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OCTOBER 26 - OCTOBER 28, 2005 |
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Princeton University Graduate Student Seminar |
Topic: |
Regular Homotopy Classes of Singular Maps |
Presenter: |
Andras Juhasz, Princeton University |
Date: |
Wednesday, October 26, 2005, Time: 12:30 p.m., Location: Fine Hall 224 |
Abstract: |
Two locally generic maps $f,g : M^n --> R^{2n-1}$ are called regularly homotopic if they lie in the same path-component of the space of locally generic maps. Our main result is that if $n$ is not equal to $3$ and $M^n$ is a closed n-manifold then the regular homotopy class of every locally generic map $f : M^n --> R^{2n-1}$ is completely determined by the number of its singular points provided that $f$ is singular (i.e., $f$ is not an immersion). In the case $n=3$ a geometric classification is given for immersions of orientable $3$-manifolds into $5$-space up to regular homotopy. |
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Joint Princeton University and Institute for Advaced Study Number Theory Seminar |
Topic: |
Distribution of rational points on equivariant compactifications of semi-simple groups |
Presenter: |
Ramin Takloo-Bighash, Princeton University |
Date: |
Wednesday, October 26, 2005, Time: 2:00 p.m., Location: Fine Hall 314 |
Abstract: |
In this talk, I will explain a new result on the distribution of rational points of bounded height on "wonderful" compactifications of semi-simple groups of adjoint type. A special case of the result is the conjecture of Manin on the distribution of rational points with bounded anti-canonical height for this class of varieties. This is joint work with Joseph A. Shalika and Yuri Tschinkel. |
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Discrete Mathematics Seminar |
Topic: |
Hyperbolic van der Warden and Valiant Schrijver conjectures |
Presenter: |
Leonid Gurvits, Los Alamos Laboratory |
Date: |
Wednesday, October 26, 2005, Time: 2:15 p.m., Location: Fine Hall 224 |
Abstract: |
See http://www.math.princeton.edu/~bsudakov/gurvitz.pdf |
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Special Analysis Seminar *** Please note special time, date, and location |
Topic: |
Variations around the Ginzburg-Landau model for a superconducting cylinder |
Presenter: |
Myrto Sauvageot, Laboratoire Jacques-Louis Lions |
Date: |
Wednesday, October 26, 2005, Time: 3:00 p.m., Location: Fine Hall 601 |
Abstract: |
This talk will propose a study of classes of solutions for the Ginzburg-Landau equations related to a superconducting cylinder with applied magnetic field. It is presented from two points of view : vorticity, i.e. the precise location of the zeros of the wave function, and of the maxima of its modulus; and bifurcation phenomena leading from one class of solutions to another, which roughly speaking correspond to transitions between superconducting phases as observed by physicists. |
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Department Colloquium |
Topic: |
Zariski-dense subgroups and number theory |
Presenter: |
Gopal Prasad, University of Utah |
Date: |
Wednesday, October 26, 2005, Time: 4:30 p.m., Location: Fine Hall 314 |
Abstract: |
This talk will be devoted to some recent results obtained jointly with Andrei Rapinchuk on Zariski-dense subgroups of real semi-simple Lie groups. After giving examples of Zariski-dense subgroups which arise naturally, I will describe our results about existence of elements with very interesting properties in such subgroups. The proof of existence of these elements requires p-adic considerations even when the semi-simple Lie group is compact. I will mention several applications of our results: to the Auslander problem, to study of lengths of closed geodesics in locally symmetric spaces, to a problem of Yves Benoist. Some of these applications require results (and a conjecture) from transcendental number theory. |
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Analysis Seminar |
Topic: |
Functional versions of some Geometric Inequalities |
Presenter: |
Vitali Milman, University of Tel Aviv |
Date: |
Thursday, October 27, 2005, Time: 4:00 p.m., Location: Fine Hall 214 |
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Topology Seminar |
Topic: |
Volume and angle structures on 3-manifolds |
Presenter: |
Feng Luo, Rutgers University |
Date: |
Thursday, October 27, 2005, Time: 4:30 p.m., Location: Fine Hall 314 |
Abstract: |
We introduce a finite dimensional variational approach to find constant curvature metrics on triangulated closed 3-manifolds. The approach is based on the Schlaefli formula for volume of tetrahedra. Schlaefli formula suggests that the volume is best expressed in terms of dihedral angles than in edge lengths. Based on this observation, we defined the concept of an angle structure on a tetrahedron and on a triangulated closed 3 manifold, and defined their volume. These are natural generalizations of constant sectional curvature metrics and their volume. It is shown that the volume functional can be extended continuously to the compact closure of the moduli space of angle structure, verifying a conjecture of John Milnor. The main result shows that for a 1-vertex triangulation of a closed 3-manifold if the volume function on the moduli space of all angle structures has a local maximum point, then either the manifold admits a constant curvature Riemannian metric, or the manifold is reducible. |
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OCTOBER 31 - NOVEMBER 4, 2005 |
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Joint Princeton University and Institute for Advaced Study Number Theory Seminar |
Topic: |
Rational Homology Spheres and Automorphic Forms |
Presenter: |
Frank Calegari, Harvard University |
Date: |
Wednesday, November 2, 2005, Time: 2:00 p.m., Location: Fine Hall 314 |
Abstract: |
Let K be an imaginary quadratic field. Modular forms for K are related to the cohomology of arithmetic 3-manifolds. By using the Galois representations associated to such forms we produce an explicit tower of rational homology three spheres with certain properties, answering a question of Cooper. Along the way we give the world's most complicated proof that the modular curve X_0(1) has genus zero. (Joint work with Nathan Dunfield) |
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NOVEMBER 7 - 11, 2005 |
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PACM Colloquium |
Topic: |
Bounds on the Optimal Density of Sphere Packings in High Dimensions |
Presenter: |
Sal Torquato, Chemistry, Princeton University |
Date: |
Monday, November 7, 2005, Time: 4:00 p.m., Location: Fine Hall 214 |
Abstract: |
Sphere packings in high dimensions are of great interest to mathematicians and physicists, and have direct applications in communications theory. Remarkably, no one has been able to provide exponential improvement on a 100-year-old lower bound on the maximal packing density due to Minkowski in d-dimensional Euclidean space \Re^d. The asymptotic behavior of this bound is controlled by 2^{-d} in high dimensions. Using an optimization procedure that we introduced earlier [1] and a conjecture concerning the existence of disordered sphere packings in \Re^d, we obtain a provisional lower bound on the density whose asymptotic behavior is controlled by 2^{-0.7786}, thus providing the putative exponential improvement of Minkowski's bound [2]. The conjecture states that a hard-core nonnegative tempered distribution is a pair correlation function of a translationally invariant disordered sphere packing in \Re^d for asymptotically large d if and only if the Fourier transform of the autocovariance function is nonnegative. The conjecture is supported by two explicit analytically characterized disordered packings, numerical simulations in low dimensions, and known necessary conditions that only have relevance in very low dimensions. A byproduct of our approach is an asymptotic lower bound on the average kissing number whose behavior is controlled by 2^{0.2213}, which is to be compared to the best known asymptotic lower bound on the individual kissing number of 2^{0.2075}. Interestingly, our optimization procedure is precisely the dual of a primal linear program devised by Cohn and Elkies [3] to obtain upper bounds on the density, and hence has implications for linear programming bounds.
- S. Torquato and F. H. Stillinger, "Controlling the Short-Range Order and Packing Densities of Many-Particle Systems," Journal of Physical Chemistry B, 106, 8354 (2002); ibid, 106, 11406 (2002).S. Torquato and F. H. Stillinger, "New Provisional Lower Bounds on the Optimal Density of Sphere Packings," http://arxiv.org/abs/math.MG/0508381.
- H. Cohn and N. Elkies, "New upper bounds on sphere packings I," Annals of Mathematics, 157, 689 (2003); H. Cohn, "New upper bounds on sphere packings II," Geometry and Topology, 6, 329 (2002).
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Algebraic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Ch. Hacon, University of Utah |
Date: |
Tuesday, November 8, 2005, Time: 4:30 p.m., Location: Fine Hall 322 |
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Mathematical Physics Seminar |
Topic: |
Infrared representations, number bounds and renormalization in QED |
Presenter: |
Thomas Chen, Princeton University |
Date: |
Tuesday, November 8, 2005, Time: 4:30 p.m., Location: Jadwin 343 |
Abstract: |
We discuss some recent work related to the infrared problem in non-relativistic Quantum Electrodynamics (QED). It is explained how some fundamental results which have long been established for Nelson's model (infrared representations, aspects of scattering theory) can now also be proved for QED. Key to the analysis is a bound on the infrared renormalized electron mass in the case where the interaction Hamiltonian has critical scaling (a problem of endpoint type). This estimate is derived by use of an isospectral renormalization group method designed for the spectral analysis of Hamiltonians in quantum field theory. This is in part based on joint work with V. Bach, J. Fr\"ohlich, and I.M. Sigal.
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Discrete Mathematics Seminar |
Topic: |
On a conjecture of Berge and Simonovits on hypergraph products |
Presenter: |
Dhruv Mubayi, University of Illinois at Chicago |
Date: |
Wednesday, November 9, 2005, Time: 2:15 p.m., Location: Fine Hall 224 |
Abstract: |
See http://www.math.princeton.edu/~bsudakov/mubayi2005-2006.pdf |
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Department Colloquium |
Topic: |
TBA |
Presenter: |
Christopher Hacon, University of Utah |
Date: |
Wednesday, November 9, 2005, Time: 4:30 p.m., Location: Fine Hall 314 |
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Analysis Seminar |
Topic: |
Long range scattering for the Maxwell-Schroedinger system |
Presenter: |
Giorgio Velo, Universitã di Bologan and INFN |
Date: |
Thursday, November 10, 2005, Time: 4:00 p.m., Location: Fine Hall 214 |
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Topology Seminar |
Topic: |
Counting subgroups and covering spaces in dimension 3 |
Presenter: |
Marc Lackenby, Oxford University |
Date: |
Thursday, November 10, 2005, Time: 4:30 p.m., Location: Fine Hall 314 |
Abstract: |
How many finite-sheeted covering spaces does a 3-manifold have, as a function of the covering degree? For hyperbolic 3-manifolds, the answer is not known, not even asymptotically. But it seems that if we are to make progress with important questions such as the Virtually Haken conjecture, then a good understanding of the `landscape' of all finite-sheeted covering spaces is required. In particular, we should know how many there are! In my talk, I will give some new lower bounds. For arithmetic 3-manifolds, these will be exponential in the covering degree. For general closed hyperbolic 3-manifolds, I will provide a slightly weaker lower bound, which uses a new theorem on the behaviour of mod p homology of finite index subgroups of a group. |
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Geometric Analysis Seminar |
Topic: |
TBA |
Presenter: |
Xiaodong Wang, Michigan State University |
Date: |
Friday, November 11, 2005, Time: 3:00 p.m., Location: Fine Hall 314 |
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NOVEMBER 14 - 18, 2005 |
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PACM Colloquium |
Topic: |
Homological Methods for Sensor Networks |
Presenter: |
Robert Ghrist, Mathematics, University of Illinois |
Date: |
Monday, November 14, 2005, Time: 4:00 p.m., Location: Fine Hall 214 |
Abstract: |
As sensor engineering and manufacturing evolve to produce smaller devices, we will have the problem of dealing with large numbers of very localized objects. What types of global problems can be solved by a swarm of local sensors? Topologists solved a similar problem nearly a century ago. This talk will demonstrate the surprising effectiveness of homology theory in sensor networks. |
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Algebraic Geometry Seminar |
Topic: |
Quasi-reductive group schemes |
Presenter: |
Gopal Prasad, IAS |
Date: |
Tuesday, November 15, 2005, Time: 4:30 p.m., Location: Fine Hall 322 |
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Operations Research and Financial Engineering Seminar |
Topic: |
TBA |
Presenter: |
Adrian Lewis, Cornell University |
Date: |
Tuesday, November 15, 2005, Time: 4:30 p.m., Location: Room E-219, Engineering Quad |
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Princeton University Graduate Student Seminar |
Topic: |
Szemeredi's Regularity Lemma |
Presenter: |
Po-Shen Loh, Princeton University |
Date: |
Wednesday, November 16, 2005, Time: 12:30 p.m., Location: Fine Hall 224 |
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Statistical Mechanics Seminar |
Topic: |
The Bose Gas, Part I |
Presenter: |
Jakob Yngvason, University of Vienna |
Date: |
Wednesday, November 16, 2005, Time: 2:00 p.m., Location: Jadwin 343 |
Abstract: |
This will be the first of several lectures on the theory of the Bose gas and its various properties at or near absolute zero temperature. |
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NOVEMBER 21 - 25, 2005 |
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PACM Colloquium |
Topic: |
Seismic tomography: some mathematical aspects |
Presenter: |
Guust Nolet, Geosciences, Princeton University |
Date: |
Monday, November 21, 2005, Time: 4:00 p.m., Location: Fine Hall 214 |
Abstract: |
"Seismic tomography" is the term geophysicists use for a collection of methods to use seismic waves to image the interior of the Earth, much like in a CAT scan. Tomographic imaging has led to important discoveries, such as the observation that ocean floor subducts to the bottom of the Earth's mantle and - more recently - that plumes of hot material rise up from the lower mantle.
In its simplest form, the approximations of geometrical optics are applied to high frequency seismic waves. These waves then follow raypaths and the most useful observable is a travel time along the ray: T = \int ds / v(r). In a typical interpretation, \mathcal O (10^6) data with a signal-to-noise ratio of order 1 are inverted for \mathcal O (10^4-10^5) parameters. The mathematical challenge is mostly that of an adequate regularization of the problem that minimizes artifacts. More accurate travel time measurements can be obtained using cross-correlation on digital seismograms with sensitivity to lower frequency. For such waves a first order perturbation theory is needed to include the effects of wave diffraction around small anomalies. The travel time becomes then frequency dependent, and T is given by a volume integral, with an increase by several orders of magnitude in the numerical effort. Finally, for the lowest frequency waves we use the whole waveform as data. These waveforms can be modeled by summation of normal modes, but the problem is inherently nonlinear and again a ray approximation is needed to render the inverse problem feasible. The challenge is to relax this constraint and take effects of diffraction into account. We shall speculate about the possible role of wavelets in meeting these challenges. |
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Special Topology Seminar *** Note special date |
Topic: |
TBA |
Presenter: |
Ilya Kapovich, University of Illinois (Urbana/Champaign) |
Date: |
Tuesday, November 22, 2005, Time: 4:30 p.m., Location: Fine Hall 314 |
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Statistical Mechanics Seminar |
Topic: |
Ultraviolet stability and multiscale analysis |
Presenter: |
Giovanni Gallavotti, University of Rome |
Date: |
Wednesday, November 23, 2005, Time: 2:00 p.m., Location: Jadwin 343 |
Abstract: |
An exposition of the key ideas and methods used to establish the lower bound on the ground state energy in two and three dimensional scalar quantum field theories. |
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Discrete Mathematics Seminar |
Topic: |
TBA |
Presenter: |
Jozsef Beck, Rutgers University |
Date: |
Wednesday, November 23, 2005, Time: 2:15 p.m., Location: Fine Hall 224 |
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NOVEMBER 28 - DECEMBER 2, 2005 |
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PACM Colloquium |
Topic: |
Thermally-driven rare events and large deviation theory |
Presenter: |
Maria Reznikoff, Mathematics, Princeton University |
Date: |
Monday, November 28, 2005, Time: 4:00 p.m., Location: Fine Hall 214 |
Abstract: |
Thermal or stochastic effects are prevalent in physical, chemical, and biological systems. Particularly in small systems, noise can overpower the deterministic dynamics and lead to &rare events,& events which would never be seen in the absence of noise. One example is the thermally-driven switching of the magnetization in small memory elements. Wentzell-Freidlin large deviation theory is a mathematical tool for studying rare events. It estimates their probability and also the &most likely switching pathway,& which is the pathway in phase space by which rare events are most likely to occur. We explain how large deviation theory and concepts from stochastic resonance may be applied to analyze thermally-activated magnetization reversal in the context of the spatially uniform Landau-Lifschitz-Gilbert equations. The time-scales of the experiment are critical. One surprising and physically relevant result is that in multiple-pulse experiments, nonconvential &short-time switching pathways& can dominate. The effect is dramatic: the usual pathway (connected with the Arrhenius-law) underestimates the probability of switching by an exponential factor.An advantage of the method via large deviation theory is that it generalizes to systems with spatial variation. To discuss the complications and richness that emerge when spatial variation is taken into account, we consider the (simpler) Allen-Cahn equation. In this context, the rare event of interest is phase transformation from u \equiv -1 to u \equiv +1, and the most likely switching pathway is a pathway through function space. A natural reduced problem emerges in the &sharp-interface limit.& We give a brief overview of some results (rigorous in d = 1, heuristic in d > 1.)
The first part of the talk is joint work with Bob Kohn and Eric Vanden-Eijnden. The second part includes work that is also joint with Felix Otto and Yoshihiro Tonegawa. |
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Joint Princeton University and Institute for Advaced Study Number Theory Seminar *** Please note special day, time, and location |
Topic: |
Serre's modularity conjecture |
Presenter: |
Chandrashekhar Khare, University of Utah |
Date: |
Monday, November 28, 2005, Time: 4:30 p.m., Location: TBA |
Abstract: |
The title refers to a conjecture that Serre made in the early 1970's, that has proved to be very influential. I will sketch the main ideas of the proof of the level 1 case of Serre's conjecture. If time permits, I will indicate how these ideas can be extended to prove almost all of Serre's conjecture. The latter is joint work with J-P. Wintenberger. |
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Operations Research and Financial Engineering Seminar |
Topic: |
TBA |
Presenter: |
Tom Salisbury, York University |
Date: |
Tuesday, November 29, 2005, Time: 4:30 p.m., Location: Room E-219, Engineering Quad |
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Discrete Mathematics Seminar |
Topic: |
TBA |
Presenter: |
Ben Green, Clay Institute, University of Bristol and MIT |
Date: |
Wednesday, November 30, 2005, Time: 2:15 p.m., Location: Fine Hall 224 |
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Department Colloquium |
Topic: |
TBA |
Presenter: |
Yum-Tong Siu, Harvard University |
Date: |
Wednesday, November 30, 2005, Time: 4:30 p.m., Location: Fine Hall 314 |
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DECEMBER 5 - 9, 2005 |
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PACM Colloquium |
Topic: |
The Boosting Approach to Machine Learning |
Presenter: |
Robert Schapire, Computer Science, Princeton University |
Date: |
Monday, December 5, 2005, Time: 4:00 p.m., Location: Fine Hall 214 |
Abstract: |
Machine learning studies the design of computer algorithms that automatically make predictions about the unknown based on past observations. Often, the goal is to learn to categorize objects into one of a relatively small set of classes. Boosting, one method for solving such learning problems, is a general technique for producing a very accurate classification rule by combining rough and moderately inaccurate "rules of thumb." While rooted in a theoretical framework of machine learning, boosting has been found to perform quite well empirically. After introducing the boosting algorithm AdaBoost, I will explain the underlying theory of boosting, including our explanation of why boosting often does not suffer from overfitting. I also will touch on some of the other theoretical perspectives on boosting, and describe some recent applications and extensions. |
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Operations Research and Financial Engineering Seminar |
Topic: |
TBA |
Presenter: |
Paolo Guasoni, Boston University |
Date: |
Tuesday, December 6, 2005, Time: 4:30 p.m., Location: Room E-219, Engineering Quad |
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Discrete Mathematics Seminar |
Topic: |
TBA |
Presenter: |
Mario Szegedy, Rutgers University |
Date: |
Wednesday, December 7, 2005, Time: 2:15 p.m., Location: Fine Hall 224 |
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Geometric Analysis Seminar |
Topic: |
TBA |
Presenter: |
Pierre Albin, MIT |
Date: |
Friday, December 9, 2005, Time: 3:00 p.m., Location: Fine Hall 314 |
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DECEMBER 12 - DECEMBER 16, 2005 |
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PACM Colloquium |
Topic: |
Turbulence and Large-scale Geophysical Circulations |
Presenter: |
Geoff Vallis, Geosciences/Atmospheric & Oceanic Sciences, Princeton University |
Date: |
Monday, December 12, 2005, Time: 4:00 p.m., Location: Fine Hall 214 |
Abstract: |
The large-scale circulation is not only affected but is essentially effected by turbulent flows. This turbulence is not the small-scale turbulence that is (unfortunately) sometimes connoted by the word turbulence, but is turbulence up to the scale of the large-scale flow itself. This is largely two-dimensional, so-called geostrophic turbulence. We will discuss what is known and what is unknown about such flow, the problems of both simulating it and of understanding it, and whether these two are the same. |
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Operations Research and Financial Engineering Seminar |
Topic: |
TBA |
Presenter: |
Pierre-Louis Lions |
Date: |
Tuesday, December 13, 2005, Time: 4:30 p.m., Location: Room E-219, Engineering Quad |
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Discrete Mathematics Seminar |
Topic: |
TBA |
Presenter: |
Prasad Tetali, Georgia Tech |
Date: |
Wednesday, December 14, 2005, Time: 2:15 p.m., Location: Fine Hall 224 |
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