SEMINARS
Updated: 2-3-2010

   
FEBRUARY 2010
   
   
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.

   
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.
   
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.
   
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.
   
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.
   
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.
   
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.
   
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.
   
Algebraic Geometry Seminar
Topic: TBA
Presenter: Maksym Fedorchuk, Columbia University
Date:  Tuesday, February 9, 2010, Time: 4:30 p.m., Location: Fine Hall 322
   
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.
   
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
   
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.

   
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
   
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.
   
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
   
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.
   
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.
   
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.
   
Algebraic Geometry Seminar
Topic: TBA
Presenter: Chenyang Xu, MIT
Date:  Tuesday, February 16, 2010, Time: 4:30 p.m., Location: Fine Hall 322
   
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
   
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
   
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
   
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.
   
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
   
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
   
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
   
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
   
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
   
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
   
   
MARCH 2010
   
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.
   
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
   
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
   
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
   
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
   
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.
   
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
   
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
   
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
   
Analysis Seminar
Topic: TBA
Presenter: Michael Weinstein, Columbia University
Date:  Monday, March 22, 2010, Time: 4:00 p.m., Location: Fine Hall 110
   
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
   
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
   
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
   
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
   
Algebraic Geometry Seminar
Topic: TBA
Presenter: Maksym Fedorchuk, Columbia University
Date:  Tuesday, March 30, 2010, Time: 4:30 p.m., Location: Fine Hall 322
   
APRIL 2010
   
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
   
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
   
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
   
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
   
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
   
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
   
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
   
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
   
Algebraic Geometry Seminar
Topic: TBA
Presenter: Dragos Oprea, UCSD
Date:  Tuesday, April 20, 2010, Time: 4:30 p.m., Location: Fine Hall 322
   
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
   
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
   
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
   
MAY 2010
   
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
   
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