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01/04/22Seminario15:3016:301200 Biblioteca StoricaAlessia CaponeraEPFLNonparametric 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.
29/03/22Seminario16:0017:001201 Dal PassoDaniele CassaniUniversità degli Studi dell'InsubriaSome limiting cases in nonlocal Schroedinger equations
( MS Teams Link for the streaming )

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
25/03/22Seminario14:3015:301201 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.
22/03/22Seminario16:0017:001201 Dal PassoPiero Montecchiari Università Politecnica Delle MarcheNondegeneracy 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
22/03/22Seminario14:3015:301201 Dal PassoDavide Lombardo
Università di Pisa
Geometry Seminar
On the distribution of rational points on ramified covers of abelian varieties

Let A be an abelian variety over a number field K, with A(K) Zariski-dense in A. In this talk I will show that for every irreducible ramified cover π : X → A the set A(K) \ π (X(K)) of K-rational points of A that do not lift to X(K) is still Zariski-dense in A, and that in fact it even contains a finite-index coset of A(K). This result is motivated by Lang's conjecture on the distribution of rational points on varieties of general type and confirms a conjecture of Corvaja and Zannier concerning the "weak Hilbert property" in the special case of abelian varieties.
15/03/22Seminario16:0017:001201 Dal PassoAnna Maria CandelaUniversita' di BariSoliton solutions for quasilinear modified Schroedinger equations
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Link to the abstract
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006
15/03/22Seminario14:3015:301201 Dal PassoMark de Cataldo
Stony Brook
Geometry Seminar
Some things I know and some I don't about moduli spaces of Higgs bundles

I report on two joint works: with my current student Siqing Zhang, and with Davesh Maulik (MIT), Junliang Shen (Yale) and Siqing Zhang. The Dolbeault moduli space of Higgs bundles over a complex algebraic curve is one of the ingredients in the Nonabelian Hodge Theory of the curve. Much is known and much is not known about this theory. From my current point of view, I consider some of the structures on the cohomology ring of these moduli spaces. I will start by introducing the P=W conjecture in Nonabelian Hodge Theory, mostly as motivation for the two joint works. The first work provides a cohomological shadow of a (strictly speaking non-existing) Nonabelian Hodge Theory for curves over fields of positive characteristic, and it unearths a new pattern for moduli of Higgs bundles in positive characteristic, which we call p-multiplicativity. The second work applies the first over a finite field to provide indirect evidence for the P=W conjecture over the complex numbers.
11/03/22Seminario16:0017:001201 Dal Passo
Università di Bologna
Algebra & Representation Theory Seminar (ARTS)
"Generalized Root Systems"
- in live & streaming mode -
( please click HERE to attend the talk in streaming )
N.B.: This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006

  In Lie theory we define root systems in several contexts: Lie algebras, superalgebras, affine algebras, etc. There is even more: Kostant defines a more general notion of root systems, by taking roots with respect to a generic toral subalgebra (i.e. not necessarily maximal). All these notions of root systems do not behave well with respect to quotients: the quotient (or projection) of a root systems is not in general a root system. We present here a more general notion of root system, inspired by Kostant, which accomodates all of the above examples and behaves well with respect to quotients and projections.
  We give a classification theorem for rank 2 generalized root system: there are only 14 of them up to combinatorial equivalence, moreover they are all quotients of Lie algebra root systems. We also prove that root systems of contragredient Lie superalgebras are quotients of root systems of Lie algebras, up to combinatorial equivalence.
  In the end, we relate our construction with the problem of determining the conjugacy class of two Levi subgroups in a Lie (super)algebra.
  N.B.: please click HERE to attend the talk in streaming.
11/03/22Seminario14:3015:301201 Dal Passo
University of Copenhagen
Algebra & Representation Theory Seminar (ARTS)
"Symmetric groups, Hurwitz spaces and moduli spaces of surfaces"
- in live & streaming mode -
( please click HERE to attend the talk in streaming )
N.B.: this talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006

08/03/22Seminario14:3015:301201 Dal PassoMatilde Manzaroli
University of Tübingen
Geometry Seminar
Real fibered morphisms of real del Pezzo surfaces

A morphism of smooth varieties of the same dimension is called real fibered if the inverse image of the real part of the target is the real part of the source. It goes back to Ahlfors that a real algebraic curve admits a real fibered morphism to the projective line if and only if the real part of the curve disconnects its complex part. Inspired by this result, in a joint work with Mario Kummer and Cédric Le Texier, we are interested in characterising real algebraic varieties of dimension n admitting real fibered morphisms to the n-dimensional projective space. We present a criterion to construct real fibered morphisms that arise as finite surjective linear projections from an embedded variety; this criterion relies on topological linking numbers. We address special attention to real algebraic surfaces. We classify all real fibered morphisms from real del Pezzo surfaces to the projective plane and determine when such morphisms arise as the composition of a projective embedding with a linear projection.

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