13h às 14h
Uma nova perspectiva para a Computação Visual: Do clássico ao cognitivo
Luiz Velho (IMPA)
Resumo: Nesta palestra, destacamos a necessidade de um novo modelo de Computação Visual adequado para a era da Inteligência Artificial. Iniciamos apresentando uma perspectiva histórica do campo e, em seguida, argumentamos que o modelo matemático clássico de câmera deve ser atualizado para incorporar noções perceptuais inspiradas no olho humano. Concluímos esboçando direções para pesquisas futuras a fim de alcançar esses objetivos.

14h às 15h
Phase Retrieval and Partial Differential Equations
João Pedro Ramos (IMPA)
Abstract: In general terms, whenever we speak about ‘phase retrieval’, we refer to recovering a function f belonging to a special class, modulo multiplicative constants, from measurements of the form |Tf|, where T is an operator related to the problem at hand.
In spite of the purely mathematical interest in such problems, problems of phase retrieval-type have been of utmost importance in several applied areas, such as mathematical physics, signal processing and crystallography.
In this talk, we shall see how phase retrieval in such applied contexts translates into precise mathematical objects. In particular, we shall investigate the particular case of the Pauli problem, where one attempts to recover f modulo multiplicative constants from |f| and |\widehat{f}|.
As it turns out, this problem has a direct relationship to the Schrödinger equation and the related problem of phase retrieval for such equation. We shall explore recent partial progress in thise problems and, time permitting, investigate the phase retrieval problem for several other partial differential equations.

15h às 15h:30min - Coffee Break

15h30min às 16h30min
Around the Birch and Swinnerton-Dyer Conjecture for abelian varieties defined over finitely genereted fields in characteristic p>0
Amilcar Pacheco (UERJ)
Abstract: Starting from Tate's seminal Bourbaki seminar from 1966, where he proposed an analogue for the Birch and Swinnerton-Dyer conjecture for abelian varieties over one variable function fields over finite fields, we will develop the discussion of its extension to the case where instead of considering the function field of a curve, we take the function field of a variety over a finite field. We give a necessary and sufficient condition for the equality between the algebraic and the analytic ranks of the abelian variety. We also propose a formula for the special value of the L-function of the abelian variety, which encodes interesting information that do not appear in the 1-dimensional case.