| 03/02/21 | Seminario | 16:00 | 17:00 | | Vincenzo Morinelli | Tor Vergata |
Covariant homogeneous nets of standard subspaces
- in streaming mode -
(see the instructions in the abstract)
In Algebraic Quantum Field Theory (AQFT), a canonical algebraic construction of the fundamental free field models was provided by Brunetti Guido and Longo in 2002. The Brunetti-Guido-Longo (BGL) construction relies on the identification of spacetime regions called wedges and one-parameter groups of Poincaré symmetries called boosts, the Bisognano-Wichmann property and the CPT-theorem. The last two properties make geometrically meaningful the Tomita-Takesaki theory.
In this talk we recall this fundamental structure and explain how the one-particle picture can be generalized. The BGL-construction can start just by considering the Poincaré symmetry group and forgetting about the spacetime. Then it is natural to ask what kind of Lie groups can support a one-particle net and in general a QFT. Given a Z_2-graded Lie group we define a local poset of abstract wedge regions. We provide a classification of the simple Lie algebras supporting abstract wedges in relation with some special wedge configurations. This allows us to exhibit an analog of the Haag-Kastler axioms for one-particle nets undergoing the action of such general Lie groups without referring to any specific spacetime. This set of axioms supports a first quantization net obtained by generalizing the BGL-construction. The construction is possible for a large family of Lie groups and provides several new models.
Based on the joint work with Karl-Hermann Neeb (FAU Erlangen-Nürnberg)
"Covariant homogeneous nets of standard subspaces"
https://arxiv.org/abs/2010.07128
Link al seminario: https://teams.microsoft.com/l/meetup-join/19%3a428ea736adc6424c8ae37f187c91b51b%40thread.tacv2/1611656244968?context=%7b%22Tid%22%3a%2224c5be2a-d764-40c5-9975-82d08ae47d0e%22%2c%22Oid%22%3a%22e6325df7-3e74-4c88-ab0b-65ff8a758e69%22%7d |
| 28/01/21 | Seminario | 16:00 | 17:00 | | Michele Gianfelice | Università della Calabria |
DinAmicI: Another Internet Seminar (DAI Seminar)
Stochastic stability of classical Lorenz flow under impulsive type forcing
- in streaming mode -
(see the instructions in the abstract)
Inspired by the problem of modeling the so called anthropogenic forcing in climatology, e.g. the effects of the emissions of greenhouse gases in the atmosphere, we introduce a novel type of random perturbation for the classical Lorenz flow and prove its stochastic stability. The perturbation acts on the system in an impulsive way, hence is not of diffusive type. Namely, given a cross-section M for the unperturbed flow, each time the trajectory of the system crosses M the phase velocity field is changed with a new one sampled at random from a suitable neighborhood of the unperturbed one. The resulting random evolution is therefore described by a piecewise deterministic Markov process. The proof of the stochastic stability for the unperturbed flow is then carried on working either in the framework of the Random Dynamical Systems or in that of semi-Markov processes. Joint work with Sandro Vaienti.
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.
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| 21/01/21 | Seminario | 14:00 | 15:00 | | Alessandra Pluda | Università di Pisa | Seminario di Equazioni Differenziali
Motion by curvature of networks: analysis of singularities and
“restarting” theorems
(MS Teams link for the streaming at the end of the abstract)
A regular network is a finite union of sufficiently smooth
curves whose end points meet in
triple junctions. I will present the state-of-the-art of the problem of
the motion by curvature of a regular network
in the plane mainly focusing on singularity formation. Then I will
discuss the need of a “restarting”
theorem for networks with multiple junctions of order bigger than three
and I will give an idea of a possible strategy to prove it.
This is a research in collaboration with Jorge Lira (University of
Fortaleza), Rafe Mazzeo (Stanford University) and Mariel Saez (P.
Universidad Catolica de Chile).
MS Teams Link for the streaming
Note:
This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006 |
| 14/01/21 | Seminario | 16:00 | 17:00 | | Andrea Venturelli | Université d'Avignon (France) | DinAmicI: Another Internet Seminar (DAI Seminar)
”Hyperbolic motion in the Newtonian N-body problem with arbitrary limit shape”
- in streaming mode -
(see the instructions in the abstract)
We prove for the N-body problem the existence of hyperbolic motions for any prescribed limit shape and any given initial configuration of the bodies. The energy level h>0 of the motion can also be chosen arbitrarily. Our approach is based on the construction of a global viscosity solutions for the Hamilton-Jacobi equation H(x,du(x))=h. Our hyperbolic motion is in fact a calibrating curve of the viscosity solution. The presented results can also be viewed as a new application of Marchal’s theorem, whose main use in recent literature has been to prove the existence of periodic orbits. Joint work with Ezequiel Maderna.
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.
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| 14/01/21 | Seminario | 14:00 | 15:00 | | Matteo Muratori | Politecnico di Milano | Nonlinear diffusion equations on noncompact manifolds and relations with stochastic completeness
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
Prova |
| 18/12/20 | Seminario | 14:30 | 16:30 | | Terza Giornata DinAmica | DinAmicI on-line workshop | (See Abstract below for the schedule)
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
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)
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
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. |