SEMINARS
Updated: 9-21-2011

SEPTEMBER 2011
 
Discrete Mathematics Seminar
Topic: Erdos-Ko-Rado-like theorems for rainbow matchings.
Presenter: Ron Aharoni, Technion, Haifa
Date: Thursday, September 22, 2011, Time: 2:15 p.m., Location: Fine Hall 224
Abstract: Let f(n,k,r) be the smallest number such that every set of more than f(n,k,r) r-sets in [n] contains a matching of size k. The Erdos-Ko-Rado theorem states that f(n,2,r)=\binom{n-1}{r-1}. A natural conjecture is that if F_1, F_2, ...F_k \subseteq \binom{[n]}{r} are all of size larger than f(n,k,r) then they possess a rainbow matching, that is, a choice of disjoint edges, one from each F_i. This is known for k=2 (Matsumoto-Tokushige) and r=2 (Meshulam). We consider the analogue of this conjecture in r-partite hypergraphs, and prove the cases r=3 and k=2. Joint work with David Howard.
 
Topology Seminar
Topic: Transverse invariants in Heegaard Floer homology
Presenter: Vera Vertesi, IAS/MIT
Date: Thursday, September 22, 2011, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: Using the language of Heegaard Floer knot homology recently two invariants were defined for Legendrian knots. One in the standard contact 3-sphere defined by Ozsvath, Szabo and Thurston in the combinatorial settings of knot Floer homology, one by Lisca, Ozsvath, Stipsicz and Szabo in knot Floer homology for a general contact 3--manifold. Both of them naturally generalizes to transverse knots. In this talk I will give a characterization of the transverse invariant, similar to the one given by Ozsvath and Szabo for the contact invariant. Namely for transverse braids both transverse invariants are given as the bottommost elements with respect to the filtration of knot Floer homology given by the axis. The above characterization allows us to prove that the two invariants are the same in the standard contact 3--sphere. This is a joint work with J. Baldwin and D.S. Vela-Vick.
 
Inaugural Math-Physics GR Seminar: Princeton University Gravity Group Astrophysics/Cosmology Lunch
Topic: The mathematical approach to general relativity
Presenter: Mihalis Dafermos, University of Cambridge
Date: Friday, September 23, 2011, Time: 12:00 p.m., Location: Jadwin Hall, Room 102 - Lunch will be provided
 
Differential Geometry and Geometric Analysis Seminar
Topic: Hessian estimates for special Lagrangian equations with critical and supercritical phases
Presenter: Yu Yuan, University of Washington
Date: Friday, September 23, 2011, Time: 3:00 p.m., Location: Fine 314
Abstract: We talk about a priori Hessian estimates for special Lagrangian equation with critical and supercritical phases in general higher dimensions. The "gradient" graphs of solutions are minimal Lagrangian submanifolds. Our unified approach leads to sharper estimates even for the previously known three dimensional or convex solution cases. Recent counterexamples for subcritical phase equations will also be mentioned. This is joint work with Dake Wang.
 
Analysis Seminar
Topic: Long-time strong instability and unbounded orbits for some nonlinear Schrodinger equations
Presenter: Zaher Hani, New York University
Date: Monday, September 26, 2011, Time: 4:00 p.m., Location: Fine Hall 314
Abstract: We establish a relation between long-time strong instability and the existence (in a certain generic sense) of unbounded orbits for dynamical systems on a Banach space. We then discuss some consequences of this relation for nonlinear Schrodinger equations. Namely, we prove long-time strong instability of plane wave solutions for the cubic nonlinearity and the existence of unbounded orbits for certain nonlinearities that are close (but not quite equal) to the cubic one.
 
PACM Colloquium
Topic: Understanding 3D Shapes Jointly
Presenter: Leonidas Guibas, Stanford University
Date: Monday, September 26, 2011, Time: 4:30 p.m., Location: Fine 214
Abstract: The use of 3D models in our economy and life is becoming more prevalent, in applications ranging from design and custom manufacturing, to prosthetics and rehabilitation, to games and entertainment. Although the large-scale creation of 3D content remains a challenging problem, there has been much recent progress in design software tools, like Google SketchUp for buildings or Spore for creatures, or in low cost 3D acquisition hardware, like the Microsoft Kinect scanner. As a result, large commercial 3D shape libraries, such as the Google 3D Warehouse, already contain millions of models. These libraries, however, can be unwieldy, when the need arises to efficiently incorporate models into various workflows. Mathematical formulations, efficient algorithms, and software tools are required to support navigation and search over 3D model repositories. In this talk we examine the problem of facilitating these navigation and search tasks by automatically extracting relationships between shapes in a collection and understanding their common or shared structure. By effectively organizing the collection into (possibly overlapping) groups of related shapes, by separating what is common from what is variable within each group and across groups, and by understanding the main axes of variability, we can facilitate a whole slew of operations that make large 3D repositories much more navigable, searchable, compressible, and visualizable. We will present a quick summary of tools for efficiently computing informative shape descriptors as well as structure preserving maps between shapes at different levels of resolution. The main part of the talk, however, is aimed beyond pairwise relationships, to the study and analysis of many shapes jointly, looking at networks of maps between shapes in order to extract joint structure, derive consistent segmentations, infer phenotypic relationships, etc. This is preliminary work on what we believe to be a large open area for research -- the joint understanding of collections of related geometric data sets.
 
Algebraic Geometry Seminar
Topic: Recent advances in connecting and contrasting test ideals and multiplier ideals
Presenter: Kevin Tucker, Princeton University
Date: Tuesday, September 27, 2011, Time: 4:30 p.m., Location: Fine 322
Abstract: This talk will focus on two distinct measures of singularities: test ideals (in positive characteristic) and multiplier ideals (characteristic zero). Though known for over a decade to be related via reduction to characteristic p > 0, recent advances have provided a uniform description of these invariants using regular alterations. This description, which shall be presented in detail, simultaneously sheds new light on both the connection and differences between test and multiplier ideals. Parts of the talk are based on joint works with Manuel Blickle, Karl Schwede, and Wenliang Zhang.
 
Statistical Mechanics Seminar
Topic: Some new results on the ground state of the strong coupling (solid)limit of the Bose-Hubbard Model; Possible applicability to solid He-4
Presenter: P.W. Anderson, Princeton University
Date: Wednesday, September 28, 2011, Time: 2:00 p.m., Location: Fine 224
Abstract: The Mott insulator is accepted as the appropriate ground manifold for the strongly interacting Fermion Hubbard model, with solid He-3 as the simplest exemplar. It is a manifold because of the spin degrees of freedom, which order antiferromagneticallly due to atom exchange, below a critical temperature. No corresponding effect of exchange has been known for the Bose solid. I show that in fact the Bose-Hubbard model solid has a corresponding manifold of phase degrees of freedom which can conduct particle currents and which exhibit an ordering transition. The possible applicability to the observed "supersolidity " phenomena in solid He-4 will be discussed.
 
Department Colloquium
Topic: The black hole stability problem
Presenter: Mihalis Dafermos, University of Cambridge
Date: Wednesday, September 28, 2011, Time: 4:30 p.m., Location: Fine 314
 
Discrete Mathematics Seminar
Topic: The size of a hypergraph and its matching number
Presenter: Benny Sudakov, UCLA
Date: Thursday, September 29, 2011, Time: 2:15 p.m., Location: Fine Hall 224
Abstract: More than 40 years ago, Erdos asked to determine the maximum possible number of edges in a k-uniform hypergraph on n vertices with no matching of size t (i.e., with no t disjoint edges). Although this is one of the most basic problem on hypergraphs, progress on Erdos' question remained elusive. In addition to being important in its own right, this problem has several interesting applications. In this talk we present a solution of Erdos' question for t < n/(3k2). This improves upon the best previously known range t = O (n/k3), which dates back to the 1970's. Joint work with H. Huang and P. Loh.
 
Algebraic Topology Seminar
Topic: v1-periodic homotopy groups of SU(n)
Presenter: Don Davis, Lehigh University
Date: Thursday, September 29, 2011, Time: 3:00 p.m., Location: Fine Hall 214
Abstract: I will survey the various results that have been obtained during the past 22 years on the v1-periodic homotopy groups of SU(n). The most recent work has been combinatorial fine tuning to make the statements more explicit. I will discuss conceptual differences between 2-primary and odd-primary groups and implications for actual homotopy groups.
   
Differential Geometry and Geometric Analysis Seminar
Topic: A Bernstein type theorem for entire Willmore graphs
Presenter: Jingyi Chen, University of British Columbia
Date: Friday, September 30, 2011, Time: 3:00 p.m., Location: Fine 314
Abstract: We show that every two-dimensional entire graphical solution to the Willmore equation with square integrable second fundamental form is a plane. This is joint work with Tobias Lamm.
 
IAS-PU Symplectic Geometry Seminar
Topic: TBA
Presenter: Andras Stipsicz, Renyi/IAS
Date: Friday, September 30, 2011, Time: 4:30 p.m., Location: IAS, Room S-101
 
OCTOBER 2011
 
Analysis Seminar
Topic: On the uniqueness of solutions to the 3D periodic Gross-Pitaevskii hierarchy
Presenter: Vedran Sohinger, University of Pennsylvania
Date: Monday, October 3, 2011, Time: 4:00 p.m., Location: Fine Hall 314
Abstract: In this talk, we present a uniqueness result for solutions to the Gross-Pitaevskii hierarchy on the three-dimensional torus, under the assumption of an a priori spacetime bound. We show that this a priori bound is satisfied for factorized solutions coming from a solution of the nonlinear Schrodinger equation, thus obtaining a periodic analogue of the uniqueness result on R3 previously proved by Klainerman and Machedon. This is joint work with Gigliola Staffilani.
 
PACM Colloquium
Topic: Complexity theory applied to voting theory
Presenter: Don Saari, University of California - Irvine
Date: Monday, October 3, 2011, Time: 4:30 p.m., Location: Fine 214
Abstract: As it will be shown with results and examples, the paradoxes associated with standard voting rules are surprisingly likely and are so complex that one must worry about the legitimacy of election outcomes. To extract an understanding of what can happen and why, it is shown how lessons from complexity theory, where complicated behavior is due to a combination of simple interactions, explain many mysteries both in this area and for related topics such as nonparametric statistics, etc. Indeed, all paradoxes of standard rules, including Arrow's seminal "Impossibility Theorem," reflect simple but hidden symmetry structures connecting the preferences of voters.
 
Algebraic Geometry Seminar
Topic: TBA
Presenter: Claudiu Raicu, Princeton University
Date: Tuesday, October 4, 2011, Time: 4:30 p.m., Location: Fine 322
 
Statistical Mechanics Seminar
Topic: Time Evolution and Stationary States of Classical and Quantum Systems
Presenter: J. L. Lebowitz, Rutgers University
Date: Wednesday, October 5, 2011, Time: 2:00 p.m., Location: Fine 224
Abstract: I will review both old and recent work about the time dependence and steady states of isolated macroscopic systems as well as those in contact with infinite thermal reservoirs. The emphasis will be on quantum systems and will include a discussion of the micro/macro connection in isolated ones and the derivation of a master equation for open oes.
 
Department Colloquium
Topic: Stability Theorems for some Sharp Inequalities and their Applications
Presenter: Eric Carlen, Rutgers University
Date: Wednesday, October 5, 2011, Time: 4:30 p.m., Location: Fine 314
Abstract: We explain recent results on stability theorems for some classical functional and ge- ometric inequalities, along with two applications: one to evolution equations, and one to statistical mechanics. The inequalities in question include certain Gagliardo-Nirenberg- Sobolev inequalities, the Brun-Minkowski inequality, for example. In these inequalities, all of the cases of equality are known, and indeed, Minkowski's contribution to the Brun- Minkowski inequality was to both determine the cases of equality. One can now ask if, in such an inequality, one almost has equality, is one in some sense near to one of the known cases of equality? A stability theorem is a theorem that provides a positive answer to this sort of question, and as indicated above, we shall explain and sketch the proofs of several such results, and we shall also explain two of the applications that motivated these investigations, which were carried out in collaboration with Alessio Figalli and Francesco Maggi. Though we shall keep the discussion of the applications non-technical as be ts a colloquium talk, we nonetheless hope to convey an understanding of why it might be very useful to solve some of the many open problems in this field.
 
Discrete Mathematics Seminar
Topic: TBA
Presenter: Eli Berger
Date: Thursday, October 6, 2011, Time: 2:15 p.m., Location: Fine Hall 224
 
PACM Colloquium
Topic: A new model for self-organized dynamics: From particle to hydrodynamic descriptions
Presenter: Eitan Tadmor, University of Maryland
Date: Monday, October 10, 2011, Time: 4:30 p.m., Location: Fine 214
Abstract: Self-organized dynamics is driven by "rules of engagement", which describe how each agent interacts with its neighbors. They consist of long-term attraction, mid-range alignment and short-range repulsion. Many self-propelled models are driven by the balance between these three forces, which yield emerging structures of interest. Examples range from consensus of voters and traffic flows to the formation of flocks of birds or school of fish, tumor growth etc. We introduce a new particle-based model, driven by self-alignment, which addresses several drawbacks of existing models for self-organized dynamics. The model is independent of the number of agents: only their geometry in phase space is involved. We will explain the emerging flocking behavior of the proposed model in the presence of non-symmetric interactions which decay sufficiently slow, and discuss the difficulties of tracing graph connectivity otherwise. The methodology is based on the new notion of active sets, which carries over from particle to kinetic and hydrodynamic descriptions, and we discuss the unconditional flocking at the level of hydrodynamic description.
 
Algebraic Geometry Seminar
Topic: Toric mirror maps revisited
Presenter: Hsian-Hua Tseng, Ohio State University
Date: Tuesday, October 11, 2011, Time: 4:30 p.m., Location: Fine 322
Abstract: For a compact semi-Fano toric manifold X, Givental's mirror theorem says that a generating function of 1-point genus 0 descendant Gromov-Witten invariants, the J-function of X, coincides up to a mirror map with a function I_X which is written using the combinatorics of X. The procedure of obtaining the mirror map, which involves expanding I_X as a suitable power series, is somewhat mysterious. In this talk we'll describe some attempts at understanding the mirror maps more geometrically.
 
Discrete Mathematics Seminar
Topic: TBA
Presenter: Shachar Lovett
Date: Thursday, October 13, 2011, Time: 2:15 p.m., Location: Fine Hall 224
 
Topology Seminar
Topic: TBA
Presenter: Kristen Hendricks, Columbia University
Date: Thursday, October 13, 2011, Time: 4:30 p.m., Location: Fine Hall 314
 
Special Seminar (no Joint IAS-PU Seminar)
Topic: Quasimorphisms, almost complex structures and moment maps
Presenter: Egor Shelukhin, Tel Aviv University
Date: Friday, October 14, 2011, Time: 4:30 p.m., Location: Fine 322
Abstract: We consider the action of the group of Hamiltonian diffeomorphisms on the space of compatible almost complex structures of a symplectic manifold, with the scalar curvature as an equivariant moment map (due to Donaldson and Fujiki). While the Mabuchi K-energy measures 'displacement' transverse to the orbits, we propose a way to measure 'displacement' along an orbit, to obtain a function on the universal cover of the group satisfying the homomorphism property up to a uniformly bounded error - a quasimorphism. This construction agrees with previous results of Ruelle, Barge-Ghys, Entov and Py. Moreover, the same construction works in finite-dimensional settings, giving the (essentially unique) Guichardet-Wigner quasimorphisms on Hermitian Lie groups.
 
PACM Colloquium
Topic: Optimization of Polynomial Roots, Eigenvalues and Pseudospectra
Presenter: Michael L. Overton, Courant Institute of Mathematical Sciences, NYU
Date: Monday, October 17, 2011, Time: 4:30 p.m., Location: Fine 214
Abstract: The root radius and root abscissa of a monic polynomial are respectively the maximum modulus and the maximum real part of its roots; both these functions are nonconvex and are non-Lipschitz near polynomials with multiple roots. We begin the talk by giving constructive methods for efficiently minimizing these nonconvex functions in the case that there is just one affine constraint on the polynomial's coefficients. We then turn to the spectral radius and spectral abscissa functions of a matrix, which are analogously defined in terms of eigenvalues. We explain how to use nonsmooth optimization methods to find local minimizers and how to use nonsmooth analysis to study local optimality conditions for these nonconvex, non-Lipschitz functions. Finally, the pseudospectral radius and abscissa of a matrix $A$ are respectively the maximum modulus or maximum real part of elements of its pseudospectrum (the union of eigenvalues of all matrices within a specified distance of $A$). These functions are also nonconvex but, it turns out, locally Lipschitz, although the pseudospectrum itself is not a Lipschitz set-valued map. We discuss applications from control and from Markov chain Monte Carlo as examples throughout the talk. Coauthors of relevant papers include Vincent Blondel, Jim Burke, Kranthi Gade, Mert Gurbuzbalaban, Adrian Lewis and Alexandre Megretski.
 
Algebraic Geometry Seminar
Topic: TBA
Presenter: Zsolt Patakfalvi, Princeton University
Date: Tuesday, October 18, 2011, Time: 4:30 p.m., Location: Fine 322
 
Department Colloquium
Topic: TBA
Presenter: Tsachik Gelander, Hebrew University of Jerusalem
Date: Wednesday, October 19, 2011, Time: 4:30 p.m., Location: Fine 314
 
Topology Seminar
Topic: TBA
Presenter: Andras Stipsicz, Renyi/IAS
Date: Thursday, October 20, 2011, Time: 4:30 p.m., Location: Fine Hall 314
 
PACM Colloquium
Topic: Existence and regularity for a class of degenerate diffusions arising in population genetics
Presenter: Charles Epstein, University of Pennsylvania
Date: Monday, October 24, 2011, Time: 4:30 p.m., Location: Fine 214
Abstract: Infinite population limits of standard Markov chain models lead to Markov processes on polyhedral domains that are formally generated by degenerate elliptic operators. These operators are characterized, in part, by the first order vanishing, along the boundary, of the coefficient of the second normal derivative term. This fact places these operators beyond those which have thus far been successfully analyzed using methods of geometric analysis. I will present an approach to these operators, which I have been pursuing with Rafe Mazzeo, based on an-isotropic Holder spaces, which leads to a rather complete existence, uniqueness and regularity theory.
 
Algebraic Geometry Seminar
Topic: TBA
Presenter: Javier Fernández de Bobadilla de Olazabal, ICMAT, CSIC
Date: Tuesday, October 25, 2011, Time: 4:30 p.m., Location: Fine 322
 
IAS-PU Symplectic Geometry Seminar
Topic: TBA
Presenter: Fraydoun Rezakhanlou, UC Berkeley
Date: Friday, October 28, 2011, Time: 4:30 p.m., Location: IAS, Room S-101
 
NOVEMBER 2011
 
Algebraic Topology Seminar
Topic: TBA
Presenter: Herman Gluck, University of Pennsylvania
Date: Thursday, November 3, 2011, Time: 3:00 p.m., Location: Fine Hall 214
   
Algebraic Geometry Seminar
Topic: TBA
Presenter: Claire Voisin, Institut de Mathématiques de Jussieu
Date: Tuesday, November 8, 2011, Time: 4:30 p.m., Location: Fine 322
 
Algebraic Topology Seminar
Topic: TBA
Presenter: Roman Mikhailov, IAS
Date: Thursday, November 10, 2011, Time: 3:00 p.m., Location: Fine Hall 214
   
IAS-PU Symplectic Geometry Seminar
Topic: TBA
Presenter: Penka Georgieva, Princeton University
Date: Friday, November 11, 2011, Time: 4:30 p.m., Location: Fine 322
 
PACM Colloquium
Topic: TBA
Presenter: Vladimir Rokhlin, Yale University
Date: Monday, November 14, 2011, Time: 4:30 p.m., Location: Fine 214
 
Algebraic Geometry Seminar
Topic: TBA
Presenter: Franklin Vera Pacheco, University of Toronto
Date: Tuesday, November 15, 2011, Time: 4:30 p.m., Location: Fine 322
 
Department Colloquium
Topic: TBA
Presenter: Alessio Figalli, University of Texas-Austin
Date: Wednesday, November 16, 2011, Time: 4:30 p.m., Location: Fine 314
 
Topology Seminar
Topic: TBA
Presenter: Ciprian Manolescu, UCLA
Date: Thursday, November 17, 2011, Time: 4:30 p.m., Location: Fine Hall 314
 
IAS-PU Symplectic Geometry Seminar
Topic: TBA
Presenter: Tara Holm, Cornell University
Date: Friday, November 18, 2011, Time: 4:30 p.m., Location: Fine 322
 
PACM Colloquium
Topic: TBA
Presenter: Frederik Simons, Princeton University
Date: Monday, November 21, 2011, Time: 4:30 p.m., Location: Fine 214
 
Algebraic Geometry Seminar
Topic: TBA
Presenter: J. M. Landsberg, Texas A&M University
Date: Tuesday, November 22, 2011, Time: 4:30 p.m., Location: Fine 322
 
PACM Colloquium
Topic: TBA
Presenter: Andrea Montanari, Stanford University
Date: Monday, Novermber 28, 2011, Time: 4:30 p.m., Location: Fine 214
 
Algebraic Geometry Seminar
Topic: TBA
Presenter: David Eisenbud, UC Berkeley, MSRI
Date: Tuesday, November 29, 2011, Time: 4:30 p.m., Location: Fine 322
 
DECEMBER 2011
 
PACM Colloquium
Topic: TBA
Presenter: Peter Constantin, Princeton University
Date: Monday, December 5, 2011, Time: 4:30 p.m., Location: Fine 214
 
Algebraic Geometry Seminar
Topic: TBA
Presenter: Wenliang Zhang, University of Michigan
Date: Tuesday, December 6, 2011, Time: 4:30 p.m., Location: Fine 322
 
IAS-PU Symplectic Geometry Seminar
Topic: TBA
Presenter: Nigel Hitchin, Oxford University and Simons Center
Date: Friday, December 9, 2011, Time: 4:30 p.m., Location: Fine 322
 
Algebraic Geometry Seminar
Topic: TBA
Presenter: Ching-Jui Lai, University of Utah
Date: Tuesday, December 13, 2011, Time: 4:30 p.m., Location: Fine 322
 
IAS-PU Symplectic Geometry Seminar
Topic: TBA
Presenter: Urs Frauenfelder, IAS visitor
Date: Friday, December 16, 2011, Time: 4:30 p.m., Location: IAS, Room S-101
 
FEBRUARY 2012
 
Algebraic Topology Seminar
Topic: TBA
Presenter: Dave Anderson, University of Washington
Date: Thursday, February 9, 2012, Time: 3:00 p.m., Location: Fine Hall 214
 
Algebraic Topology Seminar
Topic: TBA
Presenter: Suyoung Choi, Ajou University, Korea
Date: Thursday, February 19, 2012, Time: 3:00 p.m., Location: Fine Hall 214
 
Algebraic Topology Seminar
Topic: TBA
Presenter: Alex Suciu, Northeastern University
Date: Thursday, February 23, 2012, Time: 3:00 p.m., Location: Fine Hall 214