Pagina 36

Date | Type | Start | End | Room | Speaker | From | Title |
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04/03/21 | Seminario | 14:00 | 15:00 | Weiwei Ao | Wuhan University | Symmetry and symmetry breaking for the fractional Caffarelli-Kohn-Nirenberg inequality
( MS Teams Link for the streaming )In this talk, I will discuss about a fractional version of the Caffarelli-Kohn-Nirenberg inequality.
We first study the existence and nonexistence of extremal solutions. We also show some results for the symmetry and symmetry breaking region for the minimizers. In order to get these result we reformulate the fractional Caffarelli-Kohn-Nirenberg inequality in cylindrical variables. We also get the non-degeneracy and uniqueness of minimizers in the radial symmetry class. This is joint work with Azahara DelaTorre and Maria del Mar Gonzalez. NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006 | |

25/02/21 | Seminario | 16:00 | 17:00 | Paolo Giulietti | Università di Pisa | DinAmicI: Another Internet Seminar (DAI Seminar) Infinite mixing for accessible skew products
- in streaming mode -
(see the instructions in the abstract)
I will present some decay of correlations results on skew products which are locally accessible. The results rely on the study of a twisted transfer operator and could be generalized to many other situations. I will also present numerical counterparts to such results.
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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25/02/21 | Seminario | 14:00 | 15:00 | Jacopo Bellazzini | Universita' di Pisa | Ground state energy threshold and blow-up for NLS with competing nonlinearities
( MS Teams Link for the streaming )Aim of the talk is to discuss qualitative properties of the nonlinear Schr\"odinger equation with combined nonlinearities, where the leading term is an intracritical focusing power-type nonlinearity, and the perturbation is given by a power-type defocusing one. Fixed the mass of the problem, we completely answer the question wether the ground state energy , which is a threshold between global existence and formation of singularities, is achieved. As a byproduct of the variational characterization of the ground state energy, we show the existence of blowing-up solutions in finite time, for any initial data with energy below the ground state energy threshold in case of cylindrical symmetry.
N.B.: this talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006
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18/02/21 | Colloquium | 14:00 | 15:00 | Toshiyuki Kobayashi | The University of Tokyo | A foundation of group-theoretic analysis on manifolds
( MS Teams Link for the streaming )
Symmetry of geometry is inherited by symmetry of function spaces, called the regular representation. From this viewpoint, the classical theory of expansions such as Fourier series or spherical harmonics may be interpreted as "analysis and synthesis" of the regular representation.
In this talk, we address the following fundamental questions about the regular representation on manifolds X acted algebraically by reductive Lie groups G such as GL(n,R).
A. Does the group G "control well" the space of function on X?
B. What can we say about "spectrum" for L^2(X)?
We highlight "multiplicity" for A and "temperdness" for B, and explain some geometric ideas of the solution.
N.B.: this talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006
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11/02/21 | Seminario | 16:00 | 17:00 | Misha Bialy | Tel Aviv University | DinAmicI: Another Internet Seminar (DAI Seminar) Birkhoff-Poritsky conjecture for centrally-symmetric billiards
- in streaming mode -
(see the instructions in the abstract)
In this talk I shall discuss Birkhoff-Poritsky conjecture for centrally-symmetric C^2-smooth convex planar billiards.
We assume that the domain A between the invariant curve of 4-periodic orbits and the boundary of the phase cylinder is foliated by C^0-invariant curves.
Under this assumption we prove that the billiard curve is an ellipse.
Other versions of Birkhoff-Poritsky conjecture follow from this result.
For the original Birkhoff-Poritsky formulation we show that if a neighborhood of the boundary of billiard domain has
a C^1-smooth foliation by convex caustics of rotation numbers in the interval (0, 1/4]
then the boundary curve is an ellipse.
The main ingredients of the proof are :
(1) the non-standard generating function for convex billiards; (2) the remarkable structure of the invariant curve consisting of 4-periodic orbits; and (3) the integral-geometry approach initiated in [B0], [B1] for rigidity results of circular billiards. Surprisingly, we establish a Hopf-type rigidity for billiards in the ellipse. Based on a joint work with Andrey E. Mironov (Novosibirsk). Note: | |

11/02/21 | Seminario | 14:00 | 15:00 | Luca Martinazzi | Universita' di Padova | Entire solutions to a prescribed curvature equation in R^4 and the Nirenberg problem Several existence and non-existence results for the Nirenberg problem of prescribing the Gauss curvature on a closed surface are classically known. In higher dimension, analog results hold with the Q-curvature replacing the Gauss curvature. In many cases a non-existence result is associated with a blow-up phenomenon which leads to entire solutions of the Liouville equation $-Delta u = e^{2u}$ in dimension 2 or higher-dimensional analogs. On the other hand, Borer, Galimberti and Struwe studied a blow-up phenomenon which could lead to solutions to the equation
$$-Delta u =(1-|x|^2)e^{2u} in R^2$$ (1)
or
$$Delta^2 u =(1-|x|^2)e^{4u} in R^4$$ (2)
While non-existence results have been shown for (1) by Struwe, the question remained opened for (2). We recently gave a positive answer with A. Hyder, giving sharp conditions under which (2) admits solutions with controlled behaviour at infinity, hence answering an open question by Struwe. More related open questions will be discussed.
MS Teams Link for the streaming
Note: This talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006 | |

04/02/21 | Seminario | 14:00 | 15:00 | Lorenzo Valvo | Università degli Studi di Roma | Seminario di Equazioni Differenziali Hamiltonian Control of Magnetic Field Lines: Computer Assisted Results Proving the Existence of KAM Barriers
(MS Teams link for the streaming at the end of the abstract) A control theory for Hamiltonian systems, based on KAM theory, was introduced in [Ciraolo, 2004] and applied to a model of magnetic field in [Chandre, 2006]. By a combination of Frequency Analysis and of a rigorous (Computer Assisted) KAM algorithm we show that in the phase space of the magnetic field, due to the control term, a set of invariant tori appears, and it acts as a transport barrier. Our analysis, which is common (but often also limited) to celestial mechanics, is very general and can be applied to quasi-integrable Hamiltonian systems satisfying a few additional mild assumptions.
MS Teams Link for the streaming
Note:
This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006 | |

04/02/21 | Seminario | 10:00 | 11:00 | Gary Froyland | University of New South Wales (Australia) | DinAmicI: Another Internet Seminar (DAI Seminar) The dynamic ocean
- in streaming mode -
(see the instructions in the abstract)
The circulation of our oceans strongly influences climate, weather and biology. Our ocean currents are dynamic, and fluctuate to varying extents. I will introduce data-driven numerical tools that can tease apart dynamic components of the ocean, with information sourced from ocean drifters, satellite imagery, and ocean models. These components, their lifecycles, and their response to external forcing, help us to build a dynamic picture of our ocean.
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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.
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