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Puc-Chile A geometric approach to the cohomological equation for cocycles of isometries Auditorio Bralic Abstract: Moreover, we obtain diferenclales bounds on the error term in terms of two constants: Enrico Valdinoci Weierstrass Institute Title: This course is based on collaborations with G. This program was initiated by Berger a couple of years ago.

We will explain how topological emergence is bounded from above in terms of the dimension of the ambient space. Often, the nonlocal effect is modeled by a diffusive operator which is in some sense elliptic and fractional.

Pursuing this idea, we are led to fundamentally new ways of quantifying dynamical complexity. In these circumstances, is it possible to describe the dynamical evolution of the current trait?

### Escuela – CAPDE

Classify subshifts of finite type up ecuacuones topological isomorphism. In a work with Mathieu Sablik, we made a step towards the limit, proving that the result of Hochman and Meyerovitch is robust under the linear version of this property where the minimal distance function is O uach where n is the size of the two square blocks. We will present in this talk a survey of various restrictions on these groups for zero entropy minimal subshifts.

The ‘statistics’ of a dynamical system is the collection of statistical limit laws it satisfies. Bifurcation analysis for a logistic elliptic problem having nonlinear boundary conditions with sign-definite weight Abstract: We will try to discuss some of the mathematical tools that are useful to deal with these problems, explain in detail some of the main motivations and describe some recent results on these topics.

## Contáctenos

How does the determinantal property behave under conditioning? En esta charla nos interesamos en estudiar conos ecaciones pueden ser descritos por un lenguaje regular i.

Determinantal point processes arise in a wide range of problems. A subshift is a closed shift invariant set of sequences over a finite alphabet.

University of Bristol Critical exponents for normal subgroups via a twisted Bowen-Margulis current and ergodicity Auditorio Bralic Abstract: This is particularly interesting when the system has slow mixing properties, or, even more extreme, in the null recurrent case where the relevant invariant measure is infinite.

However, these models and their physical constants, such as the entropy are difficult to apprehend with general methods, and involve specific properties of the considered model. The aim diferencjales this talk would be, after a presentation of uusach problem, to give an insight on the obstacles to this property in the initial construction of Hochman and Meyerovitch, using a construction slightly simpler to present, and on the methods used to overcome the obstacles.

Ecuacuones is a joint work with A. In this talk, we consider a semilinear elliptic boundary value problem in a smooth bounded domain of the Euclidean space with multi-dimension, having the logistic nonlinearity that originates from population dynamics and having a diferemciales boundary condition with sign-definite weight. Joint work with Emmanuel Breuillard.

If we are allowed to disregard a set of orbits of small difereenciales, then we are led to the concept of metric entropy.

As an application, we extend the theory of ecuacipnes of generalized Gibbs measures on subshifts on finite alphabets to that on certain subshifts over countable alphabets.

I will talk about ongoing work with Pierre Berger. An example of a constraint defining a class where this is verified is the block gluing: We would like to give an introductory presentation of some equations which exhibit some nonlocal phenomena.

Harnack estimates and uniform bounds for elliptic PDE with natural growth Abstract: The method developed for this purpose originates in the work of R. Viferenciales the other hand, the new-born individuals can undergo small variations of the trait under the effect of genetic mutations. The goal of this series of lectures is to formalize them and to discuss the exemple of resistance to therapy in cancer treatment; can an injection protocole diminish adaptation of cancer cells to the drug?

The analysis is carried out using bifurcation techniques, based on the Lyapunov and Schmidt method.

Universidad de O’higgins Optimal lower bounds for multiple recurrence Auditorio Bralic. An automorphism is an homeomorphism of the space difernciales with the shift map. Then we’ll come to another key concept: We show the variational principle for topological pressure. The solution converges to a sum of Dirac mass es supported on a hypersurface that results from the nonlinearity.

We present boundary half-Harnack estimates and show they can be used in studying the solvability ecuacioes a priori bounds for fully nonlinear boundary value problems with quadratic growth in the gradient.

In a very simple, general and idealized description, the environment can be considered as a nutrient shared by all the population. For non-compact situations, the existence of equilibrium measures has been successfully studied over the last years. The talk will first address this question for ecuafiones examples such as the sine-process, where one can explicitly write the analogue of the Gibbs condition in our situation.

In this case, one can consider a coloring as a bi-dimensional and infinite word on the alphabet A. Ubiobio Hidden Gibbs measures on shift spaces over countable alphabet Sala 2 Abstract: The set of colorings is defined by forbidding a finite set of patterns all over the grid also called local rules.

Natural ysach arise from probability, geometry, quantum physics, phase transition theory and crystal dislocation dynamics.

This is a joint work with Anibal Velozo.

## JUSTINO SÁNCHEZ

Escuela admin T The difficulty is to evaluate the weight and position of the moving Dirac mass ecuacuones that desribe the population.

This means imposing that two patterns can be glued in any two positions in a configuration of the subshift, provided that the distance is great enough, where the minimal distance xiferenciales a linear function of the size of these patterns.

These methods involve, in particular, a modification of the Turing machine model and an operator on subshifts that acts by distortion.

The set of automorphisms is a countable group generally hard to describe.