SEMINARS
Updated: 3-12-2008
   
MARCH 2008
   
Automorphic Forms and Galois Representations Seminar
Topic: Galois representations arising from some compact unitary Shimura varieties
Presenter: Sug Woo Shin, Institute for Advanced Study
Date:  Wednesday, March 12, 2008, Time: 1:30 p.m., Location: Fine Hall 314
   
Department Colloquium
Topic: Chaoticity of the Teichm\"uller flow
Presenter: Artur Avila, IMPA and Clay Math. Inst.
Date:  Wednesday, March 12, 2008, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: A non-zero Abelian differential on a compact Riemann surface determines an atlas, outside the singularities, whose coordinate changes are translations. The vertical flow with respect to this translation structure generalizes the genus one notion of rational and irrational flows on tori. A fundamental tool in the understanding of the dynamics of vertical flows is the Teichm\"uller flow (acting on the moduli space of Abelian differentials), regarded as a renormalization operator. The chaotic nature of the dynamics of the Teichm\"uller flow has been a much researched topic, and currently it is known that it displays exponential decay of correlations. (This is equivalent to the spectral gap for the ambient SL(2) action, a very familiar result in genus 1.) Even much weaker aspects of the chaoticity of the Teichm\"uller flow however can be exploited in the description of the dynamics of typical vertical flows. Two such results are the proofs of the Kontsevich-Zorich conjecture and of weak mixing for interval exchange transformations.
   
Ergodic Theory and Statistical Mechanics Seminar
Topic: Spherical billiards with many 3-periodic orbits
Presenter: Yuliy Baryshnikov, Bell Laboratories
Date:  Thursday, March 13, 2008, Time: 2:00 p.m., Location: Fine Hall 401
Abstract: It is known that the Lebesgue measure of 3-periodic trajectories in a planar (Birkhoff) billiards is zero (and a well-known conjecture states that the same is true for any period). On the sphere, however, it is easy to construct a billiard domain with 2-dimensional family of 3-periodic orbits (take the intersection of the sphere with the positive octant). In this talk I will explain why this is essentially the only possible construction.
   
Discrete Mathematics Seminar
Topic: Sumsets in finite fields and Cayley sum graphs
Presenter: Noga Alon, Tel Aviv University and IAS
Date:  Thursday, March 13, 2008, Time: 2:15 p.m., Location: Fine Hall 314
Abstract: I will sketch a proof of the fact that for a prime p, every complement of a set of roughly sqrt p elements of the finite field Z_p is a sumset, that is, is of the form A+A, whereas there are complements of sets of size roughly p^{2/3} which are not sumsets. This improves estimates of Green and Gowers, and can also be used to settle a recent problem of Nathanson. The proofs combine probabilistic arguments with properties of Cayley sum graphs derived from their eigenvalues.
   
Geometry, Representation Theory, and Moduli Seminar ***Please note special date, time and location
Topic: Wall-crossing formula for motivic Donaldson-Thomas invariants
Presenter: Y. Soibelman, Kansas State University
Date:  Thursday, March 13, 2008, Time: 4:00 p.m., Location: Fine Hall 1201
Abstract: In joint work with Maxim Kontsevich we suggest an approach to the count of stable objects in a 3d Calabi-Yau category based on the ideas of motivic integration and derived algebraic geometry. As a corollary we obtain a wall-crossing formula for the corresponding invariants. I plan to discuss this circle of ideas as well as the relationship of our approach to certain birational symplectic automorphisms of tori (cluster transformations).
   
Princeton University and Institute for Advanced Study Number Theory
Topic: Iwasawa theory of elliptic curves for supersingular primes
Presenter: BD Kim, Northwestern University
Date:  Thursday, March 13, 2008, Time: 4:30 p.m., Location: Fine Hall 214
Abstract: Studying the Selmer groups of elliptic curves for a supersingular prime is difficult. It turned out we should instead use the plus/minus Selmer groups defined by Kobayashi. In this talk, we will see the plus/minus Selmer group theory for supersingular primes is very analogous to the Selmer group theoery for ordinary primes, and as an application, we will prove the parity conjecture of elliptic curves for supersingular primes among other things. We will report some other recent progress as well.
   
Topology Seminar
Topic: Variational principles on triangulated surfaces
Presenter: Feng Luo, Rutgers University
Date:  Thursday, March 13, 2008, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: We will discuss various applications of recently discovered 2-dimensional counterparts of the Schlaefli formula.
   
Symplectic Geometry Seminar
Topic: Special Lagrangian fibrations, instanton corrections and mirror symmetry
Presenter: Denis Auroux, MIT
Date:  Friday, March 14, 2008, Time: 2:00 p.m., Location: Fine Hall 314
Abstract: We study the extension of mirror symmetry to the case of Kahler manifolds which are not Calabi-Yau: the mirror is then a Landau-Ginzburg model, i.e. a noncompact manifold equipped with a holomorphic function called superpotential. The Strominger-Yau-Zaslow conjecture can be extended to this setting by considering special Lagrangian torus fibrations in the complement of an anticanonical divisor, and constructing the superpotential as a weighted count of holomorphic discs. In particular we show how "instanton corrections" arise in this setting from wall-crossing discontinuities in the holomorphic disc counts. Various explicit examples in complex dimension 2 will be considered.
   
Special Analysis Seminar ***Please note special time
Topic: The abstract concept of Duality and some related facts (part of a joint project with Shiri Artstein-Avidan)
Presenter: Vitali Milman, Tel Aviv University
Date:  Monday, March 24, 2008, Time: 2:30 p.m., Location: Fine Hall 110
Abstract: We discuss in the talk an unexpected observation that very minimal basic properties essentially uniquely define some classical transforms which traditionally are defined in a concrete and quite involved form. We start with a characterization of a very basic concept in Convexity: Duality and the Legendre transform. We show that the Legendre transform is, up to linear terms, the only involution on the class of convex lower semi-continious functions in R^n which reverses the (partial) order of functions. This leads to a different understanding of the concept of duality, which we call an ``abstract duality concept'', and which we then apply also to many other well known settings. It is also true that any involutive transform (on this class) which exchanges summation with inf-convolution, is, up to linear terms, the Legendre transform. The classical Fourier transform may be also defined (essentially) uniquely by the condition of exchanging convolution with product together the form of the square of the transform (the last fact is a joint work also with Semyon Alesker).
   
Analysis Seminar
Topic: Mass inequalities for Cauchy data in general relativity
Presenter: Gilbert Weinstein, University of Alabama at Birmingham
Date:  Monday, March 24, 2008, Time: 4:00 p.m., Location: Fine Hall 110
Abstract: We will survey a number of inequalities involving the total mass and other invariants for initial data for the Einstein equations in general relativity.
   
PACM Colloquium
Topic: A worldwide web of images
Presenter: Blaise Aguera y Arcas, Microsoft Live Labs
Date:  Monday, March 24, 2008, Time: 4:00 p.m., Location: Fine Hall 214
Abstract:

In this talk we'll explore the emerging potential of computer vision to transform the way we think about the interconnectedness of digital imagery and the Web, and how these relate to our physical environment. We'll begin with an introduction to the foundations of "3D computer vision", a bag of tricks which has been developing steadily for three decades, combining classical photogrammetry with machine vision. We'll then dive specifically into Photosynth, based on a combination of the Photo Tourism project (a collaboration between Microsoft Research and the University of Washington) and Seadragon, a multiresolution networked platform allowing one to play with arbitrarily many arbitrary large visual objects using only constant-time and constant-bandwidth operations. The aim of Photosynth is to allow meaningful 3D navigation within real-world environments reconstructed entirely from the photos. Interesting social dimensions are added to this application when one considers that the source photos can be mined from the existing Web, aggregated from user communities, and actively contributed to and interconnected. We'll end with some preliminary findings about the latent graph structure of Internet photography, and a glimpse of where we're heading next.

   
Algebraic Geometry Seminar
Topic: The birational geometry of Kontsevich moduli spaces
Presenter: Izzet Coskun, University of Illinois at Chicago
Date:  Tuesday, March 25, 2008, Time: 4:30 p.m., Location: Fine Hall 322
Abstract: I will describe the stable base loci of linear systems on the Kontsevich moduli spaces of maps to projective spaces and Grassmannians. This description allows us to run the log minimal model program for these moduli spaces in small degree. I will give some examples where interesting classical moduli spaces occur. This is joint work with Dawei Chen and builds on previous work with Joe Harris and Jason Starr.
   
Mathematical Physics Seminar
Topic: Minimizing the ground state energy of an electron in a randomly deformed lattice
Presenter: M. Loss, Georgia Tech.
Date:  Tuesday, March 25, 2008, Time: 4:30 p.m., Location: Jadwin 343
Abstract: We provide a characterization of the spectral minimum for a random Schrödinger operator of the form $H=-\Delta + \sum_{i \in \Z^d}q(x-i-\omega_i)$ in $L^2(\R^d)$, where the single site potential $q$ is reflection symmetric, compactly supported in the unit cube centered at $0$, and the displacement parameters $\omega_i$ are restricted so that adjacent single site potentials do not overlap. In particular, we show that a minimizing configuration of the displacements is given by a periodic pattern of densest possible $2^d$-clusters of single site potentials. This is joint work with G\"unter Stolz and Jeff Baker.
   
Operations Research and Financial Engineering Colloquium
Topic: On dimensionality of mean structure from a single data matrix
Presenter: Xuming He, University of Illinois at Urbana-Champaign
Date:  Tuesday, March 25, 2008, Time: 4:30 p.m., Location: E-219, E-Quad
Abstract: See http://orfe.princeton.edu/papers/he-abstract.pdf
   
Geometry, Representation Theory, and Moduli Seminar
Topic: TBA
Presenter: E. Carlsson, Princeton University
Date:  Wednesday, March 26, 2008, Time: 3:00 p.m., Location: Fine Hall 214
   
Ergodic Theory and Statistical Mechanics Seminar
Topic: Logarithm laws for horocycles
Presenter: Jayadev Athreya, Princeton University
Date:  Thursday, March 27, 2008, Time: 2:00 p.m., Location: Fine Hall 401
Abstract: In joint work with G. Margulis, we prove a logarithm law for unipotent flows on the space of unimodular lattices in R^n.
   
Differential Geometry and Geometric Analysis Seminar
Topic: TBA
Presenter: Marianty Ionel, University of Toledo
Date:  Friday, March 28, 2008, Time: 3:00 p.m., Location: Fine Hall 314
   
Differential Geometry and Geometric Analysis Seminar ***Please note special time
Topic: TBA
Presenter: Micah Warren, University of Washington
Date:  Friday, March 28, 2008, Time: 4:00 p.m., Location: Fine Hall 314
   
Group Actions Seminar
Topic: TBA
Presenter: Danijela Damjanovic, Harvard University
Date:  Monday, March 31, 2008, Time: 12:15 p.m., Location: Fine Hall 224
   
PACM Colloquium
Topic: Mathematical and Computational Challenges in Shear Stiffness Imaging of Tissue: Can cancerous and benign lesions be distinguished?
Presenter: Joyce McLaughlin, Mathematical Sciences, Rensselaer Polytechnic Institute
Date:  Monday, March 31, 2008, Time: 4:00 p.m., Location: Fine Hall 214
Abstract: For centuries doctors have palpated tissue to detect abnormalities. We target imaging the stiffness the doctor feels in the palpation exam, including imaging deeper than what can be felt in this exam and distinguishing between benign and cancerous lesions. Current applications include breast and prostate cancer. Current experimentalists with whom we collaborate are: Dr. Richard Ehman, Mayo Clinic; Mathias Fink, ESPCI, Paris; and Dr. Kevin Parker at the University of Rochester. We describe the challenges and opportunities for imaging, including mathematical modeling and algorithmic development, with the data from the individual experiments
   
APRIL 2008
   
Algebraic Geometry Seminar
Topic: Real singular Del Pezzo surfaces and rationally connected threefolds
Presenter: Frédéric Mangolte, Université de Savoie
Date:  Tuesday, April 1, 2008, Time: 4:30 p.m., Location: Fine Hall 322
Abstract: Recent results on classification of real algebraic threefolds will be described. Let W -> X be a real smooth projective threefold fibred by rational curves. J. Kollár proved that if the set of real points W(R) is orientable, then a connected component N of W(R) is essentially either a Seifert fibred manifold or a connected sum of lens spaces. We proved sharp estimates on the number and the multiplicities of the Seifert fibres and on the number and the torsions of the lens spaces whenever X is a geometrically rational surface. These results answer in the affirmative three questions of Kollár. They are derived from a careful study of real singular Del Pezzo surfaces with only Du Val singularities. This is joint work with F. Catanese.
   
Mathematical Physics Seminar
Topic: Localisation in the Anderson tight binding model with several particles
Presenter: Y. Suhov, University of Cambridge, UK
Date:  Tuesday, April 1, 2008, Time: 4:30 p.m., Location: Jadwin 343
Abstract: The Anderson model (which will celebrate its 50th anniversary in 2008) is among most popular topics in the random matrix and operator theory. However, so far the attention here was concentrated on single-particle models, where the random external potential is either IID or has a rapid decay of spatial correlations. Multi-particle models remained out of scope in mathematical (and, surprisingly, physical) literature. Recently, Chulaevsky and Suhov (2007) proposed a version of the multi-scale analysis (MSA) scheme tackling the multi-particle case. I'll discuss one of results in this direction: localisation in the lattice (tight binding) multi-particle models for large values of the amplitude (coupling) constant.
   
Operations Research and Financial Engineering Colloquium
Topic: Modelling high dimensional daily volatilities based on high-frequency data
Presenter: Qiwei Yao, London School of Economics
Date:  Tuesday, April 1, 2008, Time: 4:30 p.m., Location: E-219, E-Quad
Abstract: See http://orfe.princeton.edu/papers/yao-abstract.pdf
   
Geometry, Representation Theory, and Moduli Seminar
Topic: TBA
Presenter: B. Fantechi, SISSA and IAS
Date:  Wednesday, April 2, 2008, Time: 3:00 p.m., Location: Fine Hall 214
   
Discrete Mathematics Seminar
Topic: TBA
Presenter: János Pach, NYU and Courant Institute
Date:  Thursday, April 3, 2008, Time: 2:15 p.m., Location: Fine Hall 314
   
Differential Geometry and Geometric Analysis Seminar
Topic: TBA
Presenter: Jeff Cheeger, New York University
Date:  Friday, April 4, 2008, Time: 3:00 p.m., Location: Fine Hall 314
   
PACM Colloquium
Topic: Water Information Networks & Efficiency in Irrigation Systems
Presenter: Iven Mareels, Electrical & Electronic Engineering, The University of Melbourne
Date:  Monday, April 7, 2008, Time: 4:00 p.m., Location: Fine Hall 214
Abstract:

The world's sustainable water supply is heavily used (it is estimated that annually 65% of the available water resources are extracted), and with very poor efficiency (typically less than half the water taken from the environment serves the objective for which it was intended). The UNESCO World Water reports 2003/2005 identify management as one of the main issues to be addressed in order to avoid a water catastrophe. Australia is in a particularly critical situation, where management has to deal with significant climate change effects.

In this lecture we outline a sensor networks and systems engineering approach to underpin the management of an entire water catchment basin. The technology exists to construct a sensor network to monitor at a global scale the water resource and manage in closed loop the resource through the distribution infrastructure using the data derived from the sensor network. The control objective is to deliver water on demand with maximal overall efficiency. Such technology would provide the necessary data to implement a sustainable water policy in an adaptive way, where economic, environmental and social issues are properly taken into account.

We review the results from a number of substantial pilot projects in Victoria and New South Whales Australia in which, where Rubicon Systems Australia Pty. Ltd., who commercialise the technology, have realized significant gains in water efficiency in irrigation distribution. We show how this experience may lead to substantial gains in water management overall, and leads to better on farm practices, building further water savings. At present the state government of Victoria is backing this technoly with a 1 billion dollar investment to create significant water savings across the state. We discuss aspects of modeling of water dynamics followed by the control aspects enabled in the present and envisaged hardware upgrades.

   
Mathematical Physics Seminar
Topic: TBA
Presenter: E. Akkermans, Technion
Date:  Tuesday, April 8, 2008, Time: 4:30 p.m., Location: Jadwin 343
   
Geometry, Representation Theory, and Moduli Seminar
Topic: TBA
Presenter: B. Kim, KIAS
Date:  Wednesday, April 9, 2008, Time: 3:00 p.m., Location: Fine Hall 214
   
Department Colloquium
Topic: TBA
Presenter: Marc Levine, Northeastern University
Date:  Wednesday, April 9, 2008, Time: 4:30 p.m., Location: Fine Hall 314
   
Topology Seminar
Topic: On the renormalized volume of quasifuchsian manifolds
Presenter: Jean-Marc Schlenker, Toulouse
Date:  Thursday, April 10, 2008, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: The renormalized volume of quasifuchsian hyperbolic 3-manifolds was originally introduced for physical reasons. Takhtajan and Zograf (and others) discovered that it provides a Kähler potential for the Weil-Petersson metric on Teichmüller space. We will give an elementary, differential-geometric account of this result. It can be extended to quasifuchsian manifolds having cone singularities along infinite lines, yielding results on the Teichmüller space of hyperbolic metrics with cone singularities (of prescribed angles) on a closed surface. (Based on joint works with K. Krasnov, C. Lecuire, S. Moroianu.)
   
Symplectic Geometry Seminar
Topic: Mirror symmetry of Fano toric A-model and Landau-Ginzburg B-model
Presenter: Yong-Geun Oh,University of Wisconsin
Date:  Friday, April 11, 2008, Time: 2:00 p.m., Location: Fine Hall 314
   
Differential Geometry and Geometric Analysis Seminar
Topic: TBA
Presenter: Spyros Alexakis, Princeton University
Date:  Friday, April 11, 2008, Time: 3:00 p.m., Location: Fine Hall 314
   
PACM Colloquium
Topic: Airplane boarding and space-time geometry
Presenter: Eitan Bachmat, Computer Science, Ben-Gurion University and Brandeis University
Date:  Monday, April 14, 2008, Time: 4:00 p.m., Location: Fine Hall 214
Abstract:

It is hard to think of a process that is more boring than boarding an airplane. In the hope of relieving, or at least shortening, some of the pain, airlines have devised various boarding strategies such as back-to-front, window to aisle, boarding by zones or even unassigned seating. In the talk we will try to overturn the negative image that airplane boarding has and will try to portray it as a very exciting process which is modeled via space-time (a.k.a Lorentzian) geometry with a touch of random matrix theory. Using the model we will try to figure out what are the better strategies. If time permits, we will use insights from the airplane borading process to suggest an interpretation for Einstein's law of motion in which god plays the ultimate dice game. The talk is entirely self contained. Partly based on joint works with D. Berend, L. Sapir, S. Skiena, M. Elkin and V. Khachaturov.

   
Algebraic Geometry Seminar
Topic: TBA
Presenter: Rajesh Kulkarni, Michigan State University
Date:  Tuesday, April 15, 2008, Time: 4:30 p.m., Location: Fine Hall 322
   
Mathematical Physics Seminar
Topic: TBA
Presenter: lya Goldsheid, Queen Mary, University of London
Date:  Tuesday, April 15, 2008, Time: 4:30 p.m., Location: Jadwin 343
   
Mathematical Physics Seminar ***Please note special date
Topic: TBA
Presenter: P. Exner, Physics Inst., Czech Academy
Date:  Thursday, April 17, 2008, Time: 4:30 p.m., Location: Jadwin 343
   
Symplectic Geometry Seminar
Topic: TBA
Presenter: Sergio Lukic, Rutgers University
Date:  Friday, April 18, 2008, Time: 2:00 p.m., Location: Fine Hall 314
   
Differential Geometry and Geometric Analysis Seminar
Topic: TBA
Presenter: Mu-Tao Wang, Columbia University
Date:  Friday, April 18, 2008, Time: 3:00 p.m., Location: Fine Hall 314
   
Group Actions Seminar
Topic: TBA
Presenter: Francois Maucourant, Rennes 1 University
Date:  Monday, April 21, 2008, Time: 12:15 p.m., Location: Fine Hall 224
   
Analysis Seminar
Topic: TBA
Presenter: Joachim Krieger, University of Pennsylvania
Date:  Monday, April 21, 2008, Time: 4:00 p.m., Location: Fine Hall 110
   
Algebraic Geometry Seminar
Topic: TBA
Presenter: Robert Lazarsfeld, University of Michigan
Date:  Tuesday, April 22, 2008, Time: 4:30 p.m., Location: Fine Hall 322
   
Mathematical Physics Seminar
Topic: Long range order for lattice dipoles
Presenter: Alessandro Giuliani, University of Rome
Date:  Tuesday, April 22, 2008, Time: 4:30 p.m., Location: Jadwin 343
Abstract: We consider a system of classical Heisenberg spins on a cubic lattice in dimensions three or more, interacting via the dipole-dipole interaction. We prove that at low enough temperature the system displays orientational long range order, as expected by spin wave theory. The proof is based on reflection positivity methods. In particular, we demonstrate a previously unproven conjecture on the dispersion relation of the spin waves, first proposed by Froehlich and Spencer, which allows one to apply infrared bounds for estimating the long distance behavior of the spin-spin correlation functions.
   
Geometry, Representation Theory, and Moduli Seminar
Topic: TBA
Presenter: P. Johnson, University of Michigan
Date:  Wednesday, April 23, 2008, Time: 3:00 p.m., Location: Fine Hall 214
   
Department Colloquium
Topic: TBA
Presenter: Jim Bryan, UBC
Date:  Wednesday, April 23, 2008, Time: 4:30 p.m., Location: Fine Hall 314
   
Differential Geometry and Geometric Analysis Seminar
Topic: TBA
Presenter: Yisong Yang, Poly. Tech. in New York
Date:  Friday, April 25, 2008, Time: 3:00 p.m., Location: Fine Hall 314
   
PACM Colloquium
Topic: Active and Semi-Supervised Learning Theory
Presenter: Rob Nowak, Electrical and Computer Engineering, University of Wisconsin-Madison
Date:  Monday, April 28, 2008, Time: 4:00 p.m., Location: Fine Hall 214
Abstract:

Science is arguably the pinnacle of human intellectual achievement, yet the scientific discovery process itself remains an art. Human intuition and experience is still the driving force of the high-level discovery process: we determine which hypotheses and theories to entertain, which experiments to conduct, how data should be interpreted, when hypotheses should be abandoned, and so on. Meanwhile machines are limited to low-level tasks such as gathering and processing data. A grand challenge for scientific discovery in the 21st century is to devise machines that directly participate in the high-level discovery process. Towards this grand challenge, we must formally characterize the limits of machine learning. Statistical learning theory is usually based on supervised training, wherein a learning algorithm is presented with a finite set of i.i.d. labeled training examples. However, modern experimental methods often generate incredibly large numbers of unlabeled data for very little expense, while the task of labeling data is often painstaking and costly. Machine learning methods must leverage the abundance of unlabeled data in scientific problem domains. Active learning (AL) and semi-supervised learing (SSL) are two well known approaches to exploit unlabeled data. In both paradigms one has access to a large pool of unlabeled examples, and only a few labeled examples are provided or selected. AL is a sequential feedback process. Unlabeled examples that are predicted to have very informative labels, based on previously gathered labeled and unlabeled data, are selected for labeling. In SSL, labeled examples are randomly provided, without regard to potential informativeness. Today, little is known about theoretical limits of AL and SSL performance. Sparsity and complexity of the underlying data-generating distributions appear to play a central role in the performance of AL and SSL, and this talk will discuss some of the known theoretical results.

This work is joint with Rui Castro, Aarti Singh and Jerry Zhu.

   
Algebraic Geometry Seminar
Topic: TBA
Presenter: Brendan Hassett, Rice University
Date:  Tuesday, April 29, 2008, Time: 4:30 p.m., Location: Fine Hall 322
   
MAY 2008
   
Topology Seminar
Topic: TBA
Presenter: Robert Lipshitz, Columbia University
Date:  Thursday, May 1, 2008, Time: 4:30 p.m., Location: Fine Hall 314