OCTOBER 20 - 22, 2004 |
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| Discrete Mathematics Seminar | |
| Topic: | Menger Theorem for infinite graphs |
| Presenter: | Eli Berger, Institute for Advanced Study |
| Date: | Wednesday, October 20, 2004, Time: 2:30 p.m., Location: Fine Hall 224 |
| Abstract: | Click here |
| Geometry, Representation Theory, and Moduli Seminar *** Please note special time | |
| Topic: | Continued fractions, codes and identities for lengths |
| Presenter: | Greg McShane, Toulouse |
| Date: | Wednesday, October 20, 2004, Time: 2:00 p.m., Location: Fine Hall 214 |
| Abstract: | We'll discuss the relationship between the simple geodesics on a once punctured torus and badly approximable real numbers. We explain how this leads to a classification of points in X(gamma) = the set of starting points of complete geodesics perpendicular to a geodesic in the boundary of a hyperbolic surface of type g,n indicating analogies with the theory of continued fractions. |
| Geometry, Representation Theory, and Moduli Seminar | |
| Topic: | Stable maps to a loop group |
| Presenter: | Michael Thaddeus, Columbia |
| Date: | Wednesday, October 20, 2004, Time: 3:00 p.m., Location: Fine Hall 214 |
| Abstract: | I will explain how the space of principal G-bundles on a fixed curve times a variable curve can be compactified in analogy with the space of stable maps. Indeed, the resulting space can be regarded as a moduli space of stable maps to the loop group LG. The moduli space carries a perfect tangent-obstruction theory that can be used to define Gromov-Witten type invariants. I will discuss a few basic facts about these, showing, for example, that the quantum cohomology is associative. |
| Department Colloquium | |
| Topic: | Analysis and geometry of fractals |
| Presenter: | Alexandre Kirillov, University of Pennsylvania |
| Date: | Wednesday, October 20, 2004, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: | I discuss several interesting phenomena (geometric, algebraic, analytic and arithmetic) which are observed in the study of fractal sets and functions on them. Only two examples will be considered: Sierpinski and Apollonian gaskets. Main topics: 1. Definition and analytic structure of harmonic functions on the Sierpinski gasket. 2. Arithmetic properties of values of harmonic functions on the Sierpinski gasket. 3. Definition of Apollonian gaskets and geometry of circles on spheres. Generalized Descartes theorem. 4. Arithmetic properties of Farey series and curvatures of circles in Apollonian gaskets. 5. The Minkowski's "question function". |
| Ergodic Theory and Statistical Mechanics Seminar | |
| Topic: | Pseudochaotic dynamics and transport |
| Presenter: | George Zaslavsky, Courant Institute |
| Date: | Thursday, October 21, 2004, Time: 2:00 p.m., Location: Fine Hall 322 |
| Abstract: | We discuss some billiard type models with non-integrable dynamics and zero Lyapunov exponent and application of these models in physics. These models can be considered as examples of objects with long lasting nonequilibrium states and absence of a finite time of relaxation. |
| Joint Analysis Seminar | |
| Topic: | Whitney extension problems |
| Presenter: | Charles Fefferman, Princeton University |
| Date: | Thursday, October 21, 2004, Time: 3:30 p.m., Location: Fine Hall 214 |
| Topology Seminar | |
| Topic: | The Geometry of the Jones polynomial |
| Presenter: | Stavros Garoufalidis, Georgia Tech. |
| Date: | Thursday, October 21, 2004, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: | The Jones polynomial of a knot in 3-space is a powerful quantum field theory invariant.The Jones polynomial is a Laurent polynomial, and it can be enhanced to a sequence of Laurent polynomials. This sequence is not random. Instead, we will show that this sequence is q-holonomic, ie that it satisfies a recursion relation. This phenomenon can be extended to links, and to quantum invariants of higher rank Lie groups. We will show from first principles that holonomicity is a general property of statistical mechanics models. Using holonomicity, and specializing to q=1, allows us to define a 'characteristic variety of a knot', which in the SL_2 case is a complex curve in C^2. We conjecture that the characteristic variety of a knot coincides with its deformation variety. We give evidence for the 'characteristic equals deformation variety' conjecture. Time permitting, we plan to discuss briefly the implications of holonomicity to the hyperbolic volume conjecture. |
FALL BREAK - OCTOBER 25 -29 |
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| Joint Princeton University and Institute for Advanced Study Number Theory Seminar | |
| Topic: | Real zeros and size of Rankin-Selberg L-functions in the level aspect |
| Presenter: | Guillaume Ricotta, Universite de Montreal |
| Date: | Monday, October 25, 2004, Time: 4:30 p.m., Location: Fine Hall 322 |
| Abstract: | In 2002, J.B. Conrey and K. Soundararajan showed that there are infinitely many Dirichlet $L$-functions which do not vanish on the critical segment. Let $\mathcal{G}$ be the family of Dirichlet $L$-functions they considered. Following their work, a similar analytic study (especially the non-trivial real zeros but also the size on the critical line) of a family $\mathcal{F}$ of Rankin-Selberg L-functions which has the same symmetry type than $\mathcal{G}$ (namely the symplectic one) was undertaken during my thesis. Some asymptotic formula for the harmonic mollified second moment of $\mathcal{F}$ was established and obviously the asymptotic of the harmonic mollified second moment of $\mathcal{F}$ is the same than the asymptotic of the mollified second moment of $\mathcal{G}$. Let us remark that such a formula is needed to apply mollification method. The main contribution is a substancial improvement of the admissible length of the mollifier which is done by solving a shifted convolution problem by a spectral method of P. Sarnak on average thanks to large sieve inequalities for Fourier coefficients of Maass forms. Some other refinements obtained by B. Krötz and R.J. Stanton are also needed. Finally, the end of this talk will be devoted to the non-exhausted description of:
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NOVEMBER 1 - 5, 2004 |
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| Analysis Seminar | |
| Topic: | Quasilinear wave equations in exterior domains |
| Presenter: | Jason Metcalfe, Georgia Institute of Technology |
| Date: | Monday, November 1, 2004, Time: 3:00 p.m., Location: Fine Hall 314 |
| PACM Seminar | |
| Topic: | Equation-free modeling for complex, multiscale systems |
| Presenter: | Ioannis Kevrekidis, Department of Chemical Engineering, Princeton University |
| Date: | Monday, November 1, 2004, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: | In current modeling, the best available descriptions of a system often come at a fine level (atomistic, stochastic, microscopic, individual-based) while the questions asked and the tasks required by the modeler (prediction, parametric analysis, optimization and control) are at a much coarser, averaged, macroscopic level. Traditional modeling approaches start by first deriving macroscopic evolution equations from the microscopic models, and then bringing our arsenal of mathematical and algorithmic tools to bear on these macroscopic descriptions. Over the last few years, and with several collaborators, we have developed and validated a mathematically inspired, computational enabling technology that allows the modeler to perform macroscopic tasks acting on the microscopic models directly. We call this the "equation-free" approach, since it circumvents the step of obtaining accurate macroscopic descriptions. I will argue that the backbone of this approach is the design of (computational) experiments. In traditional numerical analysis, the main code "pings" a subroutine containing the model, and uses the returned information (time derivatives, function evaluations, functional derivatives) to perform computer-assisted analysis. In our approach the same main code "pings" a subroutine that sets up a short ensemble of appropriately initialized computational experiments from which the same quantities are estimated (rather than evaluated). Traditional continuum numerical algorithms can thus be viewed as protocols for experimental design (where "experiment" means a computational experiment set up and performed with a model at a different level of description). Ultimately, what makes it all possible is the ability to initialize computational experiments at will. Short bursts of appropriately initialized computational experimentation -through matrix-free numerical analysis and systems theory tools like variance reduction and estimation- bridges microscopic simulation with macroscopic modeling. Remarkably, if enough control authority exists to initialize laboratory experiments "at will", this computational enabling technology can become a set of experimental protocols for the equation-free exploration of complex system dynamics. |
| Joint Princeton University and Institute for Advanced Study Number Theory Seminar | |
| Topic: | Uniform bounds for Serre's theorem for elliptic curves over function fields |
| Presenter: | Chris Hall, University of Texas at Austin |
| Date: | Monday, November 1, 2004, Time: 4:30 p.m., Location: Fine Hall 322 |
| Algebraic Geometry Seminar | |
| Topic: | Linear systems of Jacobians and addition formulas for Theta functions |
| Presenter: | Samuel Grushevsky, Princeton University |
| Date: | Tuesday, November 2, 2004, Time: 4:30 p.m., Location: Fine Hall 322 |
| Statistical Mechanics Seminar | |
| Topic: | Local Density Fluctuations, Hyperuniformity, and Order Metrics |
| Presenter: | Salvatore Torquato, Princeton University |
| Date: | Wednesday, November 3, 2004, Time: 2:00 p.m., Location: Jadwin 343 |
| Abstract: | We study the variance in the number of points contained within a window of arbitrary size in space dimension d, and further illuminate our understanding of "hyperuniform" systems, i.e., point patterns that do not possess infinite-wavelength fluctuations. For large windows, hyperuniform systems are characterized by a local variance that grows only as the surface area (rather than the volume) of the window. We show that hyperuniform systems are at a ``critical-point'' of a type with appropriate scaling laws and critical exponents. We show that finding the global minimum of the local variance is equivalent to determining the ground state of a certain system of interacting particles, which in turn is related to a problem in number theory. We prove that the simple periodic linear array yields the global minimum value of the average variance among all infinite one-dimensional hyperuniform patterns. Contrary to the conjecture that the lattices associated with the densest packing of congruent spheres have the smallest variance regardless of the space dimension, we show that for d=3, the body-centered cubic lattice has a smaller variance than the face-centered cubic lattice. |
| Geometry, Representation Theory, and Moduli Seminar | |
| Topic: | TBA |
| Presenter: | Thomas Graber, Berkeley |
| Date: | Wednesday, November 3, 2004, Time: 3:00 p.m., Location: Fine Hall 214 |
| Joint Analysis Seminar | |
| Topic: | Curvature propagation in General Relativity--the Yang-Mills analogy |
| Presenter: | Vincent Moncrief, Yale University |
| Date: | Thursday, November 4, 2004, Time: 3:30 p.m., Location: Fine Hall 214 |
NOVEMBER 8 - 12, 2004 |
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| Analysis Seminar | |
| Topic: | Global well-posedness for the Klein-Gordon-Schrodinger system below the energy space |
| Presenter: | Nikolaos Tzirakis, IAS and University of Toronto |
| Date: | Monday, November 8, 2004, Time: 3:00 p.m., Location: Fine Hall 314 |
| Abstract: | I will show that the Klein-Gordon-Schrodinger system in one,two, and three dimensions, has a global solution below the energy space. These type of equations, in the continuum and in a spatially discrete form, are relevant to a variety of physical applications including studies of the DNA double strand and models of polarons among others. The proof uses the "I-method" recently introduced by J. Colliander, M. Keel, G. Staffilani, H. Takaoka and T.Tao, and mixed type Strichartz estimates for the solutions of Schrodinger and Klein-Gordon equation respectively. In every different case/dimension a new local well posedness result has to be proved in order to take advantage of the decay of the "modify energy" that the "I-method" introduces. |
| PACM Seminar | |
| Topic: | Multiscale Analysis and Diffusion Geometries on Digital Data Sets |
| Presenter: | Ronald Coifman, Department of Mathematics, Yale University |
| Date: | Monday, November 8, 2004, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: | We will discuss simple methodologies for analyzing and discovering geometric structures in massive data sets. We introduce multiscale Harmonic analysis on graphs and on subsets of Euclidean spaces. The methods augment spectral graph theory, kernel principal component analysis, manifold learning and other methods from machine learning. |
| Joint Princeton University and Institute for Advanced Study Number Theory Seminar | |
| Topic: | TBA |
| Presenter: | Karl Rubin, Univ. California at Irvine |
| Date: | Monday, November 8, 2004, Time: 4:30 p.m., Location: Fine Hall 322 |
| Algebraic Geometry Seminar | |
| Topic: | Canonical cooridinates on leaves |
| Presenter: | C.-L. Chai, University of Pennsylvania |
| Date: | Tuesday, November 9, 2004, Time: 4:30 p.m., Location: Fine Hall 322 |
| Abstract: | Let $k$ be an algebraically closed field of characteristic $p>0$. A leaf $C$ in the Siegel modular variety $\cal A_g$, as defined by Oort, is the locus defined by a fixed isomorphism type of polarized Barsotti-Tate group. Let $x_0$ be a closed point of $C$. It turns out that the formal completion $C^{/x_0}$ of $C$ at $x_0$ is "built up" from $p$-divisible formal groups, by a system of fibrations. This is a generalization of the Serre-Tate coordinates for the local moduli space of an ordinatry abelian variety, and plays an important role in the proof (with Oort) of the Hecke orbit conjecture. |
| Geometry, Representation Theory, and Moduli Seminar | |
| Topic: | TBA |
| Presenter: | Manfred Einsiedler, Princeton University |
| Date: | Wednesday, November 10, 2004, Time: 3:00 p.m., Location: Fine Hall 214 |
| Department Colloquium | |
| Topic: | The Sharp Form of the Strong Szego Theorem |
| Presenter: | Barry Simon, Caltech |
| Date: | Wednesday, November 10, 2004, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: | This talk will discuss a proof of the Strong Szego theorem on the second term in the asymptotics of Toeplitz determinants. After a brief discussion of the history, I'll discuss the elementary argument that reduces the sharp (optimal) result to the case of analytic symbols. I'll then present a new proof of the theorem in the analytic case. I'll present the necessary background from the theory of orthogonal polynomials on the unit circle along the way. |
| Joint Columbia University-Courant Institute-Princeton University Differential Geometry Seminar | |
| Topic: | TBA |
| Presenter: | Claude LeBrun, Columbia University |
| Date: | Friday, November 12, 2004, Time: 2:00 p.m., Location: Room 101, Warren Weaver Hall, Courant Institute |
| Joint Columbia University-Courant Institute-Princeton University Differential Geometry Seminar | |
| Topic: | TBA |
| Presenter: | Jeff Viaclovsky, MIT |
| Date: | Friday, November 12, 2004, Time: 3:30 p.m., Location: Room 101, Warren Weaver Hall, Courant Institute |
NOVEMBER 15 - 19, 2004 |
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| Analysis Seminar | |
| Topic: | TBA |
| Presenter: | Daniela De Silva, MIT |
| Date: | Monday, November 15, 2004, Time: 3:00 p.m., Location: Fine Hall 314 |
| PACM Seminar | |
| Topic: | Astrophysical Gas Dynamics |
| Presenter: | Jim Stone, Department of Astrophysical Sciences, Princeton University |
| Date: | Monday, November 15, 2004, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: | Most of the visible matter in the Universe is a plasma, that is a dilute gas of electrons, ions, and neutral particles. In many cases the dynamics of this plasma is described to a good approximation by the equations of compressible hydrodynamics, magneto-hydrodynamics (in the case that magnetic fields are present), or radiation MHD (in the case that photons provide significant energy or momentum transport). Studying multidimensional, time-dependent and/or highly nonlinear processes in astrophysical plasmas usually requires numerical methods, however developing accurate and robust methods for compressible MHD and/or radiation MHD is still an active area of research in applied mathematics. I will describe some problems in astrophysics which motivate the development of such methods, describe recent advance in numerical algorithms for MHD and their implementation on parallel processors, and describe some of what we have learned from application of the methods. |
| Joint Princeton University and Institute for Advanced Study Number Theory Seminar | |
| Topic: | TBA |
| Presenter: | Laurent Berger, IHES |
| Date: | Monday, November 15, 2004, Time: 4:30 p.m., Location: Fine Hall 322 |
| Algebraic Geometry Seminar | |
| Topic: | Doing the twist with stable varieties |
| Presenter: | Dan Abramovich, Brown University |
| Date: | Tuesday, November 16, 2004, Time: 4:30 p.m., Location: Fine Hall 322 |
| Geometry, Representation Theory, and Moduli Seminar | |
| Topic: | TBA |
| Presenter: | Dmitri Orlov, Institute for Advanced Study |
| Date: | Wednesday, November 17, 2004, Time: 3:00 p.m., Location: Fine Hall 214 |
| Geometric Analysis Seminar *** Please note change in time | |
| Topic: | On the Genus-One Gromov-Witten Invariants of Complete Intersection Threefolds |
| Presenter: | Aleksey Zinger, Stanford University |
| Date: | Friday, November 19, 2004, Time: 4:00 p.m., Location: Fine Hall 314 |
| Abstract: | I will describe a formula relating the genus-one Gromov-Witten invariants of a projective complete intersection threefold to the GW-invariants of the ambient projective space. Along with a separate desingularization result, this formula allows one to compute the genus-one GW-invariants of such threefolds. It might be possible to use this formula to verify the genus-one mirror symmetry prediction for curves in Calabi-Yau threefolds |
NOVEMBER 22 - 24, 2004 |
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| PACM Seminar | |
| Topic: | Qualitative/Quantitative Analysis of a Class of Biological Networks |
| Presenter: | Eduardo Sontag, Department of Math and BioMaPS Institute for Quantitative Biology, Rutgers University |
| Date: | Monday, November 22, 2004, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: | The analysis of signaling networks constitutes one of the central questions in systems biology: there is an pressing need for powerful mathematical tools to help understand, quantify, and conceptualize their information processing and dynamic properties. Approaches based upon detailed modeling and simulation are hampered by the fact that is virtually impossible to experimentally validate the form of the nonlinearities used in reaction terms, or, even when such forms are known, to accurately estimate coefficients (parameters). In this presentation, we show how some signaling systems may be profitably studied by first decomposing them into several subsystems, each of which is endowed with certain "qualitative" mathematical properties. These properties, in conjunction with a relatively small amount of "quantitative" data, allow the behavior of the entire, reconstituted system, to be deduced from the behavior of its parts. This novel approach emerged originally from our study of possible multi-stability or oscillations in feedback loops in cell signal transduction modeling, but turns out to be of more general applicability. (Most of the work reported in this talk was carried out in collaboration with D. Angeli, and parts of it with J. Ferrell, G. Enciso, and P. de Leenheer.) |
| Algebraic Geometry Seminar | |
| Topic: | Triangulated categories of singularities and D-branes in Landau-Ginzburg models |
| Presenter: | Dmitri Orlov, Institute for Advanced Study |
| Date: | Tuesday, November 23, 2004, Time: 4:30 p.m., Location: Fine Hall 322 |
| Abstract: | The purpose of my talk is to introduce triangulated categories related to singularities of algebraic varieties and to establish a connection of these categories with categories of D-branes in Landau-Ginzburg models. |
| Statistical Mechanics Seminar | |
| Topic: | Linear response far from equilibrium |
| Presenter: | David Ruelle, IHES |
| Date: | Wednesday, November 24, 2004, Time: 2:00 p.m., Location: Jadwin 343 |
NOVEMBER 29 - DECEMBER 3, 2004 |
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| PACM Seminar | |
| Topic: | Frames and the Fundamental Inequality |
| Presenter: | Jelena Kovacevic, Center for BioImage Informatics, Carnegie Mellon University |
| Date: | Monday, November 29, 2004, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: | In recent years, we have seen an explosion of work on frames, in particular finite frames. We find finite tight frames when the lengths of the frame elements are predetermined. In particular, we derive a ``fundamental inequality" which completely characterizes those sequences which arise as the lengths of a tight frame's elements. Furthermore, using concepts from classical physics, we show that this characterization has an intuitive physical interpretation. At the end of the talk, we also examine some recent applications of frames. |
| Joint Princeton University and Institute for Advanced Study Number Theory Seminar | |
| Topic: | Generic transfer to non-self dual automorphic representations of GL(N) |
| Presenter: | Mahdi Asgari, IAS |
| Date: | Monday, November 29, 2004, Time: 4:30 p.m., Location: Fine Hall 322 |
| Department Colloquium | |
| Topic: | Quantum and Classical Network Model |
| Presenter: | John Cardy, Oxford University and the Institute for Advanced Study |
| Date: | Wednesday, December 1, 2004, Time: 4:30 p.m., Location: Fine Hall 314 |
DECEMBER 6 - 10, 2004 |
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| PACM Seminar | |
| Topic: | Reduced Scaling Methods for Quantum Electronic Structure |
| Presenter: | Emily Carter, PACM and Mechanical & Aerospace Engineering, Princeton University |
| Date: | Monday, December 6, 2004, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: | The problem of solving the Schroedinger equation in quantum mechanics, in order to describe the behavior of N electrons, is in principle an N! hard problem in an infinite basis. This is due to the need to describe the correlated motion of electrons. Some typical approaches to solving this 3N-dimensional PDE will be introduced, including mean-field and many-body methods. An analysis of their scaling properties will be given. My research group's particular strategies for reducing the prohibitive scaling of these methods while retaining accuracy of the solution will be presented. These schemes are based on simple physical and mathematical principles, for both molecular quantum chemistry and for condensed matter electronic structure. We will end with an outlook of the applied mathematical research challenges that remain for describing large numbers (e.g., thousands) of atoms with quantum mechanics. When these challenges are overcome, we will be able to predict the behavior of complicated molecules and materials with unprecedented fidelity. |