[Seminario] RECORDATORIO INVITACIÓN SEMINARIO Sistemas Dinámicos de Santiago, 01 DE ABRIL A CONTAR DE LAS 15:30 HRS.

Maria Ines Rivera mrivera en dim.uchile.cl
Lun Abr 1 08:05:12 -03 2019

Estimados Académicos(as) y Alumnos(as),

Se les recuerda que hoy  lunes 01 de abril a contar de las 15:30 hrs.   
se realizarán 2 sesiones  del *Seminario Sistemas Dinámicos de 
Santiago*, en la sala de Seminarios  John Von Neumann CMM, ubicada en la 
Torre Norte, Piso 7 de Beauchef 851.

*TIME      (Mon 1st Apr) 3:30 pm - 4:20 pm**
**SPEAKER   Sebastián Donoso (CMM, Universidad de Chile)**
**TITLE     On subsets with no arithmetic progressions**

For $N\in \mathbb{N}$, let $\nu(N)$ be the maximal cardinality of a 
subset of \{1,\ldots,N\} that contains no
arithmetic progression of length 3. Finding upper and lower bounds for 
$\nu(N)$ has been a challenging problem for decades.

In this talk I will survey this problem and present a proof of a theorem 
by Behrend in the 40's, that gave a surprising lower bound to $\nu(N)$.

*TIME      (Mon 1st Apr) 4:30 pm - 5:30 pm**
SPEAKER   Angel Pardo (CMM, Universidad de Chile)**
TITLE     Counting problem on infinite periodic billiards and 
translation surfaces**

The Gauss circle problem consists in counting the number of integer 
points of bounded length in the plane. This problem is equivalent to 
counting the number of closed geodesics of bounded length on a flat two 
dimensional torus or, periodic trajectories, in a square billiard table.
Many counting problems in dynamical systems have been inspired by this 
problem. For 30 years, the experts try to understand the asymptotic 
behavior of closed geodesics in translation surfaces and periodic 
trajectories on rational billiards. (Polygonal billiards yield 
translation surfaces naturally through an unfolding procedure.) H. Masur 
proved that this number has quadratic growth rate.
In these talk, we will study the counting problem on infinite periodic 
rational billiards and translation surfaces.
The first example and motivation is the wind-tree model, a Z^2-periodic 
billiard model. In the classical setting, we place identical rectangular 
obstacles in the plane at each integer point; we play billiard on the 
I will first present some quite precise results that are only valid for 
the wind-tree model (and some natural generalizations) and then, a 
general result which is valid for a.e. infinite periodic translation 
surfaces that uses completely different techniques: a dynamical 
analogous, for the algebraic hull of a cocycle, to strong and 
super-strong approximation on algebraic groups.

Esperando contar con su presencia, les saluda,

Ma. Inés Rivera
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