Por José Oliveira (Universidade do Minho).

An Informal Workshop on Differential Equations and Algebraic Geometry (February 18th - February 22nd 2019).

Alin Bostan, INRIA
Duco van Straten, Mainz
Eric Delaygue, Lyon
Fernando Rodriguez Villegas, ICTP
Herwig Hauser, Viena
Julien Roques, Grenoble
Michael Wibmer, Notre Dame
Orlando Neto, Lisboa

An Informal Workshop on Differential Equations and Algebraic Geometry (January 28th - February 1st 2019).

First talk is an introductory talk by N. Katz.

The program is decided every day. This is an interactive workshop.

Nicholas Katz, Princeton
Antonio Rojas, Sevilla
Francisco Calderon, Sevilla
Herwig Hauser, Viena
Luis Narvaez, Sevilla
Orlando Neto, Lisboa
Pedro C. Silva, Lisboa

Por Vladimir I. Man'ko (Lebedev Institute, Russian Academy of Sciences).

Por José Oliveira (Universidade do Minho).

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.

Por Maurício Misquero (Universidade de Granada).

Por Harbir  Antil (George Mason University).

Por Marcel Xavier (LNCC, Petropolis, Brasil).

Abstract: The topological derivative is a scalar field that measures the sensitivity of a given shape functional with respect to an infinitesimal singular domain perturbation, such as the insertion of holes, inclusions, source-terms or even cracks. In this work, the concept of topological derivative is applied in the context of damage and fracture mechanics. In particular, the nucleation and propagation damaging process are studied.

Por Riccardo Scala (University of Rome 1, “La Sapienza”).

Abstract: We introduce the notion of area of the graph of a smooth function and the definition of the corresponding relaxed functional. We discuss some issues related to determine the domain and the exact value of it on singular maps. Finally we show how this question is related to Plateau-type problems with mixed boundary conditions and how to solve it in some specific cases.