Schedule: Wednesday, Dec 22nd, 2021 at 11:30 CET

The event will take place in Room A1.6 ("Alan Turing" building) and will be streamed via Webex, following the link https://univaq.webex.com/univaq/j.php?MTID=mb303d977d9fed32f1f1bf45af3540688
(Meeting number: 2734 718 9690; password: gAx3fr2HV8U).

Speakers: Dr. Diego Alberici, Dr. Michele Palladino, and Dr. Mario Santilli
Department of Information Engineering, Computer Science, and Mathematics, University of L'Aquila)

Diego Alberici, A multi-bath stationary measure: possible connections with spin glass theory and high-dimensional inference

Abstract: After a short presentation of my research in different areas of Statistical Mechanics (monomer-dimer models, deep Boltzmann machines, and multi-bath Langevin dynamics), I will focus on recent results about convergence of multi-bath dynamics to a stationary non-equilibrium measure. This (explicit) measure is related to the scheme proposed by F. Guerra to prove the validity of Parisi solution for the S-K spin glass model. In a joint work with N. Macris and E. Mingione we have considered two finite subsystems -coupled by a potential V(x,y)- which evolve with wildly different time-scales, in contact with two thermal baths. We have shown that when the potential satisfies two suitable logarithmic Sobolev inequalities, the long-time behaviour of the finite system is described by the aforementioned measure. Examples and open problems related to spin glass theory and high-dimensional inference will be discussed.

Michele Palladino, Optimal Control of the Moreau’s Sweeping Process

Abstract: In this talk, we will present some recent and new results on the optimal control of the Moreau’s Sweeping Process (SP). In particular, we will present a novel approach for proving a version of the Pontryagin Maximum Principle in a quite general setting. Such an approach exploits a kind of small-time local controllability property that the SP dynamics naturally satisfies in a neighborhood of the moving constraint. Open problems and further research directions will be extensively discussed.

Mario Santilli, The Alexandrov soap bubble theorem for singular hypersurfaces

Abstract: A remarkable result of Alexandrov shows that a compact and embedded smooth hypersurface in the Euclidean space is a sphere, provided its scalar mean curvature is a constant function. The aim of this talk is to discuss some generalizations of this result to a general class of  hypersurfaces arising in convex and integral geometry. These hypersurfaces can have a priori complicated singular sets. We also mention analogous generalizations in the anisotropic setting.

Bio sketch: Mario Santilli is a mathematician working in Geometric Measure Theory, Geometric Analysis and Convex Geometry. He received his bachelor degree (2010) and master degree (2013) at the University of L'Aquila. He held a position of research-student at the Max Plank Institute for Gravitational Physics (2013-2017) and he received the PhD-degree from University of Potsdam (Germany) in 2017 under the guidance of Prof. Ulrich Menne and Jan Metzger. Afterwards, he held a post-doctoral position at the University of Augsburg (Germany) from November 2017 until September 2021. From October 2021 he is an RtdB at the University of L'Aquila.