OCTOBER 13 - 15, 2004 |
|
| Statistical Mechanics Seminar | |
| Topic: | Divergent series methods from quantum fields applied to classical mechanics |
| Presenter: | G. Gallavotti, University of Rome and Rutgers University |
| Date: | Wednesday, October 13, 2004, Time: 2:00 p.m., Location: Jadwin 343 |
| Abstract: | In classical mechanics quasi periodic solutions can be described by suitable series (Lindstedt series) whose coefficients can be constructed via simple "Feynman rules". In such cases it is possible to identify and sum classes of diagrams giving rise to geometric series. For quasi periodic motions with maximal number of independent frequencies the resummations can be shown to be actually convergent (having ratio $|z|<1$: a nontrivial fact leading to a proof of the KAM theorem). If, however, the number of frequencies is smaller than maximal (physically if the motion is "resonant") then the series involved in the resummations are also actually divergent: nevertheless in this case one can impose the natural (and common) sum rule which sets the sum equal to $1/(1-z)$ and then prove that the resulting series of "renormalized graph values" is "often" a convergent series representation of the resonant motions. |
| Discrete Mathematics Seminar | |
| Topic: | Almost optimum universal graphs for bounded-degree graphs |
| Presenter: | Michael Capalbo, DIMACS |
| Date: | Wednesday, October 13, 2004, Time: 2:30 p.m., Location: Fine Hall 224 |
| Abstract: | Click here |
| Geometry, Representation Theory, and Moduli Seminar | |
| Topic: | Generalized double affine Hecke algebras and quantized del Pezzo surfaces |
| Presenter: | Pavel Etingof, MIT |
| Date: | Wednesday, October 13, 2004, Time: 3:00 p.m., Location: Fine Hall 214 |
| Abstract: | Let D be a simply laced Dynkin diagram of rank r whose affinization has the shape of a star (i.e., D4,E6,E7,E8). To such a diagram one can attach a group $G$ whose generators correspond to the legs of the affinization, have orders equal to the leg lengths plus 1, and the product of the generators is 1. The group G is then a 2-dimensional crystallographic group: $G=Z_l\ltimes Z2$, where $l$ is 2,3,4, and 6, respectively. I will define a flat deformation $H(t,q)$ of the group algebra $\bold C[G]$ of this group, by replacing the relations saying that the generators have prescribed orders by their deformations, saying that the generators satisfy monic polynomial equations of these orders with arbitrary roots (which are deformation parameters). The algebra $H(t,q)$ for D4 is the Cherednik algebra of type $C^\vee C_1$, which was studied by Noumi, Sahi, and Stokman, and controls Askey-Wilson polynomials. I'll explain that the algebra $H(t,q)$ is the universal deformation of the twisted group algebra of $G$, and this deformation is compatible with certain filtrations on $\Bbb C[G]$. I will also explain that if $q$ is a root of unity, then for generic $t$ the algebra $H(t,q)$ is an Azumaya algebra, and its center is the function algebra on an affine del Pezzo surface. For generic q, the spherical subalgebra $eH(t,q)e$ provides a quantization of such surfaces. Finally, I'll discuss connections of H(t,q) with preprojective algebras and equation "Painlev\'e VI". This is joint work with Alex Oblomkov and Eric Rains. |
| Department Colloquium | |
| Topic: | Crisis in Applied Mathematics |
| Presenter: | Wienen E, Princeton University |
| Date: | Wednesday, October 13, 2004, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: | For more than fifty years, applied mathematics has enjoyed tremendous success in many areas of physical science and engineering, most notably fluid mechanics and structural mechanics, in which macroscopic models in the form of PDEs play the major role. In contrast, it has paid relatively little attention to areas such as computational chemistry and molecular biology where the models tend to be more discrete and the physics tends to be more microscopic. In recent years, it has become increasingly clear that this lack of involvement in discrete models and microscopic physics is becoming a major obstacle to the further development of applied math. The recent explosive growth of interest on multiscale, multi-physics modeling from other scientific disciplines has made this a rather urgent issue to be dealt with. In this talk we will analyze the background ofthis problem and discuss possible solutions, particularly in the form of a new curriculum. We will also discuss the new challenges that will arise in mathematics from this change of style in applied math. |
| Ergodic Theory and Statistical Mechanics Seminar | |
| Topic: | The proof by Avila and Forni of almost sure weak mixing for interval exchange transformations |
| Presenter: | Corinna Ulcigrai and Alexander Bufetov, Princeton University |
| Date: | Thursday, October 14, 2004, Time: 2:00 p.m., Location: Fine Hall 322 |
| Abstract: | In 1965 Katok and Stepin proved that almost all exchanges of three intervals are weakly mixing. In 1980 Katok proved that no interval exchange transformations are mixing. In 1983 Veech proved almost sure weak mixing for interval exchanges under additional combinatorial assumptions on the permutation. In 2004 Avila and Forni proved almost sure weak mixing for all interval exchanges. The proof proceeds by a characterization of the weak stable mainfold of the renormalization cocycle. In the talk, we shall explain the main ideas of the proof of Avila and Forni. |
| Topology Seminar | |
| Topic: | Counting simple closed geodesics on hyperbolic surfaces and McShane identities |
| Presenter: | Maryam Mirzakhani, Princeton University |
| Date: | Thursday, October 14, 2004, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: | In this talk we show that the number of simple closed geodesics of length at most L on a hyperbolic surface X of genus g has the asymptotic behavior 6g-6 s (L) ~ n L X X we will also discuss the problem of the frequencies of different types of simple closed geodesics on hyperbolic surfaces and show that relative frequencies are universal rational numbers independent of X. |
| Geometric Analysis Seminar *** Please note special time | |
| Topic: | Resolvent and scattering theory on asymptotically hyperbolic manifolds |
| Presenter: | Colin Guillarmou, Purdue University |
| Date: | Friday, October 15, 2004, Time: 3:00 p.m., Location: Fine Hall 314 |
| Abstract: | We will review scattering theory on a class of complete manifolds with asymptotically negative constant curvatures. We will give a sufficient and necessary condition on the metric to obtain a meromorphic extension of the resolvent for the Laplacian to the complex plane and will see that essential singularities can appear without this condition. Finally we will explain the relations between scattering poles and resonances, with applications to asymptotically Einstein manifolds and convex co-compact hyperbolic manifolds. |
| Geometric Analysis Seminar *** Please note change in time | |
| Topic: | Estimates and surgery for necks in mean curvature flow |
| Presenter: | Gerhard Huisken, Max-Planck Institut fur Gravitationsphysik, Potsdam |
| Date: | Friday, October 15, 2004, Time: 4:00 p.m., Location: Fine Hall 314 |
OCTOBER 18 - 22, 2004 |
|
| Analysis Seminar | |
| Topic: | Microlocal dispersive smoothing for the nonlinear Schrödinger equation |
| Presenter: | Jeremie Szeftel, Princeton University |
| Date: | Monday, October 18, 2004, Time: 3:00 p.m., Location: Fine Hall 314 |
| Abstract: | We prove a dispersive smoothing result for the nonlinear Schrödinger equation. We deal with the linear term by using the method of W. Craig, T. Kappeler and W. Strauss. Then, we deal with the nonlinear term using J. M. Bony's Theorem and an interpolation result between weighted L^2 spaces and Sobolev spaces. |
| PACM Seminar | |
| Topic: | PlanetLab: A Platform for Introducing Disruptive Technology into the Internet |
| Presenter: | Larry Peterson, Department of Computer Science, Princeton University |
| Date: | Monday, October 18, 2004, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: | PlanetLab is a geographically distributed overlay network designed to support the deployment and evaluation of planetary-scale network services. Two high-level goals shape its design. First, to enable a large research community to share the infrastructure, PlanetLab provides {\it distributed virtualization}, whereby each service runs in an isolated slice of PlanetLab's global resources. Second, to support competition among multiple network services, PlanetLab decouples the operating system running on each node from the network-wide services that define PlanetLab, a principle referred to as {\it unbundled management}. This talk describes how PlanetLab realizes these two goals, and highlights several novel network services running on PlanetLab. |
| Joint Princeton University and Institute for Advanced Study Number Theory Seminar | |
| Topic: | Prime Numbers and Divisor Functions |
| Presenter: | John Friedlander, University of Toronto |
| Date: | Monday, October 18, 2004, Time: 4:30 p.m., Location: Fine Hall 322 |
| SPECIAL Ergodic Theory Seminar | |
| Topic: | Entropy determined dynamics or great chaos are simple |
| Presenter: | Jérôme Buzzi, CNRS Paris |
| Date: | Tuesday, October 19, 2004, Time: 2:30 p.m., Location: Fine Hall 322 |
| Abstract: | We consider dynamical systems defined by smooth maps with "large entropy", ie, larger than their 'codimension one entropy' and shall prove that wrt their invariant measures of large entropy they are completely classified by their topological entropy in the mixing case. This follows from identification with 'combinatorial' dynamical systems like countable state Markov shifts and Yoccoz puzzles. The underlying structure theorem also gives information about measures of maximum entropy, periodic orbits and a zeta function. This applies to an open class of dynamical systems containing, eg, perturbations of expanding toral automorphisms and, more interestingly, maps with large critical sets and multi-dimensional non-uniform expansion like the weak couplings of interval maps with positive entropy like (x,y)-->(1.8-x**2+eps sin(2pi y),1.5-y**2+eps sin(2pi x)) which do not seem tractable by other methods. This approach involves basic topology, counting arguments and semi-algebraic approximations of smooth maps a la Yomdin-Gromov. |
| Algebraic Geometry Seminar | |
| Topic: | On some invariants of singularities. |
| Presenter: | Mircea Mustata, University of Michigan, Ann Arbor |
| Date: | Tuesday, October 19, 2004, Time: 4:30 p.m., Location: Fine Hall 322 |
| Abstract: | I will talk about some very elementary invariants of singularities in positive characteristic. There are interesting questions about the connection between certain invariants in characteristic zero (like the log canonical threshold or the roots of the Bernstein-Sato polynomial) and the characteristic p invariants obtained for different reductions mod p. For the moment the picture is just conjectural, but I will discuss some examples supporting the conjectures. This is joint work with Shunsuke Takagi and Kei-ichi Watanabe. |
| 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: | TBA |
| Presenter: | Alexandre Kirillov, University of Pennsylvania |
| Date: | Wednesday, October 20, 2004, Time: 4:30 p.m., Location: Fine Hall 314 |
| 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. |
| 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 |
|
NOVEMBER 1 - 5, 2004 |
|
| 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. |
| 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 |
NOVEMBER 8 - 12, 2004 |
|
| Analysis Seminar | |
| Topic: | TBA |
| Presenter: | Nikolaos Tzirakis, IAS and University of Toronto |
| Date: | Monday, November 8, 2004, Time: 3:00 p.m., Location: Fine Hall 314 |
| 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. |
| 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 |
|
| 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. |
| 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 |
|
| 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 |
| Department Colloquium | |
| Topic: | TBA |
| Presenter: | John Cardy, Oxford University and the Institute for Advanced Study |
| Date: | Wednesday, November 24, 2004, Time: 4:30 p.m., Location: Fine Hall 314 |
NOVEMBER 29 - DECEMBER 3, 2004 |
|
| 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. |
DECEMBER 6 - 10, 2004 |
|
| 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. |