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| FEBRUARY 2011 |
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| Topology Seminar |
| Topic: |
Filtering smooth concordance classes of topologically slice knots |
| Presenter: |
Paul Horn, Columbia |
| Date: |
Thursday, February 3, 2011, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: |
Cochran, Orr, and Teichner introduced the n-solvable filtration of the knot concordance group, which has given a framework for recent advances in the study of knot concordance. However, it fails to detect anything about topologically slice knots, denoted T. We define a new filtration of the knot concordance group, relate it to known concordance invariants, and use Heegaard Floer homology to prove that it induces a non-trivial filtration on T. One application of this filtration is to say more about the fractal nature of the knot concordance group, i.e. the complexity of the Cochran-Orr-Teichner filtration embeds into T. This is joint work with Tim Cochran and Shelly Harvey. |
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| Differential Geometry and Geometric Analysis Seminar |
| Topic: |
TBA |
| Presenter: |
Alessio Figalli, Texas |
| Date: |
Friday, February 4, 2011, Time: 3:00 p.m., Location: Fine Hall 314 |
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| PACM Colloquium |
| Topic: |
High-dimensional reservoir neural dynamics: rules and rewards |
| Presenter: |
Xiao-Jing Wang, Yale University |
| Date: |
Monday, February 7, 2011, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: |
Neural activity recorded in behaving animals is highly variable and heterogeneous, which is especially true for neurons in the prefrontal cortex (PFC), the so called `CEO of the brain' of central importance to many cognitive functions. In this talk, I will present a reservoir-type model of randomly connected neurons to account for the diversity of neural signals in the prefrontal cortex. Specifically, I will show that such a network gives rise to mixed-selectivity of neurons that can encode task rules underlying flexible behaviors, and a broad range of time constants for short-term memory. |
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| Algebraic Geometry Seminar |
| Topic: |
TBA |
| Presenter: |
Daniel Greb,
Uni. Freiburg |
| Date: |
Tuesday, February 8, 2011, Time: 4:30 p.m., Location: Fine Hall 322 |
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| Department Colloquium |
| Topic: |
Multiple mixing and short polynomials |
| Presenter: |
David Masser, University of Basel, Switzerland |
| Date: |
Wednesday, February 9, 2011, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: |
See http://www.math.princeton.edu/~seminar/2010-11-sem/MasserAbstract02-09-2011.pdf |
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| Topology Seminar |
| Topic: |
TBA |
| Presenter: |
Rumen Zarev, Columbia |
| Date: |
Thursday, February 10, 2011, Time: 4:30 p.m., Location: Fine Hall 314 |
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| Princeton University and IAS Number Theory Seminar |
| Topic: |
Impossible intersections for elliptic curves |
| Presenter: |
David Masser, University of Basel, Switzerland |
| Date: |
Thursday, February 10, 2011, Time: 4:30 p.m., Location: TBA |
| Abstract: |
See http://www.math.princeton.edu/~seminar/2010-11-sem/MasserAbstract02-10-2011.pdf |
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| PACM Colloquium |
| Topic: |
A few computational and applied math problems in density functional theory related calculations |
| Presenter: |
Lin-Wang Wang, Lawrence Berkeley National Lab |
| Date: |
Monday, February 14, 2011, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: |
Density functional theory (DFT) has become the most widely used quantum mechanical method in material science simulations. Due to the change of computer architectures, and the corresponding change in the scope of problems amenable by the DFT method, the algorithms used in the DFT calculations are also changing. In this talk, I will discuss a few commonly used ground state based algorithms for large scale DFT calculations. I will also discuss what it will take to speed up the DFT molecular dynamics simulations by a thousand times, and the self-consistent problems often encountered in large system simulations. Some of our recent effort in implementing our planewave DFT code in GPU will also be discussed. Finally, I will present a method using auxiliary periodic boundary conditions to solve an open boundary condition scattering state problem in quantum transport calculations. |
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| Algebraic Geometry Seminar |
| Topic: |
TBA |
| Presenter: |
Tom Graber, Caltech & IAS |
| Date: |
Tuesday, February 15, 2011, Time: 4:30 p.m., Location: Fine Hall 322 |
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| Analysis Seminar |
| Topic: |
Explicit formula for the solution of the cubic Szego equation
on the real line and its applications |
| Presenter: |
Oana Pocovnicu, Universite Paris-Sud, Orsay |
| Date: |
Monday, February 21, 2011, Time: 4:00 p.m., Location: Fine Hall 314 |
| Abstract: |
In this talk we consider the cubic Szego equation: i u_t = Pi (|u|^2u)
on the real line, where Pi is the Szeg? projector on non-negative
frequencies. This equation was introduced as a model of a
non-dispersive Hamiltonian equation. Like 1-d cubic NLS and KdV, it
is known to be completely integrable in the sense that it possesses a
Lax pair structure. As a consequence, it turns out that a whole class
of finite dimensional manifolds, consisting of rational functions, is
invariant under the flow of the Szeg? equation.
First, we present an explicit formula for the solutions. Then, as an application, we prove soliton resolution in H^s, s>0, for "generic" data. Namely, we show that solutions with generic rational functions as initial data can be decomposed in H^s, for all s>0, into a sum of solitons plus a remainder, as time tends to infinity. As for non-generic data, we construct an example for which soliton resolution holds only in H^s, 0< s < 1/2, while the high Sobolev norms grow to infinity over time. As a second application, we construct explicit generalized action-angle coordinates on the manifolds of generic rational functions. In particular, this shows that most trajectories of the Szeg? equation spiral around Lagrangian toroidal cylinders (the non-compact generalizations of the Lagrangian tori in the Liouville-Arnold theorem). |
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| PACM Colloquium |
| Topic: |
TBA |
| Presenter: |
Robert Ghrist, University of Pennsylvania |
| Date: |
Monday, February 21, 2011, Time: 4:00 p.m., Location: Fine Hall 214 |
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| Algebraic Geometry Seminar |
| Topic: |
TBA |
| Presenter: |
Charles Doran, Univ. Alberta |
| Date: |
Tuesday, February 22, 2011, Time: 4:30 p.m., Location: Fine Hall 322 |
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| Topology Seminar |
| Topic: |
Right-angledness, flag complexes, asphericity |
| Presenter: |
Mike Davis, Ohio State and IAS |
| Date: |
Thursday, February 24, 2011, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: |
I will discuss three related constructions of spaces and manifolds and then give necessary and sufficient conditions for the resulting spaces to be aspherical. The first construction is the polyhedral product functor. The second construction involves applying the reflection group trick to a "corner of spaces". The third construction involves pulling back a corner of spaces via a coloring of a simplicial complex. The two main sources of examples of corners which yield aspherical results are: 1) products of aspherical manifolds with (aspherical) boundary and 2) the Borel-Serre bordification of torsion-free arithmetic groups which are nonuniform lattices. |
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| Joint Analysis Seminar and PACM Seminar |
| Topic: |
TBA |
| Presenter: |
Roman Vershynin, University of Michigan |
| Date: |
Monday, February 28, 2011, Time: 4:00 p.m., Location: Fine Hall 214 |
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| MARCH 2011 |
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| Algebraic Geometry Seminar |
| Topic: |
TBA |
| Presenter: |
Karen Smith, Univ. of Michigan |
| Date: |
Tuesday, March 1, 2011, Time: 4:30 p.m., Location: Fine Hall 322 |
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| Princeton University and IAS Number Theory Seminar |
| Topic: |
TBA |
| Presenter: |
Kartik Prasanna, University of Michigan, Ann Arbor |
| Date: |
Thursday, March 3, 2011, Time: 4:30 p.m., Location: TBA |
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| PACM Colloquium |
| Topic: |
Generalized Markov models in population genetics |
| Presenter: |
Joshua Plotkin, University of Pennsylvania |
| Date: |
Monday, March 7, 2011, Time: 4:00 p.m., Location: Fine Hall 214 |
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| Algebraic Geometry Seminar |
| Topic: |
TBA |
| Presenter: |
Kyungyong Lee, U. Conn. |
| Date: |
Tuesday, March 8, 2011, Time: 4:30 p.m., Location: Fine Hall 322 |
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| Topology Seminar |
| Topic: |
TBA |
| Presenter: |
Matt Hedden, Michigan State |
| Date: |
Thursday, March 10, 2011, Time: 4:30 p.m., Location: Fine Hall 314 |
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| PACM Colloquium |
| Topic: |
Brother, can you spare a compacton? |
| Presenter: |
Philip Rosenau, Tel Aviv University |
| Date: |
Monday, March 21, 2011, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: |
Unlike certain personal or national tragedies which may extend indefinitely, patterns observed in nature are of finite extent. Yet, as a rule, the solitary patterns predicted by almost all existing mathematical models extend indefinitely with their tails being a by product of their analytical nature. Rather then viewing such tails as a manifestation of the inherent limitation of math to model physics in detail, we adopt the opposite view: the persistence of tails in a large variety of solitary patterns points to a missing mechanism capable to constrain the pattern. Clearly, to induce a compact pattern one has to escape the curse of analyticity. Differently stated, one has to supplement the existing models with a mechanism(s) which may beget a local singularity. When this is done the resulting local loss of solution's uniqueness enables to connect a smooth part of the solution with the trivial ground state and thus to form an entity with a compact support: the compacton. We shall describe a variety of singularity inducing mechanisms that beget compact solutions of dispersive or dissipative uni and multi-dimensional phenomena. Compactified variants of the K-dV, Klein-Gordon and Schroedinger equations will be surveyed. In Part two of the lecture we shall discuss the intriguing nature of these (weakly strong or strongly weak) solutions, the underlying singularities and their relation with a discrete antecedent where a sharp fronts are replaced with tails decaying at a doubly exponential rate. |
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| Differential Geometry and Geometric Analysis Seminar |
| Topic: |
TBA |
| Presenter: |
Min-Chun Hong, University of Queensland Brisbane |
| Date: |
Friday, March 25, 2011, Time: 3:00 p.m., Location: Fine Hall 314 |
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| APRIL 2011 |
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| Joint Analysis and PACM Seminar |
| Topic: |
TBA |
| Presenter: |
Peter Jones, Yale University |
| Date: |
Monday, April 4, 2011, Time: 4:00 p.m., Location: Fine Hall 214 |
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| PACM Colloquium - Distinguished Lecture Seminar ***Please note special date |
| Topic: |
TBA |
| Presenter: |
Ray Goldstein, Cambridge University |
| Date: |
Wednesday, April 6, 2011, Time: 4:00 p.m., Location: Fine Hall 214 |
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| Differential Geometry and Geometric Analysis Seminar |
| Topic: |
TBA |
| Presenter: |
Dmitri Burago, Penn State |
| Date: |
Friday, April 8, 2011, Time: 3:00 p.m., Location: Fine Hall 314 |
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| PACM Colloquium |
| Topic: |
TBA |
| Presenter: |
Antonin Chambolle, CMAP -- Ecole Polytechnique |
| Date: |
Monday, April 11, 2011, Time: 4:00 p.m., Location: Fine Hall 214 |
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| Algebraic Geometry Seminar |
| Topic: |
TBA |
| Presenter: |
Mircea Mustaţă, U. of Michigan |
| Date: |
Tuesday, April 12, 2011, Time: 4:30 p.m., Location: Fine Hall 322 |
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| PACM Colloquium |
| Topic: |
TBA |
| Presenter: |
Gregory Rempala, Medical College of Georgia |
| Date: |
Monday, April 18, 2011, Time: 4:00 p.m., Location: Fine Hall 214 |
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| Princeton University and IAS Number Theory Seminar |
| Topic: |
TBA |
| Presenter: |
Henri Darmon, McGill University |
| Date: |
Thursday, April 21, 2011, Time: 4:30 p.m., Location: TBA |
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| PACM Colloquium |
| Topic: |
TBA |
| Presenter: |
Boaz Nadler, Weizmann Institute -- Israel |
| Date: |
Monday, April 25, 2011, Time: 4:00 p.m., Location: Fine Hall 214 |
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| Topology Seminar |
| Topic: |
TBA |
| Presenter: |
Peter Ozsvath, MIT |
| Date: |
Thursday, April 28, 2011, Time: 4:30 p.m., Location: Fine Hall 314 |
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| Differential Geometry and Geometric Analysis Seminar |
| Topic: |
TBA |
| Presenter: |
Artem Pulemotov, Chicago |
| Date: |
Friday, April 29, 2011, Time: 3:00 p.m., Location: Fine Hall 314 |
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