SEMINARS
Updated: 11-7-2007
   
NOVEMBER 2007
   
Special Seminar
Topic: Irreducibility and Cuspidality
Presenter: Dinakar Ramakrishnan, CalTech
Date:  Wednesday, November 7, 2007, Time: 1:30 p.m., Location: Fine 314
   
Statistical Mechanics Seminar
Topic: The thermodynamic limit of quantum Coulomb systems
Presenter: Mathieu Lewin, Universite de Cergy-Pontoise
Date:  Wednesday, November 7, 2007, Time: 2:00 p.m., Location: Jadwin 343
Abstract: I will present a new approach for proving the existence of the thermodynamic limit for quantum systems composed of electrons and nuclei interacting via the Coulomb potential, as in ordinary matter. In particular, I will provide a very general setting that allows us to study many different quantum systems. This is joint work with Christian Hainzl and Jan Philip Solovej.
   
Geometry, Representation Theory, and Moduli Seminar
Topic: TBA
Presenter: S. Kovács,Washington University
Date:  Wednesday, November 7, 2007, Time: 3:00 p.m., Location: Fine Hall 214
   
Special Analysis Seminar *** Please note special date and time, and location
Topic: Bilinear virial identities
Presenter: Fabrice Planchon, Universite Paris 13
Date:  Wednesday, November 7, 2007, Time: 3:15 p.m., Location: Fine 322
Abstract: We derive inequalities for the nonlinear Schrodinger equation which may be seen as extensions of local smoothing/Morawetz/interaction Morawetz estimates. Not only do they hold irrespective of the dimension, but they extend to domains as well.
   
Department Colloquium
Topic: Continuum limits of random matrices
Presenter: Bálint Virág, University of Toronto
Date:  Wednesday, November 7, 2007, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: The eigenvalue distribution of large random matrices arises naturally in many areas of mathematics. It can be understood by taking a continuum limit of the random matrix. For the sine point process, which is conjectured to describe the zeros of the Riemann zeta function, this limit is given in terms of Brownian motion in the hyperbolic plane. Other limits are 1-dimensional random Schrodinger operators. In fact, a large class of such operators show random matrix behaviour in parts of their spectra.
   
Graduate Student Seminar
Topic: The Borel-Weil-Bott Theorem
Presenter: Vivek Shende, Princeton University
Date:  Thursday, November 8, 2007, Time: 12:30 p.m., Location: Fine Hall 214
Abstract: IWhat are all the irreducible representations of a complex semisimple Lie group G? One can use the one-dimensional representations of a Borel subgroup B to produce line bundles on the flag manifold G/B; some of these bundles have (a finite dimensional vector space of) holomorphic global sections. These vector spaces carry irreducible G-actions, and in fact account for all the irreducible representations. Even the bundles without global sections have irreducible representations hiding somewhere in their higher cohomology. That may sound like quite a mouthful, but it's not so bad for, say, SL(2): G/B is just the Riemann sphere, whose line bundles can be written down quite explicitly. I'll explain what's going on in this case, then discuss SL(3), and then say a few more words about things in general.
   
   
Ergodic Theory and Statistical Mechanics Seminar
Topic: Deviation of ergodic averages for billiards in polygons
Presenter: Jayadev Athreya, Princeton University / Yale University
Date:  Thursday, November 8, 2007, Time: 2:00 p.m., Location: Fine Hall 401
Abstract: In joint work with G. Forni, we prove polynomial bounds on the deviation of ergodic averages for the billiard flow in Euclidean polygons with rational angles.
   
Discrete Mathematics Seminar
Topic: Tree embeddings in graphs
Presenter: Jan Vondrak, Princeton University
Date:  Thursday, November 8, 2007, Time: 2:15 p.m., Location: Fine Hall 224
Abstract: We study the question of embedding large trees in sparse graphs. We show that for several natural classes of graphs, any graph G contains all trees of size and maximum degree constrained by the respective parameters of G (up to constant factors). We prove this for graphs of bounded girth, K_{s,t}-free graphs, random graphs and most generally for graphs satisfying a certain pseudorandomness property. This improves some previous results. The embedding can be found using a simple randomized algorithm which can be viewed as a "self-avoiding tree-indexed random walk". Joint work with Benny Sudakov.
   
Joint Princeton University/IAS Number Theory Seminar
Topic: Modular forms and Calabi-Yau varieties
Presenter: Dinakar Ramakrishnan, Caltech
Date:  Thursday, November 8, 2007, Time: 4:30 p.m., Location: Fine Hall 214
   
Operations Research and Financial Engineering Seminar
Topic: On the Relations Between Implied and Spot Volatilities
Presenter: Valdo Durrleman, Ecole Polytechnique, Paris
Date:  Thursday, November 8, 2007, Time: 4:30 p.m., Location: E-219, E-Quad
Abstract: In the first part of the talk, we will present a result showing how one can compute the spot volatility dynamics from the implied volatility surface. Then, we will look at an application to foreign exchange options: we take the exchange rates EURUSD, USDJPY, and EURJPY and reconstruct the implied volatility smile of one exchange rate from the other two. In the third part of the talk, we study the convergence of at-the-money implied volatilities to the spot volatility in a general model with a Brownian component and a jump component of finite variation. This result is a consequence of the robustness of the Black-Scholes formula and of the central limit theorem for martingales.
   
Topology Seminar
Topic: When knots don't fiber
Presenter: Dan Silver, South Alabama
Date:  Thursday, November 8, 2007, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: In this joint work with Susan Williams we consider the conjecture: a knot is nonfibered if and only if its infinite cyclic cover has uncountably many finite covers. We prove it for a class of knots that includes all knots of genus 1. We also discuss two equivalent forms of the conjecture, one involving twisted Alexander polynomials, the other a weak form of subgroup separability.
   
Symplectic Geometry Seminar
Topic: Geometry and Fusion Energy: Geometric gyrokinetic theory for magnetic thermonuclear fusion plasmas
Presenter: Hong Qin, Princeton Plasma Physics Laboratory
Date:  Friday, November 9, 2007, Time: 1:30 p.m., Location: Fine Hall 314
Abstract: Magnetic thermonuclear fusion will bring the ultimate clean energy source to human beings. In magnetic thermonuclear fusion reactors, the physical and dynamical processes of the fusion matters, magnetized plasmas, are most comprehensively described by a non-equilibrium statistical model called gyrokinetic theory of the Vlasov-Maxwell system. It turns out that it is impossible to construct a systematic, self-consistent, and conservative gyrokinetic theory of the Vlasov-Maxwell system without using the tools of differential geometry. Geometrically or physically, gyrokinetic theory is about a symmetry, gyro-symmetry, in the Vlasov-Maxwell system for magnetized plasmas. In addition to its theoretical importance and elegance, gyro-symmetry can be employed as an effective numerical algorithm for large-scale massively parallel computer simulations for magnetized plasmas. I propose that the phase space of the space-time is a seven-dimensional fiber bundle over the four-dimensional space-time, and that a Poincaré-Cartan-Einstein 1-form on the seven-dimensional phase space determines a particle’s worldline in the phase space. Through Liouville 6-form and fiber integral, the 1-form also uniquely defines a geometrically generalized Vlasov-Maxwell system as a field theory for the collective electromagnetic field. The geometric gyrokinetic theory is then developed as a special case of the geometrically generalized Vlasov-Maxwell system with gyrosymmetry, and the 1-form again uniquely defines the gyrosymmetry. The objective is to decouple the gyrophase dynamics from the rest of the particle dynamics by finding the gyrosymmetry in the 1-form using the Lie perturbation method.
   
Differential Geometry and Geometric Analysis Seminar
Topic: The rate of change of width under flows
Presenter: Bill Minicozzi, JHU
Date:  Friday, November 9, 2007, Time: 3:00 p.m., Location: Fine Hall 314
Abstract: I will discuss a geometric invariant, that we call the width, of a manifold and first show how it can be realized as the sum of areas of minimal 2-spheres. When $M$ is a homotopy 3-sphere, the width is loosely speaking the area of the smallest 2-sphere needed to ``pull over'' $M$. Second, we will estimate the rate of change of width under various geometric flows to prove sharp estimates for extinction times. This is joint work with Toby Colding.
   
Symplectic Geometry Seminar ***Please note special date and time
Topic: Canonical deformations and mirror symmetry via real affine geometry
Presenter: Bernd Siebert, Universität Freiburg
Date:  Monday, November 12, 2007, Time: 1:30 p.m., Location: Fine Hall 314
Abstract: The limiting version of the SYZ approach to mirror symmetry suggests to put a real manifold of half the dimension at the center of the stage. This manifold is the base of two limiting torus fibrations, one related to symplectic geometry the other to complex geometry, and it is endowed with an integral affine structure away from a real codimension two discriminant locus. The basic problem with this point of view is that while it is easy to reconstruct the symplectic side via the cotangent bundle, the complex side is considered hard due to instanton corrections. In my recent paper with Mark Gross "From real affine geometry to complex geometry" we solve this problem by an algorithm producing a canonical, explicit smoothing of the "large complex structure limit" order by order. The instanton corrections arise by families of tropical disks. This gives complete control of the B-model (complex) side of mirror symmetry. The first talk on Monday will be a survey of these results, while the talks on Wednesday and Friday are aimed at explaining the algorithm in more detail together with giving necessary background material.
   
PACM Colloquium
Topic: Coherent and convex risk measures: representation results and dynamic consistency conditions
Presenter: Patrick Cheridito, Operations Res & Financial Eng, Princeton University
Date:  Monday, November 12, 2007, Time: 4:00 p.m., Location: Fine Hall 214
Abstract: Coherent and convex risk measures were introduced to address drawbacks of traditional risk measures such as variance, value-at-risk or default probability. After a short introduction I will give representation results for static risk measures. Then I will discuss dynamic risk measures and conditions for time-consistency.
   
Algebraic Geometry Seminar
Topic: Projective plane, fake projective planes and related questions
Presenter: Sai-Kee Yeung,  Purdue University
Date:  Tuesday, November 13, 2007, Time: 4:30 p.m., Location: Fine Hall 322
Abstract: Fake projective planes are complex surfaces with the same Betti numbers as the complex projective plane. The interest on such surfaces was related to a question of Severi on topological characterization of the projective plane. The first example was constructed by Mumford. The purpose of this talk is to explain uniformization of such fake projective planes and recent classification and construction of examples of fake projective planes by Gopal Prasad and myself. We will also explain more recent developments and related problems.
   
Mathematical Physics Seminar
Topic: Critical curves in conformally invariant statistical systems
Presenter: Ilya Gruzberg, University of Chicago
Date:  Tuesday, November 13, 2007, Time: 4:30 p.m., Location: Jadwin 343
Abstract:
We consider conformally invariant curves that appear at critical points of two-dimensional statistical mechanical systems. We show how to describe these curves in terms of the Coulomb gas formalism of conformal field theory (CFT). We also provide links between this description and the Schramm-Loewner evolution (SLE). The connection appears in the long-time limit of stochastic evolution of various SLE observables related to CFT primary fields. We show how the multifractal spectrum of harmonic measure and other fractal characteristics of critical curves can be obtained.

   
Operations Research and Financial Engineering Seminar
Topic: TBA
Presenter: Dimitris Bertsimas, MIT
Date:  Thursday, November 13, 2007, Time: 4:30 p.m., Location: E-219, E-Quad
   
Symplectic Geometry Seminar ***Please note special, date, location and time
Topic: Canonical deformations and mirror symmetry via real affine geometry
Presenter: Bernd Siebert, Universität Freiburg
Date:  Wednesday, November 14, 2007, Time: 1:30 p.m., Location: Fine Hall 801
Abstract: See abstract from Monday, November 12, 2007
   
Statistical Mechanics Seminar
Topic: Towards a linear response theory
Presenter: David Ruelle, IHES
Date:  Wednesday, November 14, 2007, Time: 2:00 p.m., Location: Jadwin 343
Abstract: Physical systems often exhibit nonequilibrium steady states (NESS). These are not described by the ensembles of equilibrium statistical mechanics, but by certain probability measures invariant under the dynamical system implementing time evolution. There is some agreement on how these invariant measures are selected (SRB states), but the problem of how they depend on parameters (linear response) is tricky. We shall discuss the results known for uniformly hyperbolic dynamical systems, where there are natural generalizations of the Kramers-Kronig dispersion relations and of the fluctuation-dissipation theorem. There are now also results for maps of the interval (Misiurewicz case), which are not uniformly hyperbolic. In the latter situation, one observes new phenomena, including an apparent "violation of causality", which are not fully understood.
   
Geometry, Representation Theory, and Moduli Seminar
Topic: TBA
Presenter: S. Gukov, IAS and Santa Barbara
Date:  Wednesday, November 14, 2007, Time: 3:00 p.m., Location: Fine Hall 214
   
Department Colloquium
Topic: TBA
Presenter: Isaac Held, NOAA and Princeton
Date:  Wednesday, November 14, 2007, Time: 4:30 p.m., Location: Fine Hall 314
   
Discrete Mathematics Seminar *** Please note new date
Topic: TBA
Presenter: Peter Keevash, Caltech
Date:  Thursday, November 15, 2007, Time: 2:15 p.m., Location: Fine Hall 224
   
Joint Princeton University/IAS Number Theory Seminar
Topic: Companion forms for Gsp(4)
Presenter: J. Tilouine, Paris 13
Date:  Thursday, November 15, 2007, Time: 4:30 p.m., Location: Fine Hall 214
   
Symplectic Geometry Seminar
Topic: Canonical deformations and mirror symmetry via real affine geometry
Presenter: Bernd Siebert, Universität Freiburg
Date:  Friday, November 16, 2007, Time: 1:30 p.m., Location: Fine Hall 314
Abstract: See abstract from Monday, November 12, 2007
   
Differential Geometry and Geometric Analysis Seminar
Topic: Non-variational Plateau problems in general relativity and the spacetime positive mass theorem in high dimensions
Presenter: Michael Eichmair, Stanford University
Date:  Friday, November 16, 2007, Time: 3:00 p.m., Location: Fine Hall 314
   
PACM Colloquium
Topic: A Hierarchy of Mathematical Models for Studying the Earth's Climate
Presenter: Dargan Frierson, Atmospheric Sciences, University of Washington
Date:  Monday, November 19, 2007, Time: 4:00 p.m., Location: Fine Hall 214
Abstract: The Earth's climate is a remarkably complex physical system; constructing models to study it is a difficult task which requires parameterization of a multitude of physical processes. Not surprisingly, such models quickly become difficult to understand due to the vast number of nonlinear processes that are active in them. Therefore, an important line of work in atmospheric science involves the development and use of intelligently chosen idealized models, designed to better understand the results of comprehensive climate models as well as the fundamental dynamics of atmospheric circulations. These models are simpler to interpret than the full climate models, but hopefully can still provide insight into the dynamics of their more complex cousins. In this talk, we give a summary of some topical problems in climate dynamics, and the hierarchical modeling approach we have used to study them. We will discuss physical problems such as the predicted poleward shift of the midlatitude jet stream with global warming, and changes in energy fluxes and temperature gradients in the atmosphere. Focusing on the effect of moist convection on these issues, we present a variety of idealized models that we have used to study these problems. These range from models of 3-D fluid motion on a rotating sphere in the presence of condensation, to highly idealized 1-D PDE models of diffusive energy transport.
   
Algebraic Geometry Seminar
Topic: Congruence for rational points over finite fields and coniveau over local fields
Presenter: Chenyang Xu,  Princeton University
Date:  Tuesday, November 20, 2007, Time: 4:30 p.m., Location: Fine Hall 322
Abstract: http://www.math.princeton.edu/alggeom/public_html/xu.pdf
   
Operations Research and Financial Engineering Seminar
Topic: Are Volatility Estimators Robust with Respect to Modeling Assumptions?
Presenter: Yingying Li, University of Chicago
Date:  Tuesday, November 27, 2007, Time: 4:30 p.m., Location: E-219, E-Quad
Abstract: We consider microstructure as an arbitrary contamination of the underlying latent securities price, through a Markov kernel $Q$. Special cases include additive error, rounding, and combinations thereof. Our main result is that, subject to smoothness conditions, the two scales realized volatility (TSRV) is robust to the form of contamination $Q$. To push the limits of our result, we show what happens for some models involving rounding (which is not, of course, smooth) and see in this situation how the robustness deteriorates with decreasing smoothness. Our conclusion is that under reasonable smoothness, one does not need to consider too closely how the microstructure is formed, while if severe non-smoothness is suspected, one needs to pay attention to the precise structure and also to what use the estimator of volatility will be put. This talk is based on joint work with Per A. Mykland.
   
Statistical Mechanics Seminar
Topic: On the relativistic Vlasov-Poisson equations
Presenter: Michael Kiessling, Rutgers University
Date:  Wednesday, November 28, 2007, Time: 2:00 p.m., Location: Jadwin 343
Abstract: I present recent results obtained jointly with A.S. Tahvildar-Zadeh. These include optimal Lp conditions on the initial data which guarantee that the classical Cauchy problem of the so-called relativistic Vlasov- Poisson equations in the attractive case have a global spherical solution. I also propose a new statistical mechanics derivation of these Vlasov equations based on Lorentz electromagnetism rather than Einstein gravity.
   
Geometry, Representation Theory, and Moduli Seminar
Topic: TBA
Presenter: B. Young, UBC
Date:  Wednesday, November 28, 2007, Time: 3:00 p.m., Location: Fine Hall 214
   
Operations Research and Financial Engineering Seminar
Topic: Asymptotic Behavior of Distribution Densities in Stochastic Volatility Models
Presenter: Archil Gulisashvili, Ohio University
Date:  Wednesday, November 28, 2007, Time: 4:30 p.m., Location: E-219, E-Quad
Abstract: The talk explains joint results with E. M. Stein concerning the asymptotic behavior of the distribution density of the stock price process in several known models with stochastic volatility. These models are the Hull-White, the Stein-Stein, and the Heston model. It is assumed that standard Brownian motions driving the stock price and the volatility equation are independent. Under this assumption, we find explicit formulas for leading terms in asymptotic expansions of the distribution density of the stock price with error estimates. We also study similar problems for time averages of the volatility process. As an application of these results, we obtain asymptotic formulas for the implied volatility in the stock price models mentioned above.
   
Differential Geometry and Geometric Analysis Seminar
Topic: TBA
Presenter: Simon Brendle, Stanford University
Date:  Friday, November 30, 2007, Time: 3:00 p.m., Location: Fine Hall 314
   
Columbia-NYU-Princeton Algebraic Geometry Seminar *** Please note special date and time
Topic: The Jacobian problem
Presenter: Shreeram Abhyankar, Purdue University
Date:  Friday, November 30, 2007, Time: 3:30 p.m., Location: Fine Hall 322
   
Columbia-NYU-Princeton Algebraic Geometry Seminar *** Please note special date and time
Topic: TBA
Presenter: Christopher Hacon,  University of Utah
Date:  Friday, November 30, 2007, Time: 5:00 p.m., Location: Fine Hall 322
   
DECEMBER 2007
   
PACM Colloquium
Topic: Cartesian Cut Cell Methods: Where Do Things Stand?
Presenter: Marsha Berger, Courant Institute, New York University
Date:  Monday, December 3, 2007, Time: 4:00 p.m., Location: Fine Hall 214
Abstract: We discuss some of the steps involved in preparing for and carrying out a fluid flow simulation in complicated geometry. Our goal is to automate this process as much as possible to enable high quality inviscid flow calculations. We use multilevel Cartesian meshes with irregular cells only in the region intersecting a solid object. We present some of the technical issues involved in this approach, including the special discretizations needed to avoid loss of accuracy and stability at irregular boundary cells, as well as how we obtain highly scalable parallel performance. This method is in routine use for aerodynamic calculations in several organizations, including NASA Ames Research Center. Many open problems are discussed.
   
Algebraic Geometry Seminar
Topic: TBA
Presenter: Nicholas Katz,  Princeton University
Date:  Tuesday, December 4, 2007, Time: 4:30 p.m., Location: Fine Hall 322
   
Mathematical Physics Seminar
Topic: Solution of the infrared catastrophe problem in non-relativistic QED
Presenter: Alessandro Pizzo, ETH, Switzerland
Date:  Tuesday, December 4, 2007, Time: 4:30 p.m., Location: Jadwin 343
Abstract: Within the framework of non-relativistic QED, we construct the scattering states of an electron interacting with the quantized electromagnetic field. The generic scattering state \psi_{h,\kappa}^{out/in} represents an electron with a wave function h in the momentum variable, with support in a region corresponding to small (asymptotic) velocities, accompanied by a cloud of real photons described by a Bloch-Nordsieck factor, and with an upper photon frequency cutoff \kappa. This is a joint work with T. Chen and J. Froehlich.
   
Geometry, Representation Theory, and Moduli Seminar
Topic: TBA
Presenter: A. Zinger, Stony Brook
Date:  Wednesday, December 5, 2007, Time: 3:00 p.m., Location: Fine Hall 214
   
Department Colloquium
Topic: TBA
Presenter: Clifford Taubes, Harvard University
Date:  Wednesday, December 5, 2007, Time: 4:30 p.m., Location: Fine Hall 314
   
Symplectic Geometry Seminar ***Please note special date, time, and location
Topic: Mirror symmetry for Gromov-Witten invariants of a quintic threefold
Presenter: Aleksey Zinger, Stony-Brook University
Date:  Thursday, December 6, 2007, Time: 1:00 p.m., Location: Fine Hall 224
Abstract: The mirror symmetry principle of string theory provides closed formulas for GW-invariants, with special attention devoted to a quintic threefold, Q3. The genus 0 mirror prediction for Q3 was verified 12 years ago by using the Atiyah-Bott localization theorem. In this talk, I will outline how the analoguos genus 1 localization problem is solved by making use of a number of its relations with the genus 0 localization problem. This approach confirms the 1993 BCOV mirror symmetry prediction for genus 1 GW-invariants of Q3. It also produces mirror formulas for genus 1 GW-invariants of a degree n hypersurface in P^{n-1} (Q3 is n=5), confirming a recent prediction of Klemm-Pandharipande for a sextic fourfold (n=6) and producing a puzzling combinatorial identity related to unbranched covers of tori (n=3).
   
Joint Princeton University/IAS Number Theory Seminar
Topic: TBA
Presenter: Jan Bruinier, University of Cologne
Date:  Thursday, December 6, 2007, Time: 4:30 p.m., Location: Fine Hall 214
   
PACM Colloquium
Topic: Collective motion and decision-making in animal groups
Presenter: Iain Couzin, Ecology & Evolutionary Biology, Princeton University
Date:  Monday, December 10, 2007, Time: 4:00 p.m., Location: Fine Hall 214
Abstract:

Animal groups such as bird flocks, insect swarms and fish schools are spectacular, ecologically important and sometimes devastating features of the biology of various species. Outbreaks of the desert locust, for example, can invade approximately one fifth of the Earth's land surface and are estimated to affect the livelihood of one in ten people on the planet. Using a combined theoretical and experimental approach involving insect and vertebrate groups I will address how, and why, individuals move in unison and investigate the principals of information transfer in these groups, particularly focusing on leadership and collective consensus decision-making.

For very large animal groups, despite huge differences in the size and cognitive abilities of group members, recent models from theoretical physics ('self-propelled particle', SPP, models) have suggested that general principles underlie collective motion. Such models demonstrate that some group-level properties may be largely independent of the types of animals involved. I shall present recent experimental work on locusts that validates some of the predictions of simple mechanistic models including a density-dependent "phase transition" from disordered to ordered motion.

Details of the mechanism by which individuals interact, however, also provide important biological insights into swarm behaviour. Using laboratory studies involving nerve manipulation and field experiments we demonstrate that some swarming insects are in effect on a "forced march" driven by cannibalism.

These results will be discussed in the context of the evolution of functional complexity and pattern formation in biological systems.

   
Algebraic Geometry Seminar
Topic: TBA
Presenter: Paul Hacking,  University of Washington
Date:  Tuesday, December 11, 2007, Time: 4:30 p.m., Location: Fine Hall 322
   
Differential Geometry and Geometric Analysis Seminar
Topic: On the $\sigma_2$-scalar curvature and its application
Presenter: Yuxin Ge, University Paris 12
Date:  Friday, December 14, 2007, Time: 3:00 p.m., Location: Fine Hall 314
Abstract: In this talk, we establish an analytic foundation for a fully non-linear equation $\frac{\sigma_2}{\sigma_1}=f$ on manifolds with positive scalar curvature. This equation arises from conformal geometry. As application, we prove that, if a compact 3-dimensional manifold $M$ admits a riemannian metric with positive scalar curvature and $\int \sigma_2\ge 0$, then topologically $M$ is a quotient of sphere.