Seminari/Colloquia
Pagina 39
Date  Type  Start  End  Room  Speaker  From  Title 

16/11/20  Seminario  14:00  15:00  Isaia Nisoli  Universidade Federal de Rio de Janeiro (Brasile)  DinAmicI: Another Internet Seminar (DAI Seminar)  in streaming mode  (see the instructions in the abstract)
In this talk I will present a family of one dimensional systems with random additive noise such that, as the noise size increases, the Lyapunov exponent of the stationary measure transitions from positive to negative. This phenomena is known in literature as Noise Induced Order, and was first observed in a model of the BelosouvZhabotinsky reaction and its existence was proven only recently by GalatoloMongeNisoli. In the talk I will show how this phenomena is strictly connected with nonuniform hyperbolicity and the coexistence of regions of expansion and contraction in phase space; the result is attained through a result on the continuity of the Lyapunov exponent of the stationary measure with respect to the size of the noise.
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.  
12/11/20  Seminario  16:00  17:00  Stefano Marò  Università di Pisa  DinAmicI: Another Internet Seminar (DAI Seminar)  in streaming mode  (see the instructions in the abstract)
We consider the free motion of a point particle inside a circular billiard with periodically moving
boundary, with the assumption that the collisions of the particle with the boundary are elastic so that the
energy of the particle is not preserved. It is known that if the motion of the boundary is regular enough
then the energy is bounded due to the existence of invariant curves. We show that it is nevertheless possible
that the motion of the particle is chaotic, also under regularity assumptions for the moving boundary. More
precisely, we show that there exists a class of functions describing the motion of the boundary for which
the billiard map admits invariant probability measures with positive metric entropy. The proof relies on
variational techniques based on AubryMather theory. Joint work with Claudio Bonanno.
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.  
12/11/20  Seminario  14:00  15:00  Claudianor Alves  Università Federale di Campina Grande (Brasile)  Supercritical Neumann problems on unbounded domains
In this paper, by making use of a new variational principle, we prove existence of nontrivial solutions for two different types of semilinear problems with Neumann boundary conditions in unbounded domains. Namely, we study elliptic equations and Hamiltonian systems on the unbounded domain $Omega=R^{m} imes B_r$ where $B_r$ is a ball centered at the origin with radius $r$ in $mathbb{R}^{n}$. Our proofs consist of several new and novel ideas that can be used in broader contexts. This is a joint work with Abbas Moameni that was accepted for publication in Nonlinearity.
N.B.: this talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006.
 
05/11/20  Seminario  16:30  17:30  Adrian Perez Bustamante  Georgia Institute of Technology  Gevrey estimates and domains of analyticity for asymptotic expansions of tori in weakly dissipative systems
We consider the problem of following quasiperiodic tori in perturbations of some Hamiltonian systems which involve friction and external forcing. In a first goal, we use different numerical methods (Pade approximants, Newton continuation till boundary) to obtain numerically the domain of convergence. We also study the properties of the asymptotic series of the solution. In a second goal, we study rigorously the (divergent) series of formal expansions of the torus obtained using Lindstedt method. We show that, for some systems in the literature, the series is Gevrey. We hope that the method can be of independent interest: we develop KAM estimates for the divergent series. In contrast with the regular KAM method, we lose control of all the domains, so that there is no convergence, but we can generate enough control to show that the series is Gevrey.
This is joint work with R. Calleja and R. de la Llave.
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).
 
05/11/20  Colloquium  14:30  15:30  Fabrizio Catanese  Universitat Bayreuth  Nodal surfaces, coding theory, and cubic discriminants  
27/10/20  Seminario  14:00  15:00  1201 Dal Passo  Erik Tonni  SISSA 
Modular Hamiltonians for the massless Dirac field in the presence of a boundary or of a defect
The reduced density matrix of a spatial subsystem can be written as the exponential of the modular Hamiltonian, hence this operator contains a lot of information about the entanglement of the corresponding spatial bipartition. First we consider the massless Dirac field on the halfline, imposing the most general boundary conditions that ensure the global energy conservation. This leads to two inequivalent phases where either the vector or the axial symmetry is preserved. In these two phases, we discuss the analytic expressions for the modular Hamiltonians of an interval on the halfline when the system is in its ground state, for the corresponding modular flows of the Dirac field and for the corresponding modular correlators. The method allows to obtain analytic expressions also for the modular Hamiltonians, the modular flows and the modular correlators for two disjoint equal intervals at the same distance from a pointlike defect characterised by a unitary scattering matrix, that allows both reflection and transmission.

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