11h30 - 12h00

António Goucha

Phaseless rank and amoebas

Abstract: The phaseless rank of a nonnegative matrix M is defined to be the least k for which there exists a complex matrix N such that |N|=M, entrywise speaking. In optimization terms, it is the solution to the rank minimization of a matrix under phase uncertainty on the entries. This concept has a strong connection with some algebraic objects, called amoebas. An algebraic amoeba is the image of an algebraic variety under the absolute value map. In this talk we state some results related to phaseless rank and explore its connection with amoebas.

Lunch Break

13h30 - 14h15

Rúben Sousa

Product formulas, generalized convolutions and integral transforms

Abstract: It is well-known that the ordinary convolution is closely related with the Fourier transform. It is therefore natural to ask: for other important integral transforms, can we define generalized convolution operators having analogous properties? Actually, the answer depends on the existence of a product formula for the kernel of the integral transform. In this talk, I will explain the general connection between product formulas, generalized convolutions and integral transforms. I will report on recent progress in constructing the product formula and convolution associated with the index Whittaker transform. Some applications will be presented, and the probabilistic motivation behind this work will be discussed.

14h15 - 15h00

Jorge Soares

A tour in Extreme Value Laws

Abstract: In this talk, we analyse the stochastic process that arises from a dynamical system by evaluating an observable function along a given orbit of the system. Our goal is to give sufficient conditions for the existence of an Extreme Value Law for the considered process. We will present an example where the observable function is maximized in a Cantor Set and we will prove the existence of an Extreme Value Law with Extremal Index less than 1.

António Goucha is a PhD student of the Joint PhD Program UC|UP, working at the University of Coimbra, in Optimization, under the supervision of Professor João Gouveia.

Rúben Sousa is a PhD student of the Joint PhD Program UC|UP, working at the University of Porto, in Analysis, under the supervision of Professor Semyon Yakubovich (Univ. Porto) and Professor Manuel Guerra (Univ. Lisboa).

Jorge Soares is a PhD student of the Joint PhD Program UC|UP, working at the University of Porto, in Dynamical Systems, under the supervision of Professor Jorge Milhazes de Freitas.