# Planned seminars

## 28/01/2021, Thursday, 14:00–15:00 Europe/Lisbon — Online

Enrico Serra, Politecnico di Torino

We consider the minimization of the NLS energy on a metric tree, either rooted or unrooted, subject to a mass constraint. With respect to the same problem on other types of metric graphs, several new features appear, such as the existence of minimizers with positive energy, and the emergence of unexpected threshold phenomena. We also study the problem with a radial symmetry constraint that is in principle different from the free problem due to the failure of the Polya-Szego inequality for radial rearrangements. A key role is played by a new Poincaré inequality with remainder.

## 04/02/2021, Thursday, 14:00–15:00 Europe/Lisbon — Online

Yvan Martel, École Polytechnique

The talk concerns stability properties of kinks for (1+1)-dimensional nonlinear scalar field models of the form $\partial_t^2 \phi - \partial_x^2 \phi + W'(\phi) = 0 \quad (t,x) \in {\bf \mathbb R}\times {\mathbb R}.$ We establish a simple and explicit sufficient condition on the potential $W$ for the asymptotic stability of a given moving or standing kink. We present applications of the criterion to some models of the Physics literature.

Work in collaboration with Michał Kowalczyk, Claudio Muñoz and Hanne Van Den Bosch.

See also the related work with Michał Kowalczyk and Claudio Muñoz.

## 11/02/2021, Thursday, 14:00–15:00 Europe/Lisbon — Online

Harbir Antil, George Mason University

Fractional calculus and its application to anomalous diffusion has recently received a tremendous amount of attention. In complex/heterogeneous material mediums, the long-range correlations or hereditary material properties are presumed to be the cause of such anomalous behavior. Owing to the revival of fractional calculus, these effects are now conveniently modeled by fractional-order differential operators and the governing equations are reformulated accordingly. Similarly, the potential of fractional operators has been harnessed in various scientific domains like geophysical electromagnetics, imaging science, deep learning, etc.

In this talk, fractional operators will be introduced and both linear and nonlinear, fractional-order differential equations will be discussed. New notions of optimal control and optimization under uncertainty will be presented. Several applications from geophysics, imaging science, and deep learning will be presented.

## 25/02/2021, Thursday, 14:00–15:00 Europe/Lisbon — Online

Boyan Sirakov, PUC - Rio
To be announced

## 04/03/2021, Thursday, 14:00–15:00 Europe/Lisbon — Online

Bozhidar Velichkov, Università di Pisa
To be announced

## 04/03/2021, Thursday, 15:00–16:00 Europe/Lisbon — Online

Dario Mazzoleni, Università di Pavia
To be announced

## 18/03/2021, Thursday, 14:00–15:00 Europe/Lisbon — Online

Gabriele Benomio, Princeton University
To be announced

## 18/03/2021, Thursday, 15:00–16:00 Europe/Lisbon — Online

Shrish Parmeshwar, University of Bath
To be announced