SEPTEMBER 2011 

Discrete Mathematics Seminar 
Topic: 
ErdosKoRadolike 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) rsets in [n] contains a matching of size k. The ErdosKoRado theorem states that f(n,2,r)=\binom{n1}{r1}. 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 (MatsumotoTokushige) and r=2 (Meshulam). We consider the analogue of this conjecture in rpartite 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 3sphere 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 3manifold. 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 3sphere. This is a joint work with J. Baldwin and D.S. VelaVick. 

Inaugural MathPhysics 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: 
Longtime 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 longtime 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 longtime 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 largescale 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 BoseHubbard Model; Possible applicability to solid He4 
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 He3 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 BoseHubbard 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 He4 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 kuniform 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: 
v1periodic 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 v1periodic 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 2primary and oddprimary 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 twodimensional entire graphical solution to the Willmore equation with square integrable second fundamental form is a plane. This is joint work with Tobias Lamm. 

IASPU Symplectic Geometry Seminar 
Topic: 
TBA 
Presenter: 
Andras Stipsicz, Renyi/IAS 
Date: 
Friday, September 30, 2011, Time: 4:30 p.m., Location: IAS, Room S101 

OCTOBER 2011 

Analysis Seminar 
Topic: 
On the uniqueness of solutions to the 3D periodic GrossPitaevskii 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 GrossPitaevskii hierarchy on the threedimensional 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 GagliardoNirenberg Sobolev inequalities, the BrunMinkowski 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 nontechnical as bets 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 selforganized 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: 
Selforganized dynamics is driven by "rules of engagement", which describe how each agent interacts with its neighbors. They consist of longterm attraction, midrange alignment and shortrange repulsion. Many selfpropelled 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 particlebased model, driven by selfalignment, which addresses several drawbacks of existing models for selforganized 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 nonsymmetric 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: 
HsianHua Tseng,
Ohio State University 
Date: 
Tuesday, October 11, 2011, Time: 4:30 p.m., Location: Fine 322 
Abstract: 
For a compact semiFano toric manifold X, Givental's mirror theorem says that a generating function of 1point genus 0 descendant GromovWitten invariants, the Jfunction 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 IASPU 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 Kenergy 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, BargeGhys, Entov and Py. Moreover, the same construction works in finitedimensional settings, giving the (essentially unique) GuichardetWigner 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 nonLipschitz 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, nonLipschitz 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 setvalued 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 anisotropic 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 

IASPU Symplectic Geometry Seminar 
Topic: 
TBA 
Presenter: 
Fraydoun Rezakhanlou, UC Berkeley 
Date: 
Friday, October 28, 2011, Time: 4:30 p.m., Location: IAS, Room S101 

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 


IASPU 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 TexasAustin 
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 

IASPU 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 

IASPU 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: 
ChingJui Lai, University of Utah 
Date: 
Tuesday, December 13, 2011, Time: 4:30 p.m., Location: Fine 322 

IASPU Symplectic Geometry Seminar 
Topic: 
TBA 
Presenter: 
Urs Frauenfelder, IAS visitor 
Date: 
Friday, December 16, 2011, Time: 4:30 p.m., Location: IAS, Room S101 

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 
