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