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21/06/2001, 11:00 — 12:00 — Room P3.10, Mathematics Building

Anatole Katok, *Pennsylvania State University*

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Some new results and constructions in Liouvillean dynamics

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12/06/2001, 15:00 — 16:00 — Room P3.10, Mathematics Building

George Andrews, *Pennsylvania State University*

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An old algorithm in a new era: MacMahon's partition analysis

In the late 1890's, Major Percy Alexander MacMahon developed his Partition Analysis with the object of proving his conjectures on plane partitions. While writing at length on this topic and clearly indicating its power, MacMahon eventually admitted that he was unable to apply his new tool to solve any of his conjectures on plane partitions.

In this talk, we shall begin by examining MacMahon's method from a purely elementary point of view and shall illustrate its power by considering questions of general interest such as: How many triangles are there with integer sides and perimeter n? Our object will be to illustrate the broad utility of a 19th century idea that is only now coming into its own in the era of computer algebra.

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05/06/2001, 15:00 — 16:00 — Room P3.10, Mathematics Building

António Serra, *Instituto Superior Técnico*

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Interpolating sequences

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31/05/2001, 11:00 — 12:00 — Room P3.10, Mathematics Building

C. Maeve McCarthy, *Murray State University, Kentucky*

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Optimal control of a chemotaxis system

Chemotaxis is the process by which cells aggregate under the force of a chemical attractant. The cell and chemoattractant concentrations are governed by a coupled system of parabolic partial differential equations. We investigate the optimal control of the proportion of cells being generated. The optimality system contains forward and backward reaction-diffusion and convection-diffusion equations. A numerical scheme is discussed that addresses the special needs of this coupled system.

This is joint work with K. Renee Fister, Murray State University.

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24/05/2001, 11:00 — 12:00 — Room P3.10, Mathematics Building

David Costa, *University of Nevada, Las Vegas*

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Problemas Não-Lineares em Ressonância

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22/05/2001, 15:00 — 16:00 — Room P3.10, Mathematics Building

Fernando Pablos Romo, *Universidad de Salamanca*

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Local symbols on algebraic curves

In 1968 John Tate gave a definition of the residues of differentials on curves in terms of traces of certain linear operators on infinite-dimensional vector spaces. The aim of the talk is to give a new definition of two local symbols on algebraic curves (the Tame Symbol and the Hilbert's Norm Residue Symbol) from the commutator of a central extension of groups. This definition, which involves topics of Steinberg symbols, is valid for curves over a perfect field. Moreover, when the curve is complete, analogously to Tate's construction the reciprocity laws of both symbols can be deduced from the finiteness of the cohomology groups ${H}^{0}(C,{O}_{C})$ and ${H}^{1}(C,{O}_{C})$.

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17/05/2001, 11:00 — 12:00 — Room P3.10, Mathematics Building

David Costa, *University of Nevada, Las Vegas*

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Métodos Variacionais em Equações Diferenciais

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15/05/2001, 15:00 — 16:00 — Room P3.10, Mathematics Building

Pedro Martins Rodrigues, *Instituto Superior Técnico*

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Bowen-Franks groups as invariants for ${T}^{n}$-automorphisms

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08/05/2001, 15:00 — 16:00 — Room P3.10, Mathematics Building

Ana Barroso, *Universidade de Lisboa*

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Um resultado de relaxação no espaço das funções de deformação limitada

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24/04/2001, 15:00 — 16:00 — Room P3.10, Mathematics Building

Luís Sanchez, *Universidade de Lisboa*

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Heteroclínicas para uma Equação de Quarta Ordem Conservativa

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19/04/2001, 11:00 — 12:00 — Room P3.10, Mathematics Building

Mark Vishik, *IITP, Russian Academy of Sciences*

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Attractors for equations of mathematical physics

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10/04/2001, 15:00 — 16:00 — Room P3.10, Mathematics Building

Yakov Pesin, *Pennsylvania State University*

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On the Existence of Bernoulli Diffeomorphisms with Nonzero Lyapunov Exponents on Compact Smooth Manifolds

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03/04/2001, 15:00 — 16:00 — Room P3.10, Mathematics Building

Mark Vishik, *IITP, Russian Academy of Sciences*

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Attractors for non-autonomous evolution equations

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29/03/2001, 11:00 — 12:00 — Room P3.10, Mathematics Building

David Kinderlehrer, *Carnegie Mellon University*

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Remarks about diffusion mediated transport

Diffusion mediated transport is implicated in the operation of many molecular level systems. These include some liquid crystal and lipid bilayer systems, and, especially, the motor proteins responsible for eukaryotic cellular traffic. All of these systems are extremely complex. In this expository talk we address the basic elements of transport in an environment of diffusion, concentrating on the flashing rachet. We illustrate how to characterize the properties of this process in terms of a Markov chain. It is of essential importance to understand what it means to determine a Markov chain in this manner, namely, the sense in which the discrete problem is an accurate description of the original continuous one. Here we are able to exploit some novel concepts about the dynamics of evolutionary systems including an appeal to the classical Monge transfer problem. This perspective illuminates the fundamental connection between the two problems and presents an opportunity for future applications.

This is joint work with Michal Kowalczyk.

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13/03/2001, 15:00 — 16:00 — Room P3.10, Mathematics Building

Alexander Sharkovsky, *Institute of Mathematics, National Academy of Sciences of Ukraine*

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Boundary value problems and dynamical systems

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08/03/2001, 11:00 — 12:00 — Room P3.10, Mathematics Building

Antonio Linero, *Universidad de Murcia*

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On the periodic structure of sigma-permutation maps on ${I}^{n}$ and ${T}^{n}$

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05/03/2001, 15:00 — 16:00 — Room P3.10, Mathematics Building

Diogo Gomes, *Instituto Superior Técnico*

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Métodos de equações diferenciais para sistemas hamiltonianos II

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05/03/2001, 11:00 — 12:00 — Room P4.35, Mathematics Building

Diogo Gomes, *Instituto Superior Técnico*

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Métodos de equações diferenciais para sistemas hamiltonianos I

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22/02/2001, 11:30 — 12:30 — Room P3.10, Mathematics Building

Zvi Artstein, *The Weizmann Institute of Science*

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Singularly perturbed ordinary differential equations: an overview. II

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22/02/2001, 10:00 — 11:00 — Room P3.10, Mathematics Building

Zvi Artstein, *The Weizmann Institute of Science*

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Singularly perturbed ordinary differential equations: an overview. I