Vincenzo Vespri, Università di Firenze, Simulation of the chaos of the financial market through dynamical systems, Monday, November 30, 2020, time 15:30, Webex: Franco Tomarelli personal room
Abstract:Abstract:
We will follow the fractal market approach to simulate the chaos of the behaviour of the financial markets. We will use also some hypotheses of the behavioural finance.

Nicolò De Ponti, Università degli Studi di Pavia, Entropy-Transport distances between measures and metric measure spaces, Tuesday, Febraury 11, 2020, time 15:15, Aula seminari 3° piano
Abstract:Abstract:
After providing the necessary background material, we describe a class of distances coming from optimal Entropy-Transport problems, a recent generalization of optimal transport where also creation and destruction of mass is taken into account. Inspired by previous work of Gromov and Sturm, we then use these metrics to construct new meaningful distances between metric measure spaces with finite mass. This talk is based on a joint collaboration with Andrea Mondino and Giuseppe Savaré.

Giuseppe Maria Coclite, Politecnico di Bari, Nonlinear Peridynamic Models, Wednesday, January 22, 2020, time 15:15, Sala Consiglio 7° piano
Abstract:Abstract:
Some materials may naturally form discontinuities such as cracks as a result of scale effects and long range interactions. Peridynamic models such behavior introducing a new nonlocal framework for the basic equations of continuum mechanics. In this lecture we consider a nonlinear peridynamic model and discuss its well-posedness in suitable fractional Sobolev spaces. Those results were obtained in collaboration with S. Dipierro (Perth), F. Maddalena (Bari) and E. Valdinoci (Perth).

Matteo Cozzi, University of Bath, Long-time asymptotics for evolutionary crystal dislocations models, Tuesday, December 17, 2019, time 15:30, Aula seminari 3° piano
Abstract:Abstract:
In this talk, I will discuss a recent result concerning the long-time behavior of solutions to evolutionary Peierls-Nabarro type equations, related to crystal dislocations. I will present the construction of solutions that, at large times, behave like a superposi- tion of an arbitrary finite number of fundamental dislocations, equally oriented and centered near points that evolve according to a repulsive dynamical system. This result has been obtained in collaboration with J. D ?avila and M. del Pino (University of Bath).

Matteo Caggio, Università degli Studi dell'Aquila, On the highly compressible limit for the Navier-Stokes-Korteweg model with density dependent viscosity, Tuesday, November 12, 2019, time 14:30, Aula seminari 3° piano
Abstract:Abstract:
We investigate the regime of high Mach number flows for compressible barotropic fluids with density dependent viscosity. The Korteweg model as an isothermal model of capillary and quantum compressible fluids is considered. A weak-strong uniqueness analysis is also discussed.

Hugo Tavares, Universidade de Lisboa, Sharp concentration estimates near criticality for sign-changing solutions of Dirichlet and Neumann problems, Tuesday, November 12, 2019, time 15:30, Aula seminari 3° piano
Abstract:Abstract:
Consider the slightly subcritical problem $-\Delta u_\varepsilon = |u_\varepsilon|^{\frac{4}{n-2}-\varepsilon}u_\varepsilon$ either on $\mathbb{R}^n$ ($n\geq 3$) or in a ball $B$ satisfying Dirichlet or Neumann boundary conditions. For radial solutions, we provide sharp rates and constants describing the asymptotic behavior (as $\varepsilon\to 0$) of all local minima and maxima of $u_\varepsilon$ as well as its derivative at roots. As corollaries, we complement a known asymptotic approximation of the Dirichlet nodal solution in terms of a tower of bubbles and present a similar formula for the Neumann problem. Moreover, we analyse the nonradial case with Neumann boundary conditions, namely the existence of least energy solutions and their dependence on the exponent $p$ up to the Sobolev critical exponent. These are joint works with Alberto Saldaña and Massimo Grossi.