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JANUARY |
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| Analysis Seminar *** Please note special date |
| Topic: |
The structure of entropy solutions of nonlinear scalar conservation laws |
| Presenter: |
Felix Otto, Institute for Applied Mathematics, University of Bonn |
| Date: |
Wednesday, January 25, 2006, Time: 4:00 p.m., Location: Fine Hall 214 |
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| Geometric Analysis Seminar |
| Topic: |
Holomorphic vector fields and deformation rigidity |
| Presenter: |
Ngaiming Mok, The University of Hong Kong |
| Date: |
Friday, January 27, 2006, Time: 3:00 p.m., Location: Fine Hall 314 |
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FEBRUARY |
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| Algebraic Geometry Seminar |
| Topic: |
TBA |
| Presenter: |
G. Mikhalkin, University of Toronto |
| Date: |
Tuesday, February 7, 2006, Time: 4:30 p.m., Location: Fine Hall 322 |
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| Operation Research and Financial Engineering Seminar |
| Topic: |
Detecting changes in the rate of a Poisson process |
| Presenter: |
George Moustakides, University of Thessaly |
| Date: |
Tuesday, February 7, 2006, Time: 4:30 p.m., Location: Room E-219, Engineering Quad |
| Abstract: |
We consider the Cumulative Sum (CUSUM) test as a possible candidate to sequentially detect a change in the rate of a homogeneous Poisson process. We first derive a closed form expression for the average run length of the CUSUM stopping time, which we then use to prove optimality of the CUSUM test in the sense of Lorden. Specifically, we demonstrate that the CUSUM stopping time minimizes the maximal possible conditional detection delay under the constraint, that the average period between false alarms is no less than a prescribed value. |
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| COLUMBIA-PRINCETON UNIVERSITY PROBABILITY DAY |
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| Topic: |
On the timing option in a futures contract |
| Presenter: |
Tomas Björk, Stockholm School of Economics
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| Topic: |
On the interior smoothness of harmonic functions for degenerate diffusion processes |
| Presenter: |
Nicolai Krylov, University of Minnesota |
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| Topic: |
The Andersen thermostat in molecular dynamics |
| Presenter: |
Dong Li, Princeton University |
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| Topic: |
The heat kernel at the cut locus with connections to Brownian motions |
| Presenter: |
Robert Neel, Columbia University |
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| Date: |
Friday, February 10, 2006, Time: 10:00 a.m., Location: Columbia University, Department of Mathematics, Room 312 |
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| Geometric Analysis Seminar |
| Topic: |
TBA |
| Presenter: |
Christina Sormani,
City University of New York |
| Date: |
Friday, February 10, 2006, Time: 3:00 p.m., Location: Fine Hall 314 |
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| Ergodic Theory and Statistical Mechanics Seminar |
| Topic: |
Advanced statistical properties of dispersing billiards |
| Presenter: |
Nikolai Chernov, University of Alabama at Birmingham |
| Date: |
Friday, February 10, 2006, Time: 3:30 p.m., Location: Fine Hall 322 |
| Abstract: |
A new approach to the studies of statistical properties of hyperbolic dynamical systems (based on coupling method borrowed from probability theory) emerged recently; it was introduced by L.-S. Young and modified by D. Dolgopyat. We apply it here to Sinai billiards to derive a series of new results. First we establish sharp bounds on correlations (including multiple correlations). Then we use our correlation bounds to obtain the central limit theorem (CLT), the almost sure invariance principle (ASIP), the law of iterated logarithms, and integral tests. |
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| Ergodic Theory and Statistical Mechanics Seminar |
| Topic: |
Limit laws and recurrence for the infinite horizon planar Lorentz process |
| Presenter: |
Domokos Szász, Technical University Budapest |
| Date: |
Friday, February 10, 2006, Time: 4:30 p.m., Location: Fine Hall 322 |
| Abstract: |
L. S. Young's 1998 tower construction provided exponential decay or correlations for Hölder functions for 2-D hyperbolic systems with singularities and as a consequence a CLT, for instance. Our interest is to develop further the probabilistic methods, in particular, those based on the Fourier-transform of the Perron-Frobenius operator in order to obtain more delicate probabilistic properties. The methods are also hoped to lead to a potential theory of 2-D periodic Lorentz processes. |
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| Mathematics Seminar |
| Topic: |
Classical invariant theory meets statistics |
| Presenter: |
A.Neeman, ANU |
| Date: |
Monday, February 13, 2006, Time: 2:00 p.m., Location: Fine Hall 314 |
| Abstract: |
Mixture models are a venerable old part of statistics, a part which has found extensive applications, especially in biology. There is an enormous literature on the subject going back decades. This rich literature deals primarily with the case where one assumes known the underlying distributions; for example one might assume they are normal. The nonparametric case is largely unexplored. In this talk we will explain a new result, joint with Ryan Elmore and Peter Hall, which uses classical invariant theory to solve the identifiability problem for this model. |
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| PACM Seminar |
| Topic: |
Fault-Tolerant Quantum Computation |
| Presenter: |
Barbara Terhal, IBM |
| Date: |
Monday, February 13, 2006, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: |
I will review the theory of fault-tolerant quantum computation and the use of quantum error-correcting codes in future quantum computers. I will discuss the most recent developments in this area. |
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| Algebraic Geometry Seminar |
| Topic: |
TBA |
| Presenter: |
V. Alexeev, University of Georgia |
| Date: |
Tuesday, February 14, 2006, Time: 4:30 p.m., Location: Fine Hall 322 |
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| Operation Research and Financial Engineering Seminar |
| Topic: |
TBA |
| Presenter: |
Michael Overton, New York University |
| Date: |
Tuesday, February 14, 2006, Time: 4:30 p.m., Location: Room E-219, Engineering Quad |
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| Ergodic Theory and Statistical Mechanics Seminar |
| Topic: |
Ergodic theory and lattice points |
| Presenter: |
Amos Nevo, Institute for Advanced Study |
| Date: |
Thursday, February 16, 2006, Time: 2:00 p.m., Location: Fine Hall 322 |
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| Geometric Analysis Seminar |
| Topic: |
TBA |
| Presenter: |
Natasa Sesum , Columbia University |
| Date: |
Friday, February 17, 2006, Time: 3:00 p.m., Location: Fine Hall 314 |
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| PACM Seminar |
| Topic: |
Math Problems from the Far Side of Quantum Information |
| Presenter: |
Christopher A. Fuchs, Bell Labs, Lucent Technologies |
| Date: |
Monday, February 20, 2006, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: |
The field of Quantum Information has recently rightly attracted great interest for the technological fruits it may bear. But there is a sect of its practitioners who think it stands a chance to bring us much more than that---namely, that its theoretical tools will give us a means for exploring what quantum mechanics is really all about and for settling some of the deepest problems in physics. The roots of this optimism come from a very old thought: that a quantum state has more to do with representing its user's information, than any inherent physical property of the system to which it is ascribed. What is new and nice is that quantum information teaches us how to formulate this idea precisely and even check its consistency. Nicer still for the mathematics community is the number of juicy mathematical problems the consistency-checking process poses. In this talk, I will review some of the history of this and then quickly settle on a sample problem that has been annoying me a lot lately: the question of the existence of symmetric informationally complete positive-operator-valued measures for finite dimensional Hilbert spaces. I'm not alone---it turns out to be equivalent to a 30-year-old problem in coding theory---but I will say some things about it that you may not have heard before. |
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| Operation Research and Financial Engineering Seminar |
| Topic: |
A relative performance approach to portfolio selection when there is model ambiguity |
| Presenter: |
Andrew Lim, UC Berkeley |
| Date: |
Tuesday, February 21, 2006, Time: 4:30 p.m., Location: Room E-219, Engineering Quad |
| Abstract: |
Recent interest in the topic of "investment with model ambiguity" in the finance, economics and decision theory communities has been motivated largely by efforts to incorporate "ambiguity aversion", as suggested by experiments such as the Ellsberg Paradox, in the analysis of agent behavior. Closely related work on "robust portfolio selection" in the optimization community has been driven by the observation that the solutions of classical optimal portfolio selection problems (such as "mean-variance optimization") are sensitive to statistical errors that can arise during calibration, and that the "real world" performance of such portfolios can be poor if these errors are ignored. The commonly used method for addressing these issues is some sort of "worst case" optimization which has led in turn to methodologies such as "worst case mean-variance" and "worst case utility maximization". While the "worst case approach" has its axiomatic foundations in the work of Gilboa and Schmeidler, it has also been criticized for being "overly pessimistic".
In this talk, we propose and analyze an alternative measure of` "robust performance". This alternative measure differs from the typical "worst case expected utility" and "worst case mean-variance" formulations in that the "robust performance" of a (dynamic) portfolio is evaluated not only on the basis of its performance when there is an adversarial opponent ("nature"), but also by its performance relative to a fully informed ``benchmark investor" who behaves optimally given complete knowledge of the otherwise ambiguous model. This "relative performance" approach has several important properties: (i) decisions arising from this approach are less pessimistic than the portfolios obtained from the typical "worst case expected utility" and "worst case mean-variance" formulations, (ii) the dynamic "relative performance" problem reduces to a convex static optimization problem under reasonable choices of the benchmark portfolio, and (iii) the solution of the "relative performance" problem coincides with that of a "Bayesian" portfolio choice problem with an appropriately chosen prior. The static problem is interesting in its own right: it can be interpreted as a less pessimistic alternative to the single period "worst case mean-variance" problem.
Joint work with J. George Shanthikumar and Thaisiri Watewai. |
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| Discrete Mathematics Seminar |
| Topic: |
TBA |
| Presenter: |
Michael Krivelevich, Tel Aviv University |
| Date: |
Wednesday, February 22, 2006, Time: 2:15 p.m., Location: Fine 224 |
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| PACM Seminar |
| Topic: |
Layering As Optimization Decomposition |
| Presenter: |
Mung Chiang, Electrical Engineering, Princeton University |
| Date: |
Monday, February 27, 2006, Time: 4:00 p.m., Location: Fine Hall 214 |
| Abstract: |
Layered network architecture has traditionally been designed based on engineering heuristics. Recently a mathematically rigorous, practically relevant, and unifying framework has emerged to view the network as a solver of a generalized utility maximization problem, with alternative decompositions of the problem corresponding to different layering schemes, each decomposed subproblem corresponding to a different layer, and functions of variables coordinating the subproblems as the interfaces among the layers. Such decompositions can be carried out both horizontally across geographically disparate network elements and vertically into various functional modules. This talk surveys the recent advances in establishing this framework as a systematic approach to analyze and design protocol stacks in a holistic way that reveals the underlying structures and explores network design alternatives. Connections with distributed subgradient algorithm, convex and nonconvex optimization, stochastic optimization, differential topology, and algebraic geometry will be highlighted. |
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| Operation Research and Financial Engineering Seminar |
| Topic: |
TBA |
| Presenter: |
Frank Riedel, Rheinische Friedrich-Wilhelms-Universität Bonn |
| Date: |
Tuesday, February 28, 2006, Time: 4:30 p.m., Location: Room E-219, Engineering Quad |
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