SEMINARS
Updated: 1-27-2010

   
FEBRUARY 2010
   
Geometry, Representation Theory, and Moduli Seminar
Topic: On the behavior of the test ideal under separable finite morphisms
Presenter: K. Tucker, Michigan
Date:  Monday, February 1, 2010, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: The test ideal is an invariant which measures singularities in positive characteristic commutative algebra. While appearing first in the celebrated theory of tight closure due to Hochster and Huneke, the importance test ideal in algebraic geometry is due to its mysterious correspondence with the multiplier ideal after reduction to characteristic p >> 0. I will report on recent joint work with Karl Schwede on the behavior of the test ideal under separable finite morphisms. The trace map plays a central role in our analysis, and also allows us to show an algebraic result of independent interest on the lifting properties of p^{-e}-linear maps.
   
Algebraic Geometry Seminar
Topic: TBA
Presenter: Antoine Ducros, University Paris VI
Date:  Tuesday, February 2, 2010, Time: 4:30 p.m., Location: Fine Hall 322
   
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.

   
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.
   
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: TBA
Presenter: Will Wylie, University of Pennsylvania
Date:  Friday, February 5, 2010, Time: 3:00 p.m., Location: Fine Hall 314
   
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: TBA
Presenter: Alain-Sol Sznitman, ETH, Zurich
Date:  Tuesday, February 9, 2010, Time: 4:30 p.m., Location: Jadwin 343
   
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
   
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
   
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: TBA
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
   
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
   
MARCH 2010
   
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
   
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
   
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
   
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
   
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
   
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
   
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, Mathematics and Computer Science, Darthmouth College
Date:  Monday, April 5, 2010, Time: 4:30 p.m., Location: Fine Hall 214
   
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
   
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
   
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