New Faculty Seminars

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
(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.

Bio sketch: Diego Alberici got his PhD in Bologna in 2016 after a short research period at Princeton. He spent the last two years of postdoc at EPFL, before becoming a type B researcher in L'Aquila. His research deals with Statistical Mechanics, or collective behaviors that emerge in systems composed of a large number of interacting entities. In his research he covered several topics: monomer-dimer models, spin glasses, Boltzmann machines, multi-temperature dynamics. The investigation in the direction of rigorous results give him also the opportunity to move through different areas of mathematics, such as Probability Theory and Functional Analysis.

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.

Bio sketch: Michele Palladino is Assistant Professor at University of L'Aquila - Department of Information Engineering, Computer Science and Mathematics (DISIM). He obtained a BSc in Mathematics and a MSc in Applied Mathematics at the Sapienza University of Rome in 2009 and 2011, respectively. As a recipient of a Marie Curie fellowship in the ITN-SADCO framework, he joined the Control and Power group at Imperial College in 2012 and he obtained his PhD degree in Control Theory under the supervision of Prof Richard Vinter in 2015. His work “Regularity of the Hamiltonian along the Optimal Trajectories” (in collaboration with Prof Richard Vinter) has been awarded with the “SIAM Control and Optimization Best Paper Prize” in 2017. His current research interests are in optimal control and partial differential equations with applications to mathematical biology and machine learning.

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.

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