Dipartimento di Matematica -UTV-

Date	Type	Start	End	Room	Speaker	From	Title
14/01/21	Seminario	14:00	15:00		Matteo Muratori	Politecnico di Milano	Nonlinear diffusion equations on noncompact manifolds and relations with stochastic completeness Abstract The talk is based on joint projects with G. Grillo, K. We prove that the mass conservation property for the heat flow on a complete, connected, noncompact Riemannian manifold $M$, namely stochastic completeness, is equivalent to the uniqueness of nonnegative bounded solutions for a certain class of nonlinear evolution equations. Such a connection was well known in the pure linear case only, i.e. for the heat equation itself. Here we consider equations of the type of $u_t=Delta(phi(u))$, where $phi$ is any nonnegative, concave, increasing function, $C^1$ away from the origin and satisfying $ phi(0)=0 $. We provide optimal criteria for uniqueness/nonuniqueness of nonnegative, bounded (distributional) solutions taking general nonnegative, bounded initial data $u_0$. In particular our results apply to the fast diffusion equation $u_t=Delta(u^m)$ (where $m in (0,1)$), and they show that there is a large class of manifolds in which uniqueness actually fails. This is in sharp contrast, for instance, with the Euclidean case, where existence and uniqueness hold for merely $L^1_{loc}$ initial data thanks to the theory developed by M.A. Herrero and M. Pierre in the '80s. We will also address existence/nonexistence of nonnegative, nontrivial, bounded solutions to a strictly related nonlinear elliptic equation and, if time allows, some work in progress devoted to removing the concavity assumption. The talk is based on joint projects with G. Grillo, K. Ishige and F. Punzo. MS Teams Link for the streaming Note: This talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006
02/01/21	Seminario	15:10	19:12	27	Prova	Prova	Prova Abstract Prova
18/12/20	Seminario	14:30	16:30		Terza Giornata DinAmica	DinAmicI on-line workshop	(See Abstract below for the schedule) Abstract 14:30 - Sara Di Ruzza (Università degli studi di Padova, Italy), Italy) Symbolic dynamics in a binary asteroid system. 15:30 Emanuele Haus (Università Roma Tre, Italy) Normal form and existence time for the Kirchhoff equation. Note: The abstracts of the talks and the zoom link for the streaming are posted on http://daiday2020.unisalento.it/.
17/12/20	Seminario	16:30	17:30		Giuseppe Pucacco	Università di Roma "Tor Vergata"	Normal forms for the Laplace resonance Abstract We describe a comprehensive model for systems locked in the Laplace resonance. The framework is based on the simplest possible dynamical structure provided by the Keplerian problem perturbed by the resonant coupling truncated at first order in the eccentricities. The reduced Hamiltonian, constructed by a transformation to resonant coordinates, is then submitted to a suitable ordering of the terms and to the study of its equilibria. Henceforth, resonant normal forms are computed. The main result is the identification of two different classes of equilibria. In the first class, only one kind of stable equilibrium is present: the paradigmatic case is that of the Galilean system. In the second class, three kinds of stable equilibria are possible and, at least one of them, is characterised by a high value of the forced eccentricity for the 'first planet': here the paradigmatic case is the exo-planetary system GJ-876. The normal form obtained by averaging with respect to the free eccentricity oscillations, describes the libration of the Laplace argument for arbitrary amplitudes and allows us to determine the libration width of the resonance. This activity is made in collaboration with the Departments of Mathematics of the Universities of Milano, Padova, Pisa and Roma Tor Vergata (Excellence Department project MATH@TOV).
17/12/20	Seminario	14:30	16:30		Terza Giornata DinAmica	DinAmicI on-line workshop	(See Abstract below for the schedule) Abstract 14:30 - Nicola Guglielmi (Gran Sasso Science Institute, Italy) Approximating Lyapunov exponents of switching systems. 15:30 Anna Florio (Sorbonne Universite, France) Spectral rigidity of contact 3D Axiom A flows. Note: The abstracts of the talks and the zoom link for the streaming are posted on http://daiday2020.unisalento.it/.
17/12/20	Seminario	14:00	15:00	1200 Biblioteca Storica	Vitaly Moroz	Swansea University	Asymptotic profiles of groundstates for a class of Choquard equations Abstract We study the asymptotic behaviour of groundstates for a class of singularly perturbed Choquard type equations with a local repulsion term. We identify seven different asymptotic regimes and provide a characterisation of the limit profiles of the groundstates when perturbation parameter is small. We also outline the behaviour of groundstates when perturbation is strong. This is a joint work with Zeng Liu (Suzhou, China). Seminario online su questo link.
14/12/20	Seminario	16:00	17:00		Edoardo Persichetti	Florida Atlantic University	Code-based Cryptography and Post Quantum Standardization Abstract Code-based cryptography has emerged as one of the strongest candidate to replace current cryptographic standards based on classical number theory problems such as RSA and El Gamal. In this talk, I will give an overview of the area, and describe some of my work towards the design of secure and efficient post-quantum primitives. This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV. It is also part of the series of seminars "De Cifris Schola Latina" on cryptography. The talk will be streamed on Teams. This is the link.
14/12/20	Seminario	13:00	14:00		Michele Salvi	Università di Roma "Tor Vergata"	Scale-free percolation in continuous space Abstract The scale-free percolation random graph features three fundamental properties that are often present in large real-world structures (social networks, communication networks, inter-banking system and so on), but which are never present at once in classical models: (1) Scale-free: the degree of nodes follows a power law; (2) Small-world: two nodes are typically at a very small graph distance; (3) Positive clustering coefficient: two nodes with a common neighbour have a good chance to be linked. We study a continuous version of scale-free percolation and its possible application to the statistical analysis of a dataset provided by the French Ministry of Agriculture. We discuss some stochastic processes (random walks and particle systems) on this kind of structures with the final goal of understanding how an epidemic would spread.
10/12/20	Seminario	16:00	17:00		Carlangelo Liverani	Università di Roma "Tor Vergata"	DinAmicI: Another Internet Seminar (DAI Seminar) Locating Ruelle-Pollicott resonances - in streaming mode - (see the instructions in the abstract) Abstract We study the spectrum of transfer operators associated to various dynamical systems. Our aim is to obtain precise information on discrete spectrum. To this end we propose a unitary approach. We consider various settings where new information can be obtained following different branches along the proposed path. These settings include affine expanding Markov maps, uniformly expanding Markov maps, non-uniformly expanding maps, hyperbolic diffeomorphisms. We believe this to be the germ of a general theory. Joint work with O. Butterley and N. Kiamari. Note: The zoom link to the seminar will be posted on the DinAmicI website and on Mathseminars.org. Moreover, it will be also streamed live via the youtube DinAmicI channel.
10/12/20	Seminario	14:00	15:00		Gabriele Benedetti	Ruprecht-Karls-Universitat Heidelberg	Strong magnetic fields on surfaces: trapped motions and fully periodic systems Abstract It is a central problem in experimental physics to design magnetic fields that trap charged particles in a region of space. In this talk, we show how to use the KAM theorem to trap particles constrained on a surface if the magnetic field is strong and certain non-degenerate conditions on the field or on the curvature of the surface are satisfied. Using similar ideas we show that the motion of a particle in a strong magnetic field is periodic for every initial condition if and only if the field is constant and the surface has constant curvature. This is joint work with Luca Asselle. The talk is part of the activity of the MIUR Department of Excellence Project CUP E83C18000100006.