Seminari/Colloquia
Pagina 25
Date  Type  Start  End  Room  Speaker  From  Title 

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 secondorder 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 Sobolevlike pseudodifferential 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 ( 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 PohozaevTrudinger inequality which enables us to prove the existence of variational, in particular finite energy solutions. Equivalence issues with connected higher order fractional ScroedingerPoisson 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 
25/03/22  Seminario  14:30  15:30  1201 Dal Passo  "G(3) supergeometry and a supersymmetric extension of the HilbertCartan 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 superversions of the HilbertCartan equation and Cartan's involutive system that exhibit G(2) symmetry  and compute, via Spencer cohomology groups, the TanakaWeisfeiler prolongation of the negatively graded Lie superalgebras associated with two particular choices of parabolics. I will then discuss nonholonomic superdistributions with growth vector (24 , 12 , 20) obtained as superdeformations of rank 2 distributions in a 5dimensional space, and show that the second Spencer cohomology group gives a binary quadric, thereby providing a "squareroot" 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.  
22/03/22  Seminario  16:00  17:00  1201 Dal Passo  Piero Montecchiari  Università Politecnica Delle Marche  Nondegeneracy Conditions and Multiplicity of Solutions for Differential Equations
( MS Teams Link for the streaming )
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 
22/03/22  Seminario  14:30  15:30  1201 Dal Passo  Davide Lombardo 
Let A be an abelian variety over a number field K, with A(K) Zariskidense 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 Krational points of A
that do not lift to X(K) is still Zariskidense in A, and that in fact it even contains a finiteindex 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.
 
15/03/22  Seminario  16:00  17:00  1201 Dal Passo  Anna Maria Candela  Universita' di Bari  Soliton solutions for quasilinear modified Schroedinger equations ( MS Teams Link for the streaming )
Link to the abstract
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006 
15/03/22  Seminario  14:30  15:30  1201 Dal Passo  Mark de Cataldo 
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 nonexisting) 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 pmultiplicativity. The second work applies the first over a finite field to provide indirect evidence for the P=W conjecture over the complex numbers.
 
11/03/22  Seminario  16:00  17:00  1201 Dal Passo  "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.  
11/03/22  Seminario  14:30  15:30  1201 Dal Passo  "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  
08/03/22  Seminario  14:30  15:30  1201 Dal Passo  Matilde Manzaroli 
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 ndimensional 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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