CMAFcIO

Homogenization of Schrödinger equations. Extended Effective Mass Theorems for non-crystalline matter.

Speakers: Wladimir Neves (Universidade Federal do Rio de Janeiro).

In this talk, we study the homogenization of the Schrödinger equation beyond the periodic setting. More precisely, rigorous derivation of the effective mass theorems in solid state physics for non-crystalline materials are obtained.

This is a joint work with Vernny Ccajma and Jean Silva.

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Quantitative translations for viscosity approximation methods

Speaker: Pedro Pinto (Technische Universitat Darmstadt).

Abstract: Proof mining is a research program that employs proof theoretical tools to obtain additional information from mathematical results, [1]. Its techniques have been applied successfully to many areas of Mathematics with special focus on Nonlinear Analysis. This presentation reports ongoing joint work with Ulrich Kohlenbach.

Standing wave and travelling wave solutions for a fourth order Schrödinger equation

Speaker: Jean-Baptiste Casteras (CMAFcIO, Universidade de Lisboa).

In this talk, we will be interested in standing wave solutions to a fourth order nonlinear Schrödinger equation having second and fourth order dispersion terms. This kind of equation naturally appears in nonlinear optics. In a first time, we will establish the existence of ground-state and renormalized solutions. We will then be interested in their qualitative properties, in particular their stability.

Bealer's Intensional Logic (Part II)

Speaker: Clarence Protin.

Abstract: Many intuitively valid arguments involving intensionality cannot be captured by first-order logic, even when extended by modal and epistemic operators.

Indeed, previous attempts at providing an adequate treatment of the phenomenon of intensionality in logic and language, such as those of Frege, Church, Russell, Carnap, Quine, Montague and others are fraught with numerous philosophical and technical difficulties and shortcomings.

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