the space of continuous curves. In this talk we explore the limits of detectability, taking into account the lengths of edges and their combinatorics. We further construct two efficient multi-level algorithms for edge detection. The first algorithm uses a family of rectangular filters of variable lengths and orientations. The second algorithm uses a family of curved filters constructed through a dynamic-**programming-like procedure using a modified beamlet transform. We demonstrate the power of these algorithms in applications to both noisy and natural images, showing state-of-the-art results. Joint work with Meirav Galun, Achi Brandt, and Sharon Alpert. |
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Geometry, Representation Theory, and Moduli Seminar |
Topic: |
TBA |
Presenter: |
S. Sierra, Princeton University |
Date: |
Monday, February 22, 2010, Time: 4:30 p.m., Location: Fine Hall 314 |
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Algebraic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Arend Bayer, University of Connecticut |
Date: |
Tuesday, February 23, 2010, Time: 4:30 p.m., Location: Fine Hall 322 |
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Ergodic Theory and Statistical Mechanics Seminar |
Topic: |
TBA |
Presenter: |
Vlad Vysotsky, University of Delaware |
Date: |
Thursday, February 25, 2010, Time: 2:00 p.m., Location: Fine Hall 401 |
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Differential Geometry and Geometric Analysis Seminar |
Topic: |
TBA |
Presenter: |
Jeffrey Case, UCSB |
Date: |
Friday, February 26, 2010, Time: 3:00 p.m., Location: Fine Hall 314 |
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Special Joint Columbia/Courant/Princeton Algebraic Geometry Seminar |
Topic: |
Normal forms for lattice polarized K3 surfaces and Siegel modular forms |
Presenter: |
Charles Doran, University of Alberta |
Date: |
Friday, February 26, 2010, Time: TBA, Location: NYU, WWH 101 |
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Special Joint Columbia/Courant/Princeton Algebraic Geometry Seminar |
Topic: |
Prime exceptional divisors on holomorphic symplectic varieties |
Presenter: |
Eyal Markman, University of Massachusetts, Amherst |
Date: |
Friday, February 26, 2010, Time: TBA, Location: NYU, WWH 101 |
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MARCH 2010 |
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Group Actions Seminar |
Topic: |
The algebra of pairs swapping |
Presenter: |
Francois Labourie, Orsay University |
Date: |
Tuesday, March 2, 2010, Time: 12:30 p.m., Location: Fine Hall 322 |
Abstract: |
We shall define an elementary Poisson algebra out of pair of points on any subset of the circle. We then prove that a -- related -- algebra appears both as a Poisson algebra of functions on curves in the projective space equipped with the Gelfand-Dikkii algebras, and as a -- limit -- Poisson algebra of the character variety of a surface group in SL(n,R). This gives some flesh to a suggestion by Witten that Wn algebras should be related to Hitchin components. |
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Algebraic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Jason Starr, Stony Brook University |
Date: |
Tuesday, March 2, 2010, Time: 4:30 p.m., Location: Fine Hall 322 |
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Mathematical Physics Seminar |
Topic: |
On the Boltzmann limit of a homogeneous Fermi gas |
Presenter: |
Igor Rodnianski, Princeton University |
Date: |
Tuesday, March 2, 2010, Time: 4:30 p.m., Location: Jadwin 343 |
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Ergodic Theory and Statistical Mechanics Seminar |
Topic: |
TBA |
Presenter: |
Francesco Cellarosi, Princeton University |
Date: |
Thursday, March 4, 2010, Time: 2:00 p.m., Location: Fine Hall 401 |
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Differential Geometry and Geometric Analysis Seminar |
Topic: |
TBA |
Presenter: |
Mario Bonk, Michigan |
Date: |
Friday, March 5, 2010, Time: 3:00 p.m., Location: Fine Hall 314 |
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Analysis Seminar |
Topic: |
Complex variables are not dead |
Presenter: |
Leon Ehrenpreis, Temple University, Philadelphia |
Date: |
Monday, March 8, 2010, Time: 4:00 p.m., Location: Fine Hall 110 |
Abstract: |
Our lecture will focus on two problems in pde which are solvable by ideas in holomorphic functions of complex variables. The first problem is called the strip theorem. Let f be a function defined in the strip in the complex plane l Im z l <= 1. Suppose f agrees on the boundary of each unit circle centered on the real axis, radius 1, with the solution (depending on the circle) of a suitable elliptic pde, the agreement being to order one greater than the order of the Dirichlet data. Then f satisfies this pde. If the equation is the Cauchy-Riemann equation then equality suffices. The second type of problems we discuss are the Phragmen-Lindelof theorem for pde and a form of the Heisenberg uncertainty for pde. These were introduced in Kenig's lecture at Fefferman's birthday bash. We shall put them in a general framework. |
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Algebraic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Aaron Bertram, University of Utah |
Date: |
Tuesday, March 9, 2010, Time: 4:30 p.m., Location: Fine Hall 322 |
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Ergodic Theory and Statistical Mechanics Seminar |
Topic: |
TBA |
Presenter: |
John Pardon, Princeton University |
Date: |
Thursday, March 11, 2010, Time: 2:00 p.m., Location: Fine Hall 401 |
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Differential Geometry and Geometric Analysis Seminar |
Topic: |
TBA |
Presenter: |
Pierre Albin, Courant |
Date: |
Friday, March 12, 2010, Time: 3:00 p.m., Location: Fine Hall 314 |
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Analysis Seminar |
Topic: |
TBA |
Presenter: |
Michael Weinstein, Columbia University |
Date: |
Monday, March 22, 2010, Time: 4:00 p.m., Location: Fine Hall 110 |
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Group Actions Seminar |
Topic: |
TBA |
Presenter: |
Kevin Wortman, University of Utah |
Date: |
Tuesday, March 23, 2010, Time: 12:30 p.m., Location: Fine Hall 322 |
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Algebraic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Sándor Kovács, University of Washington |
Date: |
Tuesday, March 23, 2010, Time: 4:30 p.m., Location: Fine Hall 322 |
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Ergodic Theory and Statistical Mechanics Seminar |
Topic: |
TBA |
Presenter: |
Ilya Vinogrodov, Princeton University |
Date: |
Thursday, March 25, 2010, Time: 2:00 p.m., Location: Fine Hall 401 |
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Differential Geometry and Geometric Analysis Seminar |
Topic: |
TBA |
Presenter: |
Jih-Hsin Cheng, Academia Sinica, Taiwan |
Date: |
Friday, March 26, 2010, Time: 3:00 p.m., Location: Fine Hall 314 |
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Algebraic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Maksym Fedorchuk, Columbia University |
Date: |
Tuesday, March 30, 2010, Time: 4:30 p.m., Location: Fine Hall 322 |
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APRIL 2010 |
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Ergodic Theory and Statistical Mechanics Seminar |
Topic: |
TBA |
Presenter: |
Vitaly Bergelson, Ohio State University |
Date: |
Thursday, April 1, 2010, Time: 2:00 p.m., Location: Fine Hall 401 |
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Geometry, Representation Theory, and Moduli Seminar |
Topic: |
TBA |
Presenter: |
Y. Ruan, Michigan |
Date: |
Monday, April 5, 2010, Time: 4:30 p.m., Location: Fine Hall 314 |
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PACM Colloquium |
Topic: |
TBA |
Presenter: |
Peter Winkler, AT&T Labs Research, Florham Park NJ |
Date: |
Monday, April 5, 2010, Time: 4:30 p.m., Location: Fine Hall 214 |
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PACM Colloquium |
Topic: |
TBA |
Presenter: |
Walter Willinger, Mathematics and Computer Science, Darthmouth College |
Date: |
Monday, April 12, 2010, Time: 4:30 p.m., Location: Fine Hall 214 |
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Group Actions Seminar |
Topic: |
TBA |
Presenter: |
Daryl Cooper, University of California, Santa Barbara |
Date: |
Tuesday, April 13, 2010, Time: 12:30 p.m., Location: Fine Hall 322 |
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Ergodic Theory and Statistical Mechanics Seminar |
Topic: |
TBA |
Presenter: |
Alex Kontorovich, Brown University and IAS |
Date: |
Thursday, April 15, 2010, Time: 2:00 p.m., Location: Fine Hall 401 |
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Differential Geometry and Geometric Analysis Seminar |
Topic: |
TBA |
Presenter: |
Julie Rowlett, Bonn |
Date: |
Friday, April 16, 2010, Time: 3:00 p.m., Location: Fine Hall 314 |
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Geometry, Representation Theory, and Moduli Seminar |
Topic: |
TBA |
Presenter: |
G. Bellamy, Edinburgh |
Date: |
Monday, April 19, 2010, Time: 4:30 p.m., Location: Fine Hall 314 |
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Algebraic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Dragos Oprea, UCSD |
Date: |
Tuesday, April 20, 2010, Time: 4:30 p.m., Location: Fine Hall 322 |
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Differential Geometry and Geometric Analysis Seminar |
Topic: |
TBA |
Presenter: |
Antonio Sa Barreto, Purdue |
Date: |
Friday, April 23, 2010, Time: 3:00 p.m., Location: Fine Hall 314 |
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PACM Colloquium |
Topic: |
TBA |
Presenter: |
Jonathan Weare, Courant Institute for Mathematics, NYC |
Date: |
Monday, April 26, 2010, Time: 4:30 p.m., Location: Fine Hall 214 |
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Differential Geometry and Geometric Analysis Seminar |
Topic: |
TBA |
Presenter: |
Valentino Tosatti, Columbia University |
Date: |
Friday, April 30, 2010, Time: 3:00 p.m., Location: Fine Hall 314 |
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MAY 2010 |
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Differential Geometry and Geometric Analysis Seminar |
Topic: |
TBA |
Presenter: |
Xavier Cabre, Universitat Politècnica de Catalunya |
Date: |
Friday, May 7, 2010, Time: 3:00 p.m., Location: Fine Hall 314 |
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PACM Colloquium |
Topic: |
TBA |
Presenter: |
Anthony Peirce, University of British Columbia |
Date: |
Monday, May 17, 2010, Time: 4:30 p.m., Location: Fine Hall 214 |
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