**Prof. Sara Daneri (GSSI)**

*Title: Energy driven pattern formation: an exploration into the mechanisms of self-made order.*

Abstract:

Patterns, intended as ordered regular structures, are ubiquitous in nature. At micro- and mesoscopic scale ordered structures spontaneously emerge in a surprisingly diverse set of physical and chemical systems and they usually form simple structures with some degree of regularity, such as "bubbles" or "lamellar/striped patterns". One of the leading mechanisms at the base of pattern formation at such scale is since decades recognized to be the competition between short-range attractive forces (favoring pure phases) and long-range repulsive interactions (favoring instead oscillations between different phases). Despite the numerous numerical and experimental studies on the subject, the mathematical mechanisms behind the formation of regular periodic structures is still in most physical cases poorly understood. Two main difficulties reside in the nonlocality of the interactions and in the phenomenon of symmetry breaking, namely the fact that the ground states of such systems have less degrees of symmetry than the energy they minimize. In this talk we will give an overview of the main open problems in the field and discuss some recent results in which symmetry breaking and pattern formation have been rigorously proved.

**Dr. Lorenzo Tamellini (CNR-IMATI Pavia)**

*Title: Forward and inverse uncertainty quantification for PDE/ODE with random coefficients*

Abstract:

In this talk we briefly discuss forward and inverse uncertainty quantification (UQ) problems arising in engineering and computational sciences. We focus on two practical examples (one for forward UQ and one for inverse UQ) and illustrate for each problem a) the kind of results that can be obtained, b) the methods used in each case, and c) some of the issues that might come up along the way.

The forward UQ problem is a naval engineering problem, that we tackled with a multi-fidelity approach to reduce computational costs. Here, one relevant problem to solve is the impact of the "noise" introduced by the RANS solver in the evaluations of quantities of interest of the analysis (specifically, the hydrodynamic resistance of a ferry).

The inverse UQ problem is the tuning of the uncertain parameters of a non-linear system of ODEs (specifically the SIR model, which is the famous prototype for more complex models used in epidemiology), to reliably predict the long-term behavior of the system. Here, the most relevant problem is the so-called "identifiability" of the parameters, which renders the inverse UQ approach a bit trickier than what one might expect.

There will be a small break of 10 minutes between the two talks.