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JANUARY |
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| Special Seminar |
| Topic: |
Symmetric tensors and enumeration of Hamiltonian cycles in graphs |
| Presenter: |
Peter Zograf, Steklov Mathematical Institute |
| Date: |
Friday, January 20, 2006, Time: 2:15 p.m., Location: Fine Hall 314 |
| Abstract: |
A Hamiltonian cycle is a closed path that traverses each vertex of a graph exactly once. The problem of finding a Hamiltonian cycle in a graph is a well known NP-hard problem, a discrete relative of the famous Traveling Salesman Problem. Even to decide whether a graph contains a Hamiltonian cycle (without actually finding it) is computationally NP-hard.
This talk will explain how one can enumerate Hamiltonian cycles in a graph by contracting certain symmetric tensors along the edges of the graph. The method is rather general and applies to other enumeration problems in graphs, like edge colorings, perfect matchings, etc. |
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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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| 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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| 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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| 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: |
TBA |
| Presenter: |
Andrew Lim, UC Berkeley |
| Date: |
Tuesday, February 21, 2006, Time: 4:30 p.m., Location: Room E-219, Engineering Quad |
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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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