| |
|
| SEPTEMBER 2010 |
| |
|
| Discrete Mathematics Seminar |
| Topic: |
Unfriendly partition of graphs without an infinite subdivided clique |
| Presenter: |
Eli Berger, University of Haifa |
| Date: |
Thursday, September 16, 2010, Time: 2:15 p.m., Location: Fine Hall 224 |
| Abstract: |
In this talk I prove that every graph with less than $\aleph_\omega$ vertices, which does not contain a subdivision of an infinite clique as a subgraph, must have a partition of its vertices to two sets, so that no vertex has more neighbors in its own set than in the other set. The proof uses the theorem given by Robertson Seymour and Thomas (http://www.ams.org/mathscinet/pdf/1079057.pdf), saying that such a graph has a tree decomposition with certain properties. The unfriendly partition is then constructed by analyzing some infinite game played on this tree. |
| |
|
| Ergodic Theory and Statistical Mechanics Seminar ***Please note special date *** |
| Topic: |
Dynamics of 2D point vortics and its generalizations |
| Presenter: |
Tadashi Tokieda, Cambridge University |
| Date: |
Friday, September 17, 2010, Time: 2:00 p.m., Location: Fine Hall 401 |
| |
|
| Joint Analysis/PACM Colloquium |
| Topic: |
Optimal Error Estimates in Stochastic Homogenization |
| Presenter: |
Felix Otto, Max-Planck Institute for Mathematical Sciences |
| 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 |
| |
|
| Department Colloquium |
| Topic: |
Optimal bounds on the Kuramoto-Sivashinsky equation |
| Presenter: |
Felix Otto, Max-Planck Institute of Mathematical Sciences, Leipzig, Germany |
| Date: |
Wendesday, September 22, 2010, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: |
http://www.math.princeton.edu/~seminar/2010-11-sem/OttoAbstract9-22-2010.pdf |
| |
|
| 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. |
| |
|
| 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. |
| |
|
| Algebraic Geometry Seminar |
| Topic: |
Derived Equivalence and the Picard Variety |
| Presenter: |
Christian Schnell, UIC |
| Date: |
Tuesday, September 28, 2010, Time: 4:30 p.m., Location: Fine Hall 322 |
| Abstract: |
I will explain a result, joint with Mihnea Popa, saying that if two smooth projective varieties have equivalent derived categories of coherent sheaves, then their Picard varieties are isogeneous; in particular the number of independent holomorphic one-forms is a derived invariant. A consequence of this is that derived equivalent threefolds have the same Hodge numbers. |
| |
|
| Statistical Mechanics Seminar |
| Topic: |
Dynamical stability in the planar surface tension problem for the Gates-Penrose-Lebowitz free energy function and Kawasaki dynamics |
| Presenter: |
Eric Carlen, Rutgers University |
| Date: |
Wednesday, September 29, 2010, Time: 2:00 p.m., Location: Jadwin Hall 343 |
| Abstract: |
The planar surface tension problem for the Gates-Penrose-Lebowitz free energy function concerns the minimization of this functional for profiles m(x,y) on a cylinder in $R\times C in R^d with cubic cross section C and periodic boundary conditions. It has been shown by Alberti and Belletini that the only minimizing profiles are of the form m(x,y) = n(x)$ where x is in R and y is in C and n is the instanton for the one dimensional GPL functional. As far as dynamical stability of the minimizers is concerned, the case of Glauber dynamics (spin flips) is by now well understood. However, the case of Kawasaki dynamics (spin exchanges) is different, in particular because of the conservation law and the lack of a spectral gap. We present a proof of dynamical stability in this case that is joint work with Enza Orlandi. |
| |
|
| Topology Seminar |
| Topic: |
The lens space realization problem |
| Presenter: |
Josh Greene, Columbia University |
| Date: |
Thursday, September 30, 2010, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: |
I will discuss the classification of the which spaces arise by integral Dehn surgery along a knot in the three-sphere. A related result is that if surgery along a knot produces a connected sum of lens spaces, then the knot is either a torus knot or a cable thereof, confirming the cabling conjecture in this case. The proofs rely on Floer homology and lattice theory. |
| |
|
| OCTOBER 2010 |
| |
|
| 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 |
| |
|
| 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. |
| |
|
| 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. |
| |
|
| Statistical Mechanics Seminar |
| Topic: |
Phase transition in kinetically constrained models |
| Presenter: |
Thierry Bodineau, Ecole Normale Superieur, Paris |
| Date: |
Wednesday, October 6, 2010, Time: 2:00 p.m., Location: Jadwin Hall 343 |
| Abstract: |
Kinetically constrained models are simple lattice models of glasses with a dynamical frustration: a move can be performed only if some local constraints are satisfied, for example if the local density is low enough. These models have been introduced to explain on a purely dynamical ground the glass forming phenomenology. The local constraints give rise to collective dynamics leading to hierarchical and cooperative relaxation. An important issue is to understand the structure of the dynamical heterogeneity, i.e. the regions which are mobile (active) vs the regions which are blocked (inactive). The activity of the system measures the microscopic number of moves per unit time and it has been proposed as a relevant parameter to characterize glassiness. In the first part of the talk, we will review the rich dynamical behaviour displayed by the kinetically constrained models. In the second part, we will focus on the large deviations of the activity and show that it leads to a first order phase transition. |
| |
|
| 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 |
| |
|
| 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 |
| |
|
| Topology Seminar |
| Topic: |
TBA |
| Presenter: |
Jacob Rasmussen, Cambridge/SUNY Stony Brook |
| Date: |
Thursday, October 14, 2010, Time: 4:30 p.m., Location: Fine Hall 314 |
| |
|
| PACM Colloquium |
| Topic: |
TBA |
| Presenter: |
Ali Jadbabaie, University of Pennsylvania |
| Date: |
Monday, October 18, 2010, Time: 4:00 p.m., Location: Fine Hall 214 |
| |
|
| Algebraic Geometry Seminar |
| Topic: |
TBA |
| Presenter: |
Junecue Suh, IAS |
| Date: |
Tuesday, October 19, 2010, Time: 4:30 p.m., Location: Fine Hall 322 |
| |
|
| NOVEMBER 2010 |
| |
|
| 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. |
| |
|
| 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 |
| |
|
| 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. |
| |
|
| PACM Colloquium |
| Topic: |
TBA |
| Presenter: |
Zuowei Shen, National University of Singapore |
| Date: |
Monday, November 22, 2010, Time: 4:00 p.m., Location: Fine Hall 214 |
| |
|
| DECEMBER 2010 |
| |
|
| Differential Geometry and Geometric Analysis Seminar |
| Topic: |
TBA |
| Presenter: |
Gilles Courtois, École/ Polytechnique/ |
| Date: |
Friday, December 3, 2010, Time: 3:00 p.m., Location: Fine Hall 314 |
| |
|
| PACM Colloquium |
| Topic: |
Diffusions Interacting Through Their Ranks, and the Stability of Large Equity Markets |
| Presenter: |
Ioannis Karatzas, Columbia University |
| Date: |
Monday, December 6, 2010, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: |
We introduce and study ergodic multidimensional di usion processes interacting through their ranks. These interactions give rise to invariant measures which are in broad agreement with stability properties observed in large equity markets over long time-periods. The models we develop assign growth rates and variances that depend on both the name (identity) and the rank (according to capitalization) of each individual asset. Such models are able realistically to capture critical features of the observed stability of capital distribution over the past century, all the while being simple enough to allow for rather detailed analytical study. The methodologies used in this study touch upon the question of triple points for systems of interacting di usions; in particular, some choices of parameters may permit triple (or higher-order) collisions to occur. We show, however, that such multiple collisions have no e ect on any of the stability properties of the resulting system. This is accomplished through a detailed analysis of intersection local times. The theory we develop has connections with the analysis of Queueing Networks in heavy traffic, as well as with models of competing particle systems in Statistical Mechanics, such as the Sherrington-Kirkpatrick model for spin-glasses. |
| |
|
| Algebraic Geometry Seminar |
| Topic: |
TBA |
| Presenter: |
Izzet Coskun, UIC |
| Date: |
Tuesday, December 14, 2010, Time: 4:30 p.m., Location: Fine Hall 322 |
| |
|
| |
|