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

Messoud Efendiev, *Technical University of Munich*

### On a criteria for veryfing mathematical models

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

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

### 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.

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

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

### Some recent work on coagulation equations

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

Gonçalo dos Reis, *CMAP, Ecole Polytechnique*

### 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.

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

Hossein Tehrani, *University of Nevada, Las Vegas*

### Fucik spectrum of wave operator and related jumping nonlinearity
problems

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

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

### On the dynamics of RNA viruses through nonlinear differential
equations

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

Louis Kauffman, *University of Illinois, Chicago*

### 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.

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

Saber Elaydi, *Trinity University - Texas*

### Towards a theory of periodic difference equations and population
biology

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

Massimiliano Morini, *SISSA, Itália*

### 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.

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

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

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

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

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

### Arithmetics: motives, periods and motivic Galois group

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

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

### Geometry: sheaves, topos and fields

### 05/06/2009, 11:30 — 12:30 — Room P3.10, Mathematics Building

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

### Geometry: the notions of spectrum and scheme

### 08/05/2009, 14:00 — 15:00 — Room P4.35, Mathematics Building

Emma D'Aniello, *Seconda Universitá degli Studi di Napoli*

### Topological dynamical systems and odometers

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

Alex Vladimirsky, *Cornell University*

### Homogenization and multiobjective optimization - computational
challenges

I will present two recent projects related to front propagation and
optimal control.
The first of these (joint with A. Oberman and R. Takei) deals
with 2-scale and 3-scale computations in geometric optics. We
propose a new and efficient method to homogenize first-order
Hamilton-Jacobi PDEs. Unlike the prior cell-problem methods, our
algorithm is based on homogenizing the related Finsler metric. We
illustrate by computing the effective velocity profiles for a
number of periodic and "random" composite materials.

The second project (joint with A. Kumar) deals with multiple
criteria for optimality (e.g., fastest versus shortest
trajectories) and optimality under integral constraints. We show
that an augmented PDE on a higher-dimensional domain describes all
Pareto-optimal trajectories. Our numerical method uses the
causality of this PDE to approximate its discontinuous viscosity
solution efficiently. The method is illustrated by problems in
robotic navigation (e.g., minimizing the path length and exposure
to an enemy observer simultaneously).

### 17/02/2009, 15:00 — 16:00 — Room P3.10, Mathematics Building

Andreas Döring, *Imperial College London*

### A topos approach to quantum theory

I will report on work with Chris Isham on the application of topos
theory to physics. The Kochen-Specker theorem shows that a naive
realist description of quantum systems is impossible. This can be
understood as the inapplicability of Boolean logic to quantum
systems. In order to arrive at a more realist description, one can
use the internal logic of a certain topos of presheaves. The choice
of this topos is directly motivated from the Kochen-Specker
theorem. I will show which structures within this topos are of
physical significance and how propositions about physical
quantities are assigned truth-values. The relation with
constructive Gel'fand duality is sketched.

### 10/02/2009, 15:00 — 16:00 — Room P3.10, Mathematics Building

Alexandre Baraviera, *Universidade Federal do Rio Grande do Sul*

### Iterated function systems, classical and quantum

An iterated function system (IFS) is a collection of maps that are
chosen and iterated according to some probability. The geometric
and measurable structure of the limit set is usually very
interesting and studied with the use of the well known technique of
transfer operator. In this talk we will review some results about
this problem and its quantum version, where the maps are unitary
operators acting on some suitable Hilbert space.

### 03/02/2009, 15:00 — 16:00 — Room P3.10, Mathematics Building

Florin Radulescu, *Università di Roma-Tor Vergata*

### Type
${\mathrm{II}}_{1}$ Von Neumann Representations for Hecke Operators on Maass Forms and Inequalities for their Eigenvalues

We prove that classical Hecke operators on Maass forms are a
special case of completely positive maps on II${}_{1}$ factors,
associated to a pair of isomorphic subfactors. This representation
induces several matrix inequalities on the eigenvalues of the Hecke
operators on Maass forms. These inequalities are the consequence of
a "double" action of the Hecke algebra which can be seen only in
the type II${}_{1}$ representation. The classical Hecke operators are
then a "diagonal" of this double action.

### 27/01/2009, 15:00 — 16:00 — Room P3.10, Mathematics Building

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

### Theoretical models of cooperation with ODEs: from prebiotic
evolution to complex ecosystems

The dynamics of cooperation can be studied using mean field models
given by nonlinear ordinary differential equations (ODEs). Such a
dynamics is modeled considering heterocatalytic feedback loops,
with density-dependent enhancement of reproduction rates between
cooperating replicators. These models are used to study the
dynamics of catalytic networks named hypercycles which have a
particular graph architecture and which has been suggested to be of
importance in earlier stages of prebiotic evolution. In this talk
we will introduce the mathematical formalism used for the dynamical
study of such networks, focusing on the origin of life problem and
on the dynamics of ecological systems. We will analyze several
low-dimensional catalytic networks providing their stability and
bifurcation scenarios. We will also discuss some interesting
dynamical phenomenon associated to the bifurcations implying the
transition from survival to extinction phases. We will then also
compare the results obtained with the ODEs for these kind of
networks with other computational tools typical of complex systems
analysis.