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| SEPTEMBER 2010 |
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|
| Department Colloquium |
| Topic: |
Optimal bounds on the Kuramoto-Sivashinsky equation |
| Presenter: |
Felix Otto, Max-Planck Institute of Mathematical Sciences, Leipzig, Germany |
| Date: |
Wednesday, 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 |
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|
| Discrete Mathematics Seminar |
| Topic: |
Asymptotic extremal graph theory is non-trivial |
| Presenter: |
Sergey Norin, Princeton University |
| Date: |
Thursday, September 23, 2010, Time: 2:15 p.m., Location: Fine Hall 224 |
| Abstract: |
Many fundamental theorems in extremal graph theory can be expressed as linear inequalities between homomorphism densities. Lovasz and, in a slightly different formulation, Razborov asked whether it is true that every such inequality follows from a finite number of applications of the Cauchy-Schwarz inequality. In this talk we will show that the answer to this question is negative. Further, we will show that the problem of determining the validity of a linear inequality between homomorphism densities is undecidable. Hence such inequalities are inherently difficult in their full generality. These results are joint work with Hamed Hatami.
On the other hand, the Cauchy-Schwarz inequality represents a powerful tool for obtaining particular approximate and exact results in asymptotic extremal graph theory. We will mention a couple of results obtained in this way in joint work with Hatami, Hladky and Kral, answering questions of Jagger, Stovicek and Thomason, and of Thomasse. |
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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: |
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. |
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| Mathematical Physics Seminar |
| Topic: |
Extended States in a Lifshitz Tail Regime for Random Operators on Trees |
| Presenter: |
Simone Warzel, Technical Univ. Munich |
| Date: |
Tuesday, September 28, 2010, Time: 4:30 p.m., Location: Jadwin 343 |
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|
| 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. |
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|
| Discrete Mathematics Seminar |
| Topic: |
TBA |
| Presenter: |
Irena Penev, Columbia University |
| Date: |
Thurdsay, September 30, 2010, Time: 2:15 p.m., Location: Fine Hall 224 |
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|
| 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. |
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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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|
| 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. |
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|
| Department Colloquium |
| Topic: |
Blow-up phenomena for the Yamabe equation" |
| Presenter: |
Simon Brendle, Stanford University |
| Date: |
Wednesday, October 6, 2010, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: |
The Yamabe problem asserts that any Riemannian metric on a compact
manifold can be conformally deformed to one of constant scalar curvature.
However, this metric is not, in general, unique, and there are examples of
manifolds that admit many metrics of constant scalar curvature in a given
conformal class.
It was conjectured by R. Schoen in the 1980s (and, independently, by Aubin) that the set of all metrics of constant scalar curvature 1 in a given conformal class is compact, except if the underlying manifold is conformally equivalent to the sphere $S^n$ equipped with its standard metric. The significance of Schoen's conjecture is that it would imply Morse inequalities for the total scalar curvature functional.
I will discuss counterexamples to this conjecture in dimension 52 and higher. I will also describe joint work with F. Marques, which extends these counterexamples to dimension 25 and higher. The condition $n \geq 25$ turns out to be optimal. |
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|
| Ergodic Theory and Statistical Mechanics Seminar |
| Topic: |
TBA |
| Presenter: |
John Mather, Princeton University |
| Date: |
Thursday, October 7, 2010, Time: 2:00 p.m., Location: Fine Hall 401 |
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|
| Discrete Mathematics Seminar |
| Topic: |
TBA |
| Presenter: |
Swastik Kopparty, IAS |
| Date: |
Thursday, October 7, 2010, Time: 2:15 p.m., Location: Fine Hall 224 |
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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: |
Equivariant birational maps and resolutions of categorical quotients |
| Presenter: |
Dan Edidin, University of Missouri |
| Date: |
Tuesday, October 12, 2010, Time: 4:30 p.m., Location: Fine Hall 322 |
| Abstract: |
If $X^{ss}$ is the set of semi-stable points for a linearized action of a reductive group on a smooth projective variety $X$ then there two procedures (Kirwan's procedure or change of linearization) for constructing a partial resolution of singularities of the categorical quotient $X^{ss}/G$. Both involve finding an equivariant birational map $\tilde{X} \to X^{ss}$ with $\tilde{X}$ smooth such that $G$ acts properly on $\tilde{X}$ and the induced map on quotients is proper and birational. A natural question to ask is whether (and to what extent) this procedure can be replicated for non-GIT quotients. We consider the problem for actions of diagonalizable groups and show that there is a simple combinatorial procedure that replicates Kirwan's construction for non-projective toric varieties. This talk is based on joint work with Yogesh More. |
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|
| Ergodic Theory and Statistical Mechanics Seminar |
| Topic: |
TBA |
| Presenter: |
Amit Singer and Xiuyuan Cheng, Princeton University |
| Date: |
Thursday, October 14, 2010, Time: 2:00 p.m., Location: Fine Hall 401 |
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|
| Discrete Mathematics Seminar |
| Topic: |
TBA |
| Presenter: |
Ofer Neiman, Courant Institute, NYU |
| Date: |
Thursday, October 14, 2010, Time: 2:15 p.m., Location: Fine Hall 224 |
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|
| 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 |
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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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|
| Algebraic Geometry Seminar |
| Topic: |
TBA |
| Presenter: |
Junecue Suh, IAS |
| Date: |
Tuesday, October 19, 2010, Time: 4:30 p.m., Location: Fine Hall 322 |
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|
| Ergodic Theory and Statistical Mechanics Seminar |
| Topic: |
From random tilings to representation theory |
| Presenter: |
Vadim Gorin, Moscow State University |
| Date: |
Thursday, October 21, 2010, Time: 2:00 p.m., Location: Fine Hall 401 |
| Abstract: |
Lozenge tilings of planar domains provide a simple, yet sophisticated model of random surfaces. Asymptotic behavior of such models has been extensively studied in recent years.
We will start from recent results about q-distributions on tilings of a hexagon or, equivalently, on boxed plane partitions. (This part is based on the joint work with A.Borodin and E.Rains).
In the second part of the talk we will explain how representation theory of the infinite-dimensional unitary group is related to random lozenge tilings with a certain Gibbs property. We will discuss applications of this correspondence and results on the classification of Gibbs measures on tilings of the half-plane. |
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|
| Discrete Mathematics Seminar |
| Topic: |
The size Ramsey number of a directed path |
| Presenter: |
Ido Ben-Eliezer, Tel-Aviv University |
| Date: |
Thursday, October 21, 2010, Time: 2:15 p.m., Location: Fine Hall 224 |
| Abstract: |
Given a graph H, the size Ramsey number r_e(H,q) is the minimal number m for which there is a graph G with m edges such that every q-coloring of G contains a monochromatic copy of H. We study the size Ramsey number of the directed path of length n in oriented graphs, where no antiparallel edges are allowed. We give nearly tight bounds for every fixed number of colors. For the case of two colors we show that there are constants c_1,c_2 such that \frac{c_1 n^{2} \log n}{(\log\log n)^3} \leq r_e(P_n,2) \leq c_2 n^{2}(\log n)^2.
Joint work with Michael Krivelevich and Benny Sudakov. |
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|
| Mathematical Physics Seminar |
| Topic: |
Trace Formulas for Large Random d-Regular Graphs |
| Presenter: |
Idan Oren, The Weizmann Institute |
| Date: |
Tuesday, October 26, 2010, Time: 4:30 p.m., Location: Jadwin 343 |
| Abstract: |
Trace formulas for d-regular graphs are derived and used to express the spectral density in terms of the periodic walks on the graphs under consideration. The trace formulas depend on a parameter (w) which can be tuned continuously to assign different weights to different periodic orbit contributions. At the special value w = 1, the only periodic orbits which contribute are the non back- scattering orbits, and the smooth part in the trace formula coincides with the Kesten-McKay expression. As (w) deviates from unity, non vanishing weights are assigned to the periodic walks with back-scatter, and the smooth part is modified in a consistent way. The trace formulas presented in this talk can be used as tools for showing the connection between the spectral properties of d-regular graphs and the theory of random matrices. |
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|
| Ergodic Theory and Statistical Mechanics Seminar *** Please note special date and time*** |
| Topic: |
TBA |
| Presenter: |
Domokos Szasz, Budapest University of Technology and Economics |
| Date: |
Friday, October 29, 2010, Time: 3:00 p.m., Location: Fine Hall 401 |
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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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|
| Ergodic Theory and Statistical Mechanics Seminar |
| Topic: |
TBA |
| Presenter: |
Percy Wong, Princeton University |
| Date: |
Thursday, November 11, 2010, Time: 2:00 p.m., Location: Fine Hall 401 |
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|
| Discrete Mathematics Seminar |
| Topic: |
TBA |
| Presenter: |
Oleg Pikhurko, Carnegie Mellon |
| Date: |
Thursday, November 11, 2010, Time: 2:15 p.m., Location: Fine Hall 224 |
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|
| Princeton University and Institute for Advanced Study Number Theory Seminar |
| Topic: |
TBA |
| Presenter: |
Shou-Wu Zhang, Columbia University |
| Date: |
Thursday, November 11, 2010, Time: 4:30 p.m., Location: Fine Hall 214 |
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|
| Topology Seminar |
| Topic: |
TBA |
| Presenter: |
Lenny Ng, Duke University |
| Date: |
Thursday, November 11, 2010, Time: 4:30 p.m., Location: Fine Hall 314 |
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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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|
| Ergodic Theory and Statistical Mechanics Seminar |
| Topic: |
TBA |
| Presenter: |
Percy Wong, Princeton University |
| Date: |
Thursday, November 18, 2010, Time: 2:00 p.m., Location: Fine Hall 401 |
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|
| Discrete Mathematics Seminar |
| Topic: |
TBA |
| Presenter: |
Noga Alon, Tel-Aviv University and IAS |
| Date: |
Thursday, November 18, 2010, Time: 2:15 p.m., Location: Fine Hall 224 |
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|
| PACM Colloquium |
| Topic: |
Wavelet Frames and Applications |
| Presenter: |
Zuowei Shen, National University of Singapore |
| Date: |
Monday, November 22, 2010, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: |
This talk focuses on the tight wavelet frames derived from multiresolution analysis and their applications in imaging sciences. One of the major driven forces in the area of applied and computational harmonic analysis over the last two decades is to develop and understand redundant systems that have sparse approximations of different classes of functions. Such redundant systems include wavelet frame, ridgelet, curvelet, shearlet and so on. In this talk, we will first give a brief survey on the development of the unitary extension principle and its generalizations. The unitary extension principle and its extensions give systematical constructions of wavelet frames from multiresolution analysis that can be used in various problems in imaging science. Then we will focus on applications of wavelet frames. Especially, we will discuss frame based image analysis and restorations, which includes image inpainting, image denosing, image deblurring and blind deblurring, image decomposition, and image segmentation. |
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| DECEMBER 2010 |
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|
| Ergodic Theory and Statistical Mechanics Seminar |
| Topic: |
TBA |
| Presenter: |
Zhiren Wang
, Princeton University |
| Date: |
Thursday, December 2, 2010, Time: 2:00 p.m., Location: Fine Hall 401 |
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|
| 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 |
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|
| 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. |
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|
| Algebraic Geometry Seminar |
| Topic: |
TBA |
| Presenter: |
Izzet Coskun, UIC |
| Date: |
Tuesday, December 14, 2010, Time: 4:30 p.m., Location: Fine Hall 322 |
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