| 12/04/22 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | Valerio Assenza | Heidelberg University | Seminario di Equazioni Differenziali
Magnetic Curvature and Closed Magnetic Geodesic
(MS Teams link for the streaming at the end of the abstract)
A Magnetic System describes the motion of a charged particle moving on a Riemannian Manifold under the influence of a magnetic field. Trajectories for this dynamics are called Magnetic Geodesics and one of the main tasks in the theory is to investigate the existence of Magnetic Geodesic which are closed. In general this depends on the magnetic system taken into account and on the topology of the base space. Inspired by the work of Bahri and Taimanov, I will introduce the notion of Magnetic Curvature which is a perturbation of the standard Riemannian curvature due to the magnetic interaction. We will see that Closed Magnetic Geodesic exist when the Magnetic Curvature is positive, which happens , for instance, when the magnetic field is sufficiently strong.
MS Teams Link for the streaming
Note:
This talk is part of the activity of the MIUR Department of Excellence Project MATH@TOV CUP E83C18000100006 |
| 12/04/22 | Seminario | 13:00 | 14:00 | 2001 | Deepesh Toshniwal | Delft University of Technology | Quadratic unstructured splines
Isogeometric Analysis generalizes classical finite element analysis and intends to integrate it with the field of Computer-Aided Design. A central problem in achieving this objective is the reconstruction of analysis-suitable models from Computer-Aided Design models, which is in general a non-trivial and time-consuming task. This talk will present an overview of new piecewise-quadratic spline constructions that enable model reconstruction, as well as simulation of high-order PDEs on the reconstructed models. In particular, we will discuss splines on unstructured meshes in both two and three dimensions.
This talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006. |
| 08/04/22 | Seminario | 16:30 | 17:30 | 1201 Dal Passo | Paolo PAPI | "Sapienza" Università di Roma |
Algebra & Representation Theory Seminar (ARTS)
"Collapsing levels for affine W-algebras"
- in live & streaming mode -
( click HERE to attend the talk in streaming )
I will discuss some projects in collaboration with D. Adamovic, V. Kac and P. Moseneder-Frajria regarding affine W-algebras. I will concentrate on the notion of collapsing level for not necessarily minimal W-algebras and I will illustrate some applications to the representation theory of affine algebras and, if time allows, to our conjectural classification of unitary representations for minimal W-algebras.
N.B.: please click HERE to attend the talk in streaming. |
| 08/04/22 | Seminario | 14:00 | 15:00 | 1201 Dal Passo | Vincenzo MORINELLI | Università di Roma "Tor Vergata" |
Algebra & Representation Theory Seminar (ARTS)
"About Lie theory in Algebraic Quantum Field Theory"
- in live & streaming mode -
( click HERE to attend the talk in streaming )
The relation between the geometric and the algebraic structure in algebraic quantum field theory is an intriguing topic that has been studied through several mathematical areas. A fundamental concept in Algebraic Quantum Field Theory (AQFT) is the relation between the localization property and the geometry of models. In the recent work with K.-H. Neeb, we rephrased and generalized some aspects of this relation by using the language of Lie theory.
We will start the talk introducing fundamental algebraic features of AQFT, in particular the Haag-Kastler axioms and the one particle formalism, and the presenting algebraic construction of the free field due to R.Brunetti, D. Guido and R. Longo. We will explain how this picture can be generalized. Firstly, how to determine some fundamental localization region, called wedge regions, at the Lie theory level and how a general Lie group can support a generalized AQFT. Then we show a classification of the simple Lie algebras supporting abstract wedges in relation with some special wedge configurations. The construction is possible for a large family of Lie groups and provides several new models in a generalized framework. Such a description of AQFT model generalization does not need a supporting manifold even if it is a desirable object. Time permitting, we will comment on recent developments about symmetric manifolds such models.
Based on V. Morinelli and K.-H. Neeb, Covariant homogeneous nets of standard subspaces, Commun. in Math. Phys 386 (1), 305-358 (2021).
N.B.: please click HERE to attend the talk in streaming.
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| 05/04/22 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | Luca Battaglia | Università di Roma Tre | Blow-up phenomena for a curvature problem in a disk
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We consider the problem of prescribing Gaussian and geodesic curvatures for a conformal metric on the unit disk, which is equivalent to a Liouville-type PDE with nonlinear Neumann boundary conditions. We build a family of solutions which blow up on the boundary at a critical point of a functional which is a combination of the curvatures we are prescribing. The talk is based on joint works with M. Medina and A. Pistoia.
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006
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| 05/04/22 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Luca Tasin | Universita' di Milano | Geometry Seminar
Sasaki-Einstein metrics on spheres.
I will report on a joint work with Yuchen Liu and Taro Sano in which we construct infinitely many families of Sasaki-Einstein metrics on odd-dimensional spheres that bound parallelizable manifolds, proving in this way conjectures of Boyer-Galicki-Kollar and Collins-Szekelyhidi. The construction is based on showing the K-stability of certain Fano weighted orbifold hypersurfaces. |
| 01/04/22 | Seminario | 15:30 | 16:30 | 1200 Biblioteca Storica | Alessia Caponera | EPFL | Nonparametric Estimation of Covariance and Autocovariance Operators on the Sphere
We propose nonparametric estimators for the second-order central moments of spherical random fields within a functional data context. We consider a measurement framework where each field among an identically distributed collection of spherical random fields is sampled at a few random directions, possibly subject to measurement error. The collection of fields could be i.i.d. or serially dependent. Though similar setups have already been explored for random functions defined on the unit interval, the nonparametric estimators proposed in the literature often rely on local polynomials, which do not readily extend to the (product) spherical setting. We therefore formulate our estimation procedure as a variational problem involving a generalized Tikhonov regularization term. The latter favours smooth covariance/autocovariance functions, where the smoothness is specified by means of suitable Sobolev-like pseudo-differential operators. Using the machinery of reproducing kernel Hilbert spaces, we establish representer theorems that fully characterize the form of our estimators. We determine their uniform rates of convergence as the number of fields diverges, both for the dense (increasing number of spatial samples) and sparse (bounded number of spatial samples) regimes. We moreover validate and demonstrate the practical feasibility of our estimation procedure in a simulation setting.
Based on a joint work with Julien Fageot, Matthieu Simeoni and Victor M. Panaretos.
This talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006. |
| 29/03/22 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | Daniele Cassani | Università degli Studi dell'Insubria | Some limiting cases in nonlocal Schroedinger equations
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We will present recent results for a class of Choquard type equations in the limiting Sobolev dimension in which one has the Riesz logarithmic kernel in the nonlocal part and the nonlinearity exhibits the highest possible growth, which is of exponential type. The competition between the logarithmic kernel and the exponential nonlinearity demands for new tools. A proper function space setting is provided by a new weighted version of the Pohozaev--Trudinger inequality which enables us to prove the existence of variational, in particular finite energy solutions. Equivalence issues with connected higher order fractional Scroedinger-Poisson systems will be also discussed, as well as related open problems.
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006
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| 25/03/22 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Andrea SANTI | UiT The Arctic University of Norway
Università di Roma "Tor Vergata" |
Algebra & Representation Theory Seminar (ARTS)
"G(3) supergeometry and a supersymmetric extension of the Hilbert-Cartan equation"
- in live & streaming mode -
( click HERE to attend the talk in streaming )
I will report on the realization of the simple Lie superalgebra G(3) as symmetry superalgebra of various geometric structures - most importantly super-versions of the Hilbert-Cartan equation and Cartan's involutive system that exhibit G(2) symmetry - and compute, via Spencer cohomology groups, the Tanaka-Weisfeiler prolongation of the negatively graded Lie superalgebras associated with two particular choices of parabolics. I will then discuss non-holonomic superdistributions with growth vector (2|4 , 1|2 , 2|0) obtained as super-deformations of rank 2 distributions in a 5-dimensional space, and show that the second Spencer cohomology group gives a binary quadric, thereby providing a "square-root" of Cartan's classical binary quartic invariant for (2,3,5)-distributions.
This is a joint work with B. Kruglikov and D. The.
N.B.: please click HERE to attend the talk in streaming.
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| 22/03/22 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | Piero Montecchiari | Università Politecnica Delle Marche | Nondegeneracy Conditions and Multiplicity of Solutions for Differential Equations
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We discuss some results about the existence and multiplicity problem of different kind of entire solutions
for some systems of semilinear elliptic equations, including the Allen Cahn and the NLS type models, under weak global non degeneracy conditions.
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006 |