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September 9 |
Louis Rowen
(Bar Ilan University)
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Supertropical algebra
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Recent recent in "tropical geometry" has focused on the max-plus algebra, a semiring
whose structure unfortunately is rather limited. Recently Z. Izhakian introduced a
newer algebraic structure (which we call a supertropical algebra) containing the
max-plus algebra, whose algebraic theory is much richer and enables us to prove
analogs of many of the classical theorems from commutative algebra in this setting.
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September 11 |
Sasha Kleshchev
(University of Oregon/UVa)
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Recent developments in representation theory of symmetric groups
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We will review some recent developments in representation theory of symmetric groups.
We will start with the (relatively) new approach by Okounkov and Vershik in characteristic 0,
and explain its counterpart in characteristic p, which leads to deep connections with
Kac-Moody algebras, crystal graphs, canonical bases, and ideas of categorification.
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October 2 |
Rafael Benguria
(P. Universidad Catolica de Chile)
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The zeroes of the Fourier transform of the characteristic function of
a domain and their relation with the eigenvalues of the Laplacian
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Consider the Fourier transform of the characteristic function of a
bounded, smooth domain in the Euclidean space in n dimensions. I will
present some recent results concerning the relation between the
closest zero of this function and both Dirichlet and Neumann
Eigenvalues of the Laplacian on that domain. I will motivate the
results with simple examples. I will also discuss some open problems
in this area. This is joint work with M. Levitin (Cardiff) and Leonid
Parnovski (University College, London).
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October 9 |
Ruth Williams
(UCSD)
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Stochastic networks with resource sharing
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Stochastic networks are used as models for complex systems involving
dynamic interactions subject to uncertainty. Application domains include
manufacturing, the service industry, telecommunications, and computer
systems. Networks arising in modern applications are often highly complex
and heterogeneous, with network features that transcend those of
conventional queueing models. The control and analysis of such networks
present challenging mathematical problems. In this talk, a concrete application
will be used to illustrate a general approach to the study of stochastic networks
using more tractable approximate models. Specifically, we consider a
data network model that represents the randomly varying number of flows
present in a network where bandwidth is shared fairly amongst elastic documents.
This model, introduced by Massoulie and Roberts, can be viewed as a stochastic network with simultaneous resource possession. Elegant fluid and diffusion approximations will
be used to study the performance of this model. The talk will conclude with
a summary of the current status and description of open problems associated with the
further development of approximate models for general stochastic networks.
This talk is based in part on joint work with W. N. Kang, F. P. Kelly, and N. H. Lee.
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