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July 2004 | ||
| Candidate: | Michael Rosenblum | Abstract: We consider the problem of providing flexible, rate-based, quality of service guarantees for packets sent over switches and switch networks. Our focus is solving a type of on-line, traffic scheduling problem, whose input at each time step is a set of desired traffic rates through the switch network. These traffic rates in general cannot be exactly achieved since they treat the incoming data as fluid, that is, they assume arbitrarily small fractions of packets can be transmitted at each time step. The goal of the traffic scheduling problem is to closely approximate the given sequence of traffic rates by a sequence of switch uses throughout the network in which only whole packets are sent. We prove worst-case bounds on the additional delay and buffer use that result from using such an approximation. These bounds depend on the network topology, the resources available to the scheduler, and the types of fluid policy allowed. |
| Title: | Approximating fluid schedules in packet-switched networks | |
| Date: | Friday July 23, 2004 | |
| Time: | 2:30 pm | |
| Location: | Room 1-135 | |
| Committee: | Vahid Tarokh (Harvard), co-thesis advisor Michel Goemans, co-thesis advisor Daniel Spielman |
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| Candidate: | Morten Honsen | Abstract: We define a moduli functor parametrizing finite maps from a projective (locally) Cohen-Macaulay curve to a fixed projective space. The definition of the functor includes a number of technical conditions, but the most important is that the map is almost everywhere an isomorphism onto its image. The motivation for this definition comes from trying to interpolate between the Hilbert scheme and the Kontsevich mapping space. The main result of this thesis is that our functor is represented by a proper algebraic space. As an application we obtain interesting compactifications of the spaces of smooth curves in projective space. We illustrate this in the case of rational quartics, where the resulting space appears easier than the Hilbert scheme. |
| Title: | A compact moduli space parameterizing Cohen-Macaulay curves in projective space | |
| Date: | Thursday July 29, 2004 | |
| Time: | 12:00 pm | |
| Location: | Room 1-150 | |
| Committee: | Johan DeJong, thesis advisor Jason Starr Kiran Kedlaya |
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August 2004 | ||
| Candidate: | Benoit Charbonneau |
Abstract: The main result is a computation
of the Nahm transform of a SU(2)-instanton over  x T3, called spatially-periodic instanton. It is a
singular monopole over T3, a solution to the Bogomolny
equation, whose rank is computed and behavior at the singular
points is understood under certain conditions.
A full description of the Riemannian ADHMN construction of instantons
on |
| Title: | Analytic aspects of periodic instantons | |
| Date: | Thursday August 5, 2004 | |
| Time: | 10:00 am | |
| Location: | Room 2-102 | |
| Committee: | Tomasz Mrowka, thesis advisor Victor Guillemin Peter Kronheimer (Harvard) |
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| Other Thesis Defenses | ||
| Current Term Thesis Defenses | ||
| Summer 2005 Thesis Defenses | ||
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| Fall 2004 Thesis Defenses | ||
| Summer 2004 Thesis Defenses | ||
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| Fall 2003 Thesis Defenses | ||
| Summer 2003 Thesis Defenses | ||
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| Fall 2002 Thesis Defenses | ||
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