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08/06/2010, 15:00 — 16:00 — Room P3.10, Mathematics Building

Joana Oliveira dos Santos, *Université Paris Dauphine*

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A geometric definition of the Aubry-Mather set

Given an optical Hamiltonian $H:{T}^{*}M\to {\mathbb{R}}^{m}$ on the cotangent bundle of a compact manifold $M$ without boundary its dynamics can be studied with the use of the Lagrangian action functional. Using this approach, Mather defined an important compact invariant set, that he called the Aubry set, and which has the distinguished property of being contained in a Lipschitz Lagrangian graph. In the present seminar, we will study it from a geometric point of view and give the lines of new proofs of some of its most important properties: dynamical invariance, symplectic invariance, and the graph property (which is tautological for the definition we use).

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18/05/2010, 15:00 — 16:00 — Room P3.10, Mathematics Building

Enrico Valdinoci, *Università di Roma Tor Vergata*

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Geometric properties of elliptic PDEs arising from a variational
problem

We will discuss some rigidity, monotonicity and symmetry properties
for elliptic PDEs in relation with minimal surfaces and dynamical
systems. We will discuss the relation between a problem posed by De
Giorgi for the Allen-Cahn equation and a question raised by Bangert
in a variational context studied by Moser and related to the
Aubry-Mather Theory.

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18/05/2010, 14:00 — 15:00 — Room P3.10, Mathematics Building

Saber Elaydi, *Trinity University, San Antonio, Texas*

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Invariant Manifolds in Competition Models

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07/05/2010, 11:30 — 12:30 — Room P3.10, Mathematics Building

Martin Burns, *University of Strathclyde, Glasgow*

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Steady state solutions for a quasilinear parabolic bistable
equation

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06/05/2010, 11:00 — 12:00 — Room P3.10, Mathematics Building

Michael Grinfeld, *University of Strathclyde, Glasgow*

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Modelling submonolayer deposition

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30/03/2010, 15:00 — 16:00 — Room P3.10, Mathematics Building

Josep Sardanyés, *Complex Systems Lab-Universitat Pompeu Fabra, Barcelona*

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Error threshold in RNA quasispecies models with complementation

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12/01/2010, 15:00 — 16:00 — Room P3.10, Mathematics Building

Rachid El Harti, *University Hassan I, Morocco*

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Thompson group and Dixmier problem

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26/11/2009, 11:00 — 12:00 — Room P3.10, Mathematics Building

Messoud Efendiev, *Technical University of Munich*

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On a criteria for veryfing mathematical models

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24/11/2009, 15:00 — 16:00 — Room P3.10, Mathematics Building

Lucia Scardia, *Hausdorff Center for Mathematics, Bonn, Germany*

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Convergence of equilibria for thin elastic plates under physical
growth conditions

The asymptotic behaviour of the equilibrium configurations of a
thin elastic plate is studied, as the thickness $h$ of the plate
goes to zero. More precisely, it is shown that critical points of
the functional ${E}^{h}$ describing the elastic energy of the thin
plate converge to critical points of the $\Gamma $-limit of ${E}^{h}$,
in the von Kármán regime. This is proved under the physical
assumption that the elastic energy blows up in the case of total
compression.

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03/11/2009, 15:00 — 16:00 — Room P3.10, Mathematics Building

Henry van Roessel, *University of Alberta, Edmonton, Canadá*

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Some recent work on coagulation equations

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16/10/2009, 11:00 — 12:00 — Room P3.10, Mathematics Building

Gonçalo dos Reis, *CMAP, Ecole Polytechnique*

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Quadratic growth BSDE and applications to pricing and hedging of derivatives based on non-tradable underlyings.

We consider Forward-Backward stochastic differential equations with generators that grow quadratically in the control variable (qgFBSDE). This type of equations is used to solve a utility maximization problem in incomplete markets tackling the problem of pricing a financial derivative based on non-traded underlyings such as weather derivatives. We provide new differentiability results for qgFBSDE that in turn allow closed form formulas for the hedging strategy. We present numerical results.

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28/07/2009, 15:00 — 16:00 — Room P3.10, Mathematics Building

Hossein Tehrani, *University of Nevada, Las Vegas*

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Fucik spectrum of wave operator and related jumping nonlinearity
problems

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07/07/2009, 15:00 — 16:00 — Room P3.10, Mathematics Building

Josep Sardanyés, *Complex Systems Lab-Universitat Pompeu Fabra, Barcelona*

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On the dynamics of RNA viruses through nonlinear differential
equations

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30/06/2009, 15:00 — 16:00 — Room P3.10, Mathematics Building

Louis Kauffman, *University of Illinois, Chicago*

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Virtual Knot Theory and Oriented Extensions of the Jones Polynomial

The original Jones polynomial for classical knots depends only
weakly on the orientation of the knot or link to which it is
applied. Careful examination of the orientations assigned to states
in an oriented bracket polynomial model for the Jones polynomial
reveals that there is much more topological information available
from orientation when the knot or link is embedded in a thickened
surface or regarded as a virtual link. This talk will discuss a
large scale generalization that we call the extended bracket
polynomial (taking polynomial and graphical values) and the arrow
polynomial (joint work with Heather Dye) taking polynomial values
with infinitely many new variables. The arrow polynomial is related
to the Miyazawa polynomials for virtual knots. The talk will
discuss applications of these new invariants to finding virtual
crossing number and genus of virtual knots, and we shall discuss
extensions of Khovanov homology related to these invariants.

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30/06/2009, 11:00 — 12:00 — Room P4.35, Mathematics Building

Saber Elaydi, *Trinity University - Texas*

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Towards a theory of periodic difference equations and population
biology

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23/06/2009, 15:00 — 16:00 — Room P3.10, Mathematics Building

Massimiliano Morini, *SISSA, Itália*

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Equilibrium configurations of epitaxially strained elastic films:
existence, regularity, and qualitative properties of solutions

We consider a variational model used in the physical literature to
describe the equilibrium configurations of an elastic film
epitaxially deposited on a flat rigid substratum, when a lattice
mismatch is present between the two materials. After specifying the
functional set-up, in which the minimization problem can be
properly formulated, we study the regularity and several
qualitative properties of equilibrium configurations; that is, of
local and global minimizers of the energy functional.

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16/06/2009, 15:00 — 16:00 — Room P3.10, Mathematics Building

Zdenek Kocan and Veronika Kurkova, *Silesian University in Opava, Czech Republic*

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Entropy, horseshoes and homoclinic trajectories on trees, graphs
and on dendrites

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09/06/2009, 11:30 — 12:30 — Room P3.10, Mathematics Building

Pierre Cartier, *Institut des Hautes Études Scientifiques, Paris*

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Arithmetics: motives, periods and motivic Galois group

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08/06/2009, 11:30 — 12:30 — Room P3.10, Mathematics Building

Pierre Cartier, *Institut des Hautes Études Scientifiques, Paris*

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Geometry: sheaves, topos and fields