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| SEPTEMBER 2010 |
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| Analysis Seminar *** Please note special time |
| Topic: |
Narcissistic Skyrmions |
| Presenter: |
Claude Warnick, University of Cambridge |
| Date: |
Monday, September 13, 2010, Time: 2:00 p.m., Location: Fine Hall 314 |
| Abstract: |
The Skyrme model is a nonlinear sigma-model whose topologically non-trivial target space allows the existence of so-called topological solitons. Such solitons were proposed by Skyrme to model nuclear matter. In this talk I will review the history of the model and present recent work with Gary Gibbons and Willie Wong ruling out the existence of solitons with a planar reflection symmetry. In particular, I will show that a Skyrme soliton is attracted to its mirror image, preventing a static equilibrium. |
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| Joint Analysis/PACM Colloquium |
| Topic: |
Optimal Error Estimates in Stochastic Homogenization |
| Presenter: |
Felix Otto, Institute for Applied Mathematics, University of Bonn, Germany |
| Date: |
Monday, September 20, 2010, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: |
http://www.math.princeton.edu/~seminar/2010-11-sem/OttoAbstract9-20-2010.pdf |
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| Differential Geometry and Geometric Analysis Seminar |
| Topic: |
Gradient Ricci Solitons |
| Presenter: |
Ovidiu Munteanu, Columbia University |
| Date: |
Friday, September 24, 2010, Time: 3:00 p.m., Location: Fine Hall 314 |
| Abstract: |
We present some recent development in the study of gradient shrinking Ricci solitons. We address some questions about their classification and their geometric and topological structure. |
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| PACM Colloquium |
| Topic: |
Still running! Recent work on the neuromechanics of insect locomotion |
| Presenter: |
Philip Holmes, Princeton University |
| Date: |
Monday, September 27, 2010, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: |
I will describe several models for running insects, from an energy-conserving biped with passively-sprung legs to a muscle-actuated hexapod driven by a neural central pattern generator(CPG). Phase reduction and averaging theory collapses some 300 differential equations that describe this neuromechanical model to 24 one-dimensional oscillators that track motoneuron phases. The reduced model accurately captures the dynamics of unperturbed gaits and the effects of impulsive perturbations, and phase response and coupling functions provide improved understanding of reflexive feedback mechanisms. Specifically, piecewise-holonomic constraints due to intermittent foot contacts confers asymptotic stability on the CPG-driven feedforward system, the natural dynamics features a slow subspace that permits maneuverability, and leg force sensors modulate firing patterns to mitigate large perturbations. More generally, I will argue that both simple models and large simulations are necessary to understand such complex systems. The talk will draw on joint work with Einat Fuchs, Robert Full, Raffaele Ghigliazza, Raghu Kukillaya, Josh Proctor, John Schmitt, Justin Seipel and Manoj Srinivasan. Research supported by NSF and the J. Insley Blair Pyne Fund of Princeton University. |
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| Algebraic Geometry Seminar |
| Topic: |
TBA |
| Presenter: |
Christian Schnell, UIC |
| Date: |
Tuesday, September 28, 2010, Time: 4:30 p.m., Location: Fine Hall 322 |
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| OCTOBER 2010 |
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| Differential Geometry and Geometric Analysis Seminar |
| Topic: |
TBA |
| Presenter: |
Simon Brendle, Stanford University |
| Date: |
Friday, October 1, 2010, Time: 3:00 p.m., Location: Fine Hall 314 |
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| PACM Colloquium |
| Topic: |
Vertex-disjoint paths in tournaments |
| Presenter: |
Maria Chudnovsky, Columbia University |
| Date: |
Monday, October 4, 2010, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: |
The question of linking pairs of terminals by disjoint paths is a standard and well-studied question in graph theory. The setup is: given vertices s1,..,sk and t1,..,tk, is there a set of disjoint path P1,..,Pk such that Pi is a path from si to ti? This question makes sense in both directed and undirected graphs, and the paths may be required to be edge- or vertex-disjoint. For undirected graphs, a polynomial-time algorithm for solving both the edge-disjoint and the vertex-disjoint version of the problem (where the number k of terminals is fixed) was first found by Robertson and Seymour, and is a part of their well-known Graph Minors project. For directed graphs, both problems are NP-complete, even when k=2 (by a result of Fortune, Hopcroft and Wyllie). However, if we restrict our attention to tournaments (these are directed graphs with exactly one arc between every two vertices), the situation improves. Polynomial time algorithms for solving the edge-disjoint and the vertex-disjoint paths problems when k=2 have been known for a while(these are results of Bang-Jensen, and Bang-Jensen and Thomassen, respectively). Last year, Fradkin and Seymour were able to design a polynomial-time algorithm to solve the edge-disjoint paths problem in tournaments for general(fixed) k, using a new parameter for tournaments, developed by Seymour and the speaker, called "cut-width". However, the vertex-disjoint paths problem seemed to be resistant to similar methods. This talk will focus on the polynomial-time algorithm to solve the vertex-disjoint paths problem in tournaments for general (fixed) k, that we have recently obtained in joint work with Scott and Seymour. |
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| Algebraic Geometry Seminar |
| Topic: |
Gradient ideals |
| Presenter: |
Yu-Han Liu, Princeton University |
| Date: |
Tuesday, October 5, 2010, Time: 4:30 p.m., Location: Fine Hall 322 |
| Abstract: |
Zero schemes of exact 1-forms have received more attention recently as moduli spaces associated to Calabi-Yau threefolds; they are called gradient schemes or critical schemes. In this talk I will introduce the notion of "multi-gradient schemes" as an obvious generalization and explain their classification in the codimension one and monomial cases, as well as how they naturally arise as certain moduli spaces associated to varieties with globally generated canonical bundles. |
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| PACM Colloquium |
| Topic: |
Extrapolation Models |
| Presenter: |
David Levin, Tel Aviv University |
| Date: |
Monday, October 11, 2010, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: |
http://www.math.princeton.edu/~seminar/2010-11-sem/LevinAbstract10-11-2010.pdf |
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| Algebraic Geometry Seminar |
| Topic: |
TBA |
| Presenter: |
Dan Edidin, University of Missouri |
| Date: |
Tuesday, October 12, 2010, Time: 4:30 p.m., Location: Fine Hall 322 |
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| PACM Colloquium |
| Topic: |
TBA |
| Presenter: |
Ali Jadbabaie, University of Pennsylvania |
| Date: |
Monday, October 18, 2010, Time: 4:00 p.m., Location: Fine Hall 214 |
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| NOVEMBER 2010 |
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| PACM Colloquium |
| Topic: |
Novel Phenomena and Models of Active Fluids |
| Presenter: |
Michael Shelley, Courant Institute |
| Date: |
Monday, November 8, 2010, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: |
Fluids with suspended microstructure - complex fluids - are common actors in micro- and biofluidics applications and can have fascinating dynamical behaviors. A new area of complex fluid dynamics concerns "active fluids" which are internally driven by having dynamic microstructure such as swimming bacteria. Such motile suspensions are important to biology, and are candidate systems for tasks such as microfluidic mixing and pumping. To understand these systems, we have developed both first-principles particle and continuum kinetic models for studying the collective dynamics of hydrodynamically interacting microswimmers. The kinetic model couples together the dynamics of a Stokesian fluid with that of an evolving "active" stress field. It has a very interesting analytical and dynamical structure, and predicts critical conditions for the emergence of hydrodynamic instabilities and fluid mixing. These predictions are verified in our detailed particle simulations, and are consistent with current experimental observation. |
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| Differential Geometry and Geometric Analysis Seminar |
| Topic: |
TBA |
| Presenter: |
Olivaine De Queiroz, Universidade Estadual De Campinas |
| Date: |
Friday, November 12, 2010, Time: 3:00 p.m., Location: Fine Hall 314 |
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| PACM Colloquium |
| Topic: |
A New Formalism for Electromagnetic Scattering in Complex Geometry |
| Presenter: |
Leslie Greengard, Courant Institute |
| Date: |
Monday, November 15, 2010, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: |
We will describe some recent, elementary results in the theory of electromagnetic scattering in R3. There are two classical approaches that we will review - one based on the vector and scalar potential and applicable in arbitrary geometry, and one based on two scalar potentials, due to Lorenz, Debye and Mie, valid only in the exterior (or interior) of a sphere. In extending the Lorenz-Debye-Mie approach to arbitrary geometry, we have encountered some new mathematical questions involving differential geometry, partial differential equations and numerical analysis. This is joint work with Charlie Epstein. |
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