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FEBRUARY 4 - 6, 2004 |
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| Graduate Student Seminar *** Please note change in time from last semester | |
| Topic: | Pseudoholomorphic Curves and Periodic Orbits in Hamiltonian Dynamics |
| Presenter: | Jake Solomon, MIT |
| Date: | Wednesday, February 4, 2004, Time: 11:00 a.m., Location: Fine Hall 314 |
| Abstract: | Gromov's discovery of the theory of pseudo-holomorphic curves in symplectic manifolds, combining techniques of elliptic PDE with intuition from complex algebraic geometry, has led to many striking results in classical mechanics. In this talk, I will define symplectic and contact manifolds as a vehicle for abstracting classical Hamiltonian mechanics and properly formulating Weinstein's conjecture about existence of periodic orbits in fixed energy hypersurfaces. Then, I hope to explain intuitively how one can apply pseudo-holomorphic curves to prove certain instances of Weinstein's conjecture. |
| Department Colloquium | |
| Topic: | (n,d,lambda)-graphs in Extremal Combinatorics |
| Presenter: | Noga Alon, Tel Aviv University and the Institute for Advanced Study |
| Date: | Wednesday, February 4, 2004, Time: 4:30 p.m., Location: Fine Hall 314 |
| Abstract: | An (n,d,lambda)-graph is a d-regular graph on n vertices so that the absolute value of each eigenvalue of its adjacency matrix, besides the largest one, is at most lambda. I will survey some of the remarkable pseudo-random properties of such graphs in which lambda is much smaller than d, describe various constructions, and present several applications of these graphs in the solution of problems in Extremal Combinatorics. |
| Geometric Analysis Seminar | |
| Topic: | Conformally compact Einstein manifolds and conformal invariants |
| Presenter: | Jie Qing, Princeton University |
| Date: | Friday, February 6, 2004, Time: 3:00 p.m., Location: Fine Hall 314 |
FEBRUARY 9 - 13, 2004 |
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| PACM Colloquium | |
| Topic: | Numerical methods for multiscale kinetic problems |
| Presenter: | Shi Jin, University of Wisconsin |
| Date: | Monday, February 9, 2004, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: | I will review several recent methods for kinetic problems where the mean free path has different orders of magnitude. In particular, I will present
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| Algebraic Geometry Seminar | |
| Topic: | Asymptotic intersection numbers and restricted volumes |
| Presenter: | Mihnea Popa, Harvard University |
| Date: | Tuesday, February 10, 2004, Time: 4:30 p.m., Location: Fine Hall 322 |
| Abstract: | I will describe work (partly in progress) on defining asymptotic intersection numbers of big (or pseudoeffective) line bundles on smooth projective varieties. Intuition is provided by intersecting with the positive part of a Zariski decomposition in case it exists. The technical tool is a notion of volume for restrictions of linear series. One shows that the asymptotic intersection numbers and the restricted volumes define continuous functions on the big cone of the ambient variety, and obtain an interesting decomposition of this cone given by their zero-locus. This is joint work with Ein, Lazarsfeld, Mustata and Nakamaye. |
| Mathematical Physics Seminar | |
| Topic: | Flow-line geometries and Gaussian loop ensembles |
| Presenter: | Scott Sheffield, Microsoft Research |
| Date: | Tuesday, February 10, 2004, Time: 4:30 p.m., Location: Jadwin A06 |
| Abstract: | Given a real function h on the complex plane, consider the flow lines of a complex vector field of the form e^{i(h+c)}, with c in [0, 2pi). If h is constant, these paths are the straight lines of Euclidean geometry. If h is harmonic, they are the image of Euclidean lines under a conformal map. If h is a well-behaved function with non-zero Laplacian, the flow lines are the rays of a sort of "twisted geometry" that is still reasonably tame (parallel lines do not intersect, non-parallel lines intersect at most once, triangle angles sum to 180 degrees, etc.) If, however, h is a constant C times the Gaussian free field the story is very different. Rays circle and "bounce off" themselves, 'parallel rays' converge, and non-parallel rays have multiple intersections. Individual rays look locally like Schramm-Loewner evolution with a parameter kappa that depends on C. In fact, the rays determine the boundaries of the Gaussian loop ensembles, GLE_{kappa}, which we conjecture to be the scaling limits of the O(n) loop models and other two-dimensional loop ensembles from statistical physics. |
| Discrete Mathematics Seminar | |
| Topic: | Equidistant sets under the 1-norm |
| Presenter: | Noga Alon, Tel Aviv University and the Institute for Advanced Study |
| Date: | Wednesday, February 11, 2004, Time: 2:30 p.m., Location: Fine Hall 224 |
| Abstract: | See http://www.math.princeton.edu/~bsudakov/noga2004.ps |
| Geometry, Representation, and Moduli Seminar | |
| Topic: | TBA |
| Presenter: | Ezra Getzler, Northwestern University |
| Date: | Wednesday, February 11, 2004, Time: 3:00 p.m., Location: Fine Hall 214 |
| Ergodic Theory and Statistical Mechanics Seminar | |
| Topic: | Cluster swapping and domino tilings |
| Presenter: | Scott Sheffield, Microsoft Research |
| Date: | Thursday, February 12, 2004, Time: 2:00 p.m., Location: Fine Hall 322 |
| Abstract: | We classify the ergodic Gibbs measures on the space of domino tilings of the plane. These measures are indexed by the asymptotic slopes of the corresponding height functions. Our proof uses a technique called "cluster swapping" which generalizes to other random surface models (e.g., square ice, anharmonic crystals, linear solid-on-solid models). |
| Joint Columbia University/Courant Institute/Princeton University Differential Geometry Seminar | |
| Topic: | TBA |
| Presenter: | Tom Ilmanen, ETH |
| Date: | Friday, February 13, 2004, Time: 2:00 p.m., Location: Fine Hall 314 |
| Joint Columbia University/Courant Institute/Princeton University Differential Geometry Seminar | |
| Topic: | Gauge Theory Scattering And Twistor Space |
| Presenter: | Edward Witten, Institute for Advanced Study |
| Date: | Friday, February 13, 2004, Time: 3:30 p.m., Location: Fine Hall 314 |
FEBRUARY 16 - 20, 2004 |
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| PACM Colloquium | |
| Topic: | Design of Semiconductor and Nano Devices |
| Presenter: | Martin Burger, University of California, Los Angeles and Johannes Kepler University |
| Date: | Monday, February 16, 2004, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: | The subject of this talk is the solution of mathematical problems related to the design of classical semiconductor and novel nano-scale devices. For the first class, we present optimization problems related to the drift-diffusion model, whose solution allows to improve the characteristics of currently produced devices. In particular, we discuss a novel design approach recently introduced in collaboration with Rene Pinnau (TU Darmstadt), which allows to optimize a device with a computational effort compareable to three direct simulations. For nano-scale devices, which are still in a pre-technological phase, we discuss some mathematical models of self-organized growth by elastic relaxation and surface diffusion, and their numerical solution, which might be used for design tasks in the future. |
| Algebraic Geometry Seminar | |
| Topic: | K3 sections and the effective cone of the moduli space of curves |
| Presenter: | Gavril Farkas, Princeton University |
| Date: | Tuesday, February 17, 2004, Time: 4:30 p.m., Location: Fine Hall 322 |
| Mathematical Physics Seminar | |
| Topic: | Localization lengths and Boltzmann limit for the Anderson model in dimension 3 |
| Presenter: | Thomas Chen, Courant Institute |
| Date: | Tuesday, February 17, 2004, Time: 4:30 p.m., Location: Jadwin A06 |
| Abstract: | We prove lower bounds on the localization length of eigenfunctions in the three-dimensional Anderson model at weak disorders, which are similar to those obtained by Shubin, Schlag and Wolff for dimensions one and two. In addition, we show that the macroscopic limit of the corresponding lattice random Schr\"odinger dynamics is governed by the linear Boltzmann equations. The proof comprises an extension of methods due to Erdoes and Yau. |
| Discrete Mathematics Seminar | |
| Topic: | A topological colorful Helly theorem |
| Presenter: | Roy Meshalum, Technion |
| Date: | Wednesday, February 18, 2004, Time: 2:30 p.m., Location: Fine Hall 224 |
| Abstract: | See http://www.math.princeton.edu/~bsudakov/meshulam2004.ps |
| Geometry, Representation, and Moduli Seminar | |
| Topic: | TBA |
| Presenter: | Paul Horja, University of Michigan |
| Date: | Wednesday, February 18, 2004, Time: 3:00 p.m., Location: Fine Hall 214 |
| Ergodic Theory and Statistical Mechanics Seminar | |
| Topic: | On the Ergodicity of the 2-D Dissipative Boussinesq system |
| Presenter: | Jinhoo Lee , PACM, Princeton University |
| Date: | Thursday, February 19, 2004, Time: 2:00 p.m., Location: Fine Hall 322 |
| Abstract: | We study the stationary measure for the 2-D dissipative Boussinesq system with random forcing. We follow the strategy of E-Mattingly-Sinai's paper for the 2-D Navier-Stokes equations (Comm. Math. Phys. vol.224(2001) pp. 83--106). |
| Joint Analysis Seminar *** Please note change in room from last semester | |
| Topic: | On the interaction of nearly parallel vortex filaments |
| Presenter: | Gustavo Ponce, UC Santa Barbara |
| Date: | Thursday, February 19, 2004, Time: 3:30 p.m., Location: Fine Hall 214 |
| Topology Seminar | |
| Topic: | Bounded cohomology and hyperbolic groups |
| Presenter: | Igor Mineyev, University of Illinois, Urbana and the Institute for Advanced Study |
| Date: | Thursday, February 19, 2004, Time: 4:00 p.m., Location: Fine Hall 314 |
| Abstract: | Gromov hyperbolic groups generalize fundamental groups of closed negatively curved manifolds. Bounded cohomology, due to B. E. Johnson, is defined as the usual (singular or bar-construction) cohomology with the additional boundedness assumption on cochains. I will remind both definitions and will discuss the construction of homological bicombings on hyperbolic graphs. |
FEBRUARY 23 - 27, 2004 |
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| PACM Colloquium | |
| Topic: | Testable New Theory about Early-Universe Density Fluctuations and Origins of Cosmic Structure, with Focus on Mathematical-Probability and Computational Aspects |
| Presenter: | Erik H. VanMarcke, Civil and Environmental Engineering, Princeton University |
| Date: | Monday, February 23, 2004, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: | The talk will summarize the main findings, predictions and interdisciplinary research opportunities stemming from a new probabilistic model of how complex patterns of extreme density fluctuations may have emerged from the inflation phase of the Big Bang. Based on quantum-physical principles and requiring a minimum number of (observationally-accessible) parameters, the "embryonic inflation model" yields a coherent set of testable hypotheses about the formation, evolution and composition of galaxies, stars and planets. Implying a robust (and testable, hence falsifiable) alternative to the dual paradigm of spatially-uniform light-element primordial nucleosynthesis and stellar "recycling" of matter as the sole mechanism of heavy-element production, it integrates astrophysical and planetary sciences with cosmology and galaxy formation in a coherent evolutionary framework. Overall cosmic flatness, an accelerating component, dark matter and dark energy all fit, in quantifiable and testable ways, into the framework of the theory. (Prof. VanMarcke's book on the subject, Quantum Origins of Cosmic Structure, was published in Nov. 1997, before the observation-based discovery of the "accelerating universe", which fits the theory.) |
| Mathematical Physics Seminar | |
| Topic: | Coherency effects in the multiple scattering of photons by cold atoms |
| Presenter: | Eric Akkerman, Technion |
| Date: | Tuesday, February 24, 2004, Time: 4:30 p.m., Location: Jadwin A06 |
| Discrete Mathematics Seminar | |
| Topic: | TBA |
| Presenter: | Jozsef Beck, Rutgers University |
| Date: | Wednesday, February 25, 2004, Time: 2:30 p.m., Location: Fine Hall 224 |
| Geometry, Representation, and Moduli Seminar | |
| Topic: | TBA |
| Presenter: | Paul Seidel, University of Chicago |
| Date: | Wednesday, February 25, 2004, Time: 3:00 p.m., Location: Fine Hall 214 |
| Department Colloquium | |
| Topic: | Seiberg-Witten theory and random partitions |
| Presenter: | Nikita Nekrasov, IHES |
| Date: | Wednesday, February 25, 2004, Time: 4:30 p.m., Location: Fine Hall 314 |
MARCH 1-5, 2004 |
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| Algebraic Geometry Seminar | |
| Topic: | TBA |
| Presenter: | Jim Bryan, University of British Columbia |
| Date: | Tuesday, March 2, 2004, Time: 4:30 p.m., Location: Fine Hall 322 |
| Mathematical Physics Seminar | |
| Topic: | Conformal restriction properties |
| Presenter: | Wendelin Werner, Universite Paris Sud, Orsay |
| Date: | Tuesday, March 2, 2004, Time: 4:30 p.m., Location: Jadwin A06 |
| Abstract: | This talk is based on joint work with Greg Lawler, Oded Schramm, and Roland Friedrich. We will describe the so-called restriction properties and give various equivalent descriptions of the various random sets that do satisfy this property. We will then outline how they are related to the (conjectural) scaling limit of simple two dimensional models, to representation theory and to some aspects of conformal field theory. |
| Discrete Mathematics Seminar | |
| Topic: | The intersection of a matroid and a simplicial complex |
| Presenter: | Eli Berger , Princeton University |
| Date: | Wednesday, March 3, 2004, Time: 2:30 p.m., Location: Fine Hall 224 |
| Abstract: | See http://www.math.princeton.edu/~bsudakov/berger2004.ps |
| Geometry, Representation, and Moduli Seminar | |
| Topic: | TBA |
| Presenter: | Christopher Woodward, Rutgers University |
| Date: | Wednesday, March 3,2004, Time: 3:00 p.m., Location: Fine Hall 214 |
| Department Colloquium | |
| Topic: | Critical phenomena in two dimensions, conformal invariance and Schramm-Loewner Evolutions |
| Presenter: | Wendelin Werner, Universite Paris Sud, Orsay |
| Date: | Wednesday, March 3, 2004, Time: 4:30 p.m., Location: Fine Hall 314 |
| Ergodic Theory and Statistical Mechanics Seminar | |
| Topic: | Reinforced Random Walk |
| Presenter: | Michael Keene, Wesleyan University |
| Date: | Thursday, March 4, 2004, Time: 2:00 p.m., Location: Fine Hall 322 |
| Abstract: | One of the distinguishing properties of the present scientific method is reproducibility. |
| Joint Analysis Seminar | |
| Topic: | TBA |
| Presenter: | Tristan Riviere, ETH |
| Date: | Thursday, March 4, 2004, Time: 3:30 p.m., Location: Fine Hall 214 |
| Joint Analysis Seminar *** Please note special time | |
| Topic: | Brownian loop soups and conformal field theory |
| Presenter: | Wendelin Werner, Universite Paris Sud, Orsay |
| Date: | Thursday, March 4, 2004, Time: 4:45 p.m., Location: Fine Hall 214 |
MARCH 8-12, 2004 |
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| PACM Colloquium - Distinguished Lecture Series *** Please note special time and location | |
| Topic: | Time reversal, imaging and communications in richly scattering environments |
| Presenter: | George Papanicolaou, Department of Mathematics, Stanford University |
| Date: | Monday, March 8, 2004, Time: 8:00 p.m., Location: A02 McDonnell Hall |
| Abstract: | Signals received by an array, time reversed and re-emitted into the environment will pack-propagate to the vicinity of the sources that produced them. It is remarkable that the focusing resolution in time reversal is much better in a strongly scattering medium than in a homogeneous one, assuming dissipation is negligible. This interesting phenomenon has many surprising applications in imaging and communications through clutter. I will describe time reversal and its properties, explain mathematically how super-resolution occurs in random media and introduce some imaging methods that deal effectively with clutter. I will also describe how time reversal can be used in communications. |
| Algebraic Geometry Seminar | |
| Topic: | TBA |
| Presenter: | Fabrizio Catanese, Bayreuth |
| Date: | Tuesday, March 9, 2004, Time: 4:30 p.m., Location: Fine Hall 322 |
| Department Colloquium | |
| Topic: | TBA |
| Presenter: | Charlie Fefferman, Princeton University and the Courant Institute |
| Date: | Wednesday, March 10, 2004, Time: 4:30 p.m., Location: Fine Hall 314 |
| Joint Analysis Seminar *** Please note change in room from last semester | |
| Topic: | Solving free boundary problems by variational and maximum principle methods |
| Presenter: | David Jerison, MIT |
| Date: | Thursday, March 11, 2004, Time: 3:30 p.m., Location: Fine Hall 214 |
SPRING BREAK MARCH 13 - 21, 2004 |
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MARCH 22 - 26, 2004 |
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| PACM Colloquium | |
| Topic: | TBA |
| Presenter: | James Collins, Boston University |
| Date: | Monday, March 22, 2004, Time: 4:00 p.m., Location: Fine Hall 214 |
| Algebraic Geometry Seminar | |
| Topic: | TBA |
| Presenter: | Steven Sperber, University of Minnesota and Princeton University |
| Date: | Tuesday, March 23, 2004, Time: 4:30 p.m., Location: Fine Hall 322 |
| Mathematical Physics Seminar | |
| Topic: | Dynamics of magnetic Bloch electrons |
| Presenter: | Herbert Spohn, Zentrum Mathematik and Physics Department, Technical University, Munich |
| Date: | Tuesday, March 23, 2004, Time: 4:30 p.m., Location: Jadwin A06 |
| Abstract: | As a standard model of solid state physics we consider independent electrons subject to a periodic lattice potential and a strong uniform magnetic field with rational flux per unit cell. We then explain the first order corrections to the effective Hamiltonian from the Peierls substitution. |
| Geometry, Representation, and Moduli Seminar | |
| Topic: | TBA |
| Presenter: | Michael Shapiro, Michigan State University |
| Date: | Wednesday, March 24,2004, Time: 3:00 p.m., Location: Fine Hall 214 |
MARCH 29 - APRIL 2, 2004 |
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| PACM Colloquium | |
| Topic: | Upper bounds on coarsening rates |
| Presenter: | Robert Kohn, Courant Institute of Mathematics, New York University |
| Date: | Monday, March 29, 2004, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: | I will discuss surface-energy-driven coarsening of two-phase microstructures. Such coarsening is observed in many physical systems; two basic examples are motion by surface diffusion and Mullins-Sekerka (evaporation-condensation) dynamics. Experiments and simulations suggest that solutions are in some sense statistically self-similar. There is, however, virtually nothing known with mathematical rigor. I will briefly introduce this topic, then present recent joint work with Felix Otto (Comm. Math. Phys. 2002). Our main accomplishment is an upper bound on the coarsening rate, consistent with the conjectured self-similar behavior. Our work is also interesting for its viewpoint, which is new and potentially applicable to many other problems. I will close with one such application, to epitaxial growth -- joint work with Xiaodong Yan (Comm. Pure Appl. Math. 2003). |
| Algebraic Geometry Seminar | |
| Topic: | TBA |
| Presenter: | Jun-Muk Hwang, KIAS and Harvard University |
| Date: | Tuesday, March 30, 2004, Time: 4:30 p.m., Location: Fine Hall 322 |
| Mathematical Physics Seminar | |
| Topic: | TBA |
| Presenter: | H. Tasaki, Gakushuin University |
| Date: | Tuesday, March 30, 2004, Time: 4:30 p.m., Location: Jadwin A06 |
| Geometry, Representation, and Moduli Seminar | |
| Topic: | TBA |
| Presenter: | C. C. Liu, Harvard University |
| Date: | Wednesday, March 31,2004, Time: 3:00 p.m., Location: Fine Hall 214 |
| Department Colloquium | |
| Topic: | TBA |
| Presenter: | Maciej Zworski, University of California, Berkeley |
| Date: | Wednesday, March 31, 2004, Time: 4:30 p.m., Location: Fine Hall 314 |
APRIL 5- APRIL 9, 2004 |
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| PACM Colloquium | |
| Topic: | TBA |
| Presenter: | Fernando Reitich, University of Minnesota |
| Date: | Monday, April 5, 2004, Time: 4:00 p.m., Location: Fine Hall 214 |
| Algebraic Geometry Seminar | |
| Topic: | TBA |
| Presenter: | Olivier Debarre, Strasbourg |
| Date: | Tuesday, April 6, 2004, Time: 4:30 p.m., Location: Fine Hall 322 |
APRIL 12- APRIL 18, 2004 |
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| PACM Colloquium | |
| Topic: | Vorticity and Wave Confinement A Rotationally Invariant Limiter Approach to Modeling Small Scales |
| Presenter: | John Steinhoff, University of Tennessee Space Institute |
| Date: | Monday, April 12, 2004, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: | A new computational method, Vorticity/Wave Confinement, (V/WC), is described. V/WC has been shown to efficiently treat thin features in complex fluid flow and time domain wave equation problems involving vortices and acoustic pulses. The method allows them to be propagated over arbitrarily long distances with no spreading due to numerical errors. It has also been shown to be effective in representing boundary layers on surfaces as thin vortical layers “immersed” in uniform Cartesian grids. We define these thin vortical or wave regions as “features.” Outside these features, where the flow is irrotational or the wave amplitude vanishes, the method automatically reduces to a conventional finite difference approximation to the correct continuum partial differential equation (pde). The features are treated as a type of weak solution and, within the features, a nonlinear difference equation, as opposed to finite difference approximation, is solved that does not necessarily represent a Taylor expansion discretization of a simple pde. The approach is similar to artificial compression and shock capturing schemes, where conservation laws are satisfied across discontinuities. For propagating features, the result of this conservation is that integral quantities such as total momentum and amplitude, and centroid motion are accurately computed. Effectively, the features are treated as multi-dimensional nonlinear discrete solitary waves that “live” on the computational lattice. These obey a “confinement” relation that is a generalization to multiple dimensions of 1-D discontinuity capturing schemes. A major point is that the method involves a rotationally invariant limiter – a single limiter that is a function of rotationally invariant variables. This is in contrast to conventional discontinuity capturing schemes which may involve a concatenation of separate 1-D limiters, each a function of variables along each axis. Results will be shown for convection of thin convecting vortex filaments, flow over complex surfaces “immersed” in uniform grids, and thin acoustic pulses scattering from complex surfaces. |
| Algebraic Geometry Seminar | |
| Topic: | TBA |
| Presenter: | Ravi Vakil, Stanford University |
| Date: | Tuesday, April 13, 2004, Time: 4:30 p.m., Location: Fine Hall 322 |
| Geometry, Representation, and Moduli Seminar | |
| Topic: | TBA |
| Presenter: | Alexander Braverman, Brown University |
| Date: | Wednesday, April 14, 2004, Time: 3:00 p.m., Location: Fine Hall 214 |
APRIL 19- APRIL 23, 2004 |
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| Algebraic Geometry Seminar | |
| Topic: | TBA |
| Presenter: | Mikhail Kapranov, Yale University |
| Date: | Tuesday, April 20, 2004, Time: 4:30 p.m., Location: Fine Hall 322 |