<br> 14:30 - <strong>Sara Di Ruzza</strong> (Università degli studi di Padova, Italy), Italy) <br> <em> Symbolic dynamics in a binary asteroid system.</em> <br> 15:30 <strong>Emanuele Haus</strong> (Universit&agrave; Roma Tre, Italy) <br> <em>Normal form and existence time for the Kirchhoff equation.</em> <br> <br> <strong> Note: </strong> The abstracts of the talks and the zoom link for the streaming are posted on <a href="http://daiday2020.unisalento.it/"> http://daiday2020.unisalento.it/</a>.

<br> 14:30 - <strong>Nicola Guglielmi</strong> (Gran Sasso Science Institute, Italy) <br> <em> Approximating Lyapunov exponents of switching systems.</em> <br> 15:30 <strong>Anna Florio</strong> (Sorbonne Universite, France) <br> <em>Spectral rigidity of contact 3D Axiom A flows. </em> <br> <br> <strong> Note: </strong> The abstracts of the talks and the zoom link for the streaming are posted on <a href="http://daiday2020.unisalento.it/"> http://daiday2020.unisalento.it/</a>.

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). <b> Seminario online su <a href="https://teams.microsoft.com/l/meetup-join/19%3a7f273a2aff1145dfae91372d186b1cd9%40thread.tacv2/1606733297311?context=%7b%22Tid%22%3a%2224c5be2a-d764-40c5-9975-82d08ae47d0e%22%2c%22Oid%22%3a%22d37d6fea-2e4d-4c35-88e4-99bf4cf68fe9%22%7d"> questo link</a>. </b>

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).

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. <br> <br> 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. <br> <br> The talk will be streamed on Teams. <a href="https://teams.microsoft.com/l/meetup-join/19%3ameeting_MDIxZDQyNWMtZTExNi00NTVjLTk1ZDItMDJjNGZhMjczNjJi%40thread.v2/0?context=%7b%22Tid%22%3a%2224c5be2a-d764-40c5-9975-82d08ae47d0e%22%2c%22Oid%22%3a%22c4733e0c-f6c1-43fc-9f2a-e36dbb12a33f%22%7d">This is the link</a>.

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.

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. <br> <br> <strong> Note: </strong> <em> </strong> <em> The zoom link to the seminar will be posted on the <a href="https://www.dinamici.org/dai-seminar/"> DinAmicI website </a> and on <a href="https://mathseminars.org/seminar/DinAmicI"> Mathseminars.org</a>. Moreover, it will be also streamed live via the youtube <a href="https://www.youtube.com/channel/UCyNNg155G3iLS7l-qZjboyg"> DinAmicI channel</a>. </em> </em>

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.

Lie theory, which deals with smooth groups of transformations, is one of the cornerstones of mathematics and has great importance for both theory and applications. It is also visibly limited, as the globe of Lie groups has been explored and inhabited. However, in recent years, some new geometric and algebraic structures have been recognized as being as good as Lie groups in every respect, including e.g. their contribution to the supply of special functions. My goal in this talk will be to explain where these new avenues of Lie theory lead. <br> <br> <strong> Note: </strong> <em> </strong> <em> This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006 </em> </em> <br> <br> <a href="https://teams.microsoft.com/l/meetup-join/19%3a2a9a822955b54ca39f77f84130804b56%40thread.tacv2/1606245840781?context=%7b%22Tid%22%3a%2224c5be2a-d764-40c5-9975-82d08ae47d0e%22%2c%22Oid%22%3a%229bfb10cf-6b03-47dc-906c-d23eb368824c%22%7d"> Link for the streaming (via Teams) </a>

Defining entropy on noncompact metric spaces is a tricky business, since there are several natural and nonequivalent generalizations of the usual notions of entropy for continuous maps on compact spaces. By defining entropy for transcendental maps on the complex plane as the sup over the entropy restricted to compact forward invariant subsets, we prove that with this definition the entropy of such functions is infinite. The proof relies on covering results which are distinctive to holomorphic maps. <br> <br> <strong> Note: </strong> <em> </strong> <em> The zoom link to the seminar will be posted on the <a href="https://www.dinamici.org/dai-seminar/"> DinAmicI website </a> and on <a href="https://mathseminars.org/seminar/DinAmicI"> Mathseminars.org</a>. Moreover, it will be also streamed live via the youtube <a href="https://www.youtube.com/channel/UCyNNg155G3iLS7l-qZjboyg"> DinAmicI channel</a>. </em> </em>