# Seminarios

2018-01-15
16:30hrs.
Seminario de Sistemas Dinámicos
Piere Berger. Paris Xiii
The Herman positive entropy conjecture
Abstract:
We show that any sympletic $C^\infty$-diffeomorphism which displays a
non-hyperbolic periodic point can be $C^\infty$-approximated by a
symplectic one whose metric entropy is positive.

The proof involves developments of the concept of universal dynamics,
some developments of Katok, Przytycki, Arroyo-Pujals examples, and new
techniques to ensure that up to the composition with a map of the form
$(x,y)\mapsto (x,y+\phi(x))$
with $\phi$ small, some heteroclinic links can be restored (i.e. the
stable and unstable manifolds of some hyperbolic periodic points
coincide).

Joint work with Dimitry Turaev.
Sala 1, PUC
2018-01-09
15:00hrs.
Luis Fredes. Bordeaux
Invariant mesures of discrete interacting particle systems: algebraic aspects
Abstract:
We consider a continuous time particle system on a graph L being either Z,  Z_n, a segment {1,…, n}, or Z^d, with state space Ek={0,…,k-1} for some k belonging to {infinity, 2, 3, …}. We also assume that the Markovian evolution is driven by some translation invariant local dynamics with bounded width dependence, encoded by a rate matrix T. These are standard settings, satisfied by many studied particle systems. We provide some sufficient and/or necessary conditions on the matrix T, so that this Markov process admits some simple invariant distribution, as a product measure, as the distribution of a Markov process indexed by Z or {1,…, n} (if L=Z or {1,…,n}), or as a Gibbs measure (if L=Z_n). These results are mainly obtained with some manipulations of finite words, with alphabet Ek, representing subconfigurations of the systems. For the case L=Z, we give a procedure to find the set of invariant i.i.d and Markov measures.
Sala John Von Neumann, 7mo piso, CMM http://nm.cmm.uchile.cl/seminarios/
2018-01-05
12:00 hrs.
Seminario Agco
Kurt Melhorn. Instituto Max-Planck de Informática
Markets and Fair Division of Goods
República 779 B, Sala 3er Piso.http://www.dii.uchile.cl/acgo/seminar-acgo/
2018-01-03
14:30 hrs.
Seminario Agco
Alfredo Torrico. Gatech
Robust Submodular Maximization: Offline and Online algorithms
República 779 B, Sala 3er Piso. http://www.dii.uchile.cl/acgo/seminar-acgo/