Some fixed points for a dynamical system on a probability space

Por Alexandre T. Baraviera (IME-Universidade Federal do Rio Grande do Sul).

In this talk we revisit a model introduced by Marchetti and Perez in order to understand in a rigorous way a renormalization group approach for the Coulumb gas on the lattice; the model  corresponds to a map (depending on a parameter \beta)  on the probabilities defined on the integers. Our goal is to provide another approach for the existence of  non trivial fixed  points of this map when the parameter \beta is smaller than a certain critical value.

Stabilised/Nitsche’s method for Contact Problems

Por Juha Videman (CAMGSD, Instituto Superior Técnico).

Abstract: Stabilization of mixed finite element methods for saddle point problems is a well-established technique that allows one to use finite element spaces that do not satisfy the Babuska-Brezzi condition. They were introduced and analysed in 80’s by Hughes, Franca, Brezzi, Pitkäranta and others. The analysis has, however, suffered from the fact that full regularity of the exact solution needs to be assumed.

From ultrafilters to compactness

Por Pedro Filipe (Instituto Superior Técnico, Universidade de Lisboa).

Abstract: The compactness theorem is one of the key ingredients used in Lindstrom's Theorem that characterizes first-order logic and follows directly from Godel's completeness theorem, given the finite nature of proofs. In time, alternative proofs were found that don't require the usage of a formal proof system. In this seminar we will show one of these alternative proofs using ultrafilters and ultraproducts.