16/11/21  Seminario  13:00  14:00  1201 Dal Passo  Francesco Calabrò  Università degli Studi di Napoli Federico II  The use of artificial neural networks for the numerical solution of PDEs with collocation
Artificial neural networks are nowadays a widespread tool in applied mathematics for approximation and classification purposes. In this talk, we will survey recent results on the use of neural networks in computing the solution of PDEs. First of all, we introduce the use of network functions for the computation of forward and inverse problems for PDEs. Then, we will focus on collocation methods with feedforward neural network with a single hidden layer and sigmoidal transfer functions randomly generated, the socalled extreme learning machines. We will present results on elliptic problems both in the linear (with sharp gradient) case and for the construction of bifurcation diagrams of nonlinear problems.
The results are obtained in collaboration with Gianluca Fabiani and Costantinos Siettos.
This talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006.
MS Teams link for the streaming

12/11/21  Seminario  16:00  17:00  1201 Dal Passo  Viola SICONOLFI  Università di Pisa 
Algebra & Representation Theory Seminar (ARTS)
"Zetafunctions for class two nilpotent groups"
 in live & streaming mode 
(see the instructions in the abstract)
The notion of Zetafunction for groups was introduced in a seminal paper from Grunewald, Segal and Smith and proved to be a powerful tool to study the subgroup growth in some classes of groups.
In this seminar I will introduce this Zetafunction presenting some general properties for this object. I will then focus on some results obtained for class two nilpotent groups.
I will in particular describe some combinatorial tecniques used to tackle this problem, namely the study of series associated to polyhedral integer cones.
This is a joint work with Christopher Voll and Marlies Vantomme.
N.B.: please click HERE to attend the talk in streaming

12/11/21  Seminario  14:30  15:30  1201 Dal Passo  Paolo BRAVI  "Sapienza" Università di Roma 
Algebra & Representation Theory Seminar (ARTS)
"On the multiplication of spherical functions of reductive spherical pairs"
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Let G be a simple complex algebraic group and let K be a reductive subgroup of G such that the coordinate ring of G/ K is a multiplicity free Gmodule. We consider the Galgebra structure of C[ G/ K], and study the decomposition into irreducible summands of the product of irreducible Gsubmodules in C[ G/ K]. We will present a conjectural decomposition rule for some special reductive pairs together with some partial results supporting the conjecture. We will explain how our conjecture would actually follow from an old conjecture of Stanley on the multiplication of Jack symmetric functions. We will also present a few new basic results related to Stanley's conjecture itself. The talk is based on a collaboration with Jacopo Gandini.
N.B.: please click HERE to attend the talk in streaming 
09/11/21  Seminario  16:00  17:00  1201 Dal Passo  Lorenza D'Elia  Università di Roma "Tor Vergata"  Seminario di Equazioni Differenziali
Homogenization of discrete thin structures
(MS Teams link for the streaming at the end of the abstract)
We investigate discrete thin objects which are described by a subset $X$ of $mathbb{Z}^d imes {0,dots, M1 }^k$, for some $Minmathbb{N}$ and $d,kgeq 1$. We only require that $X$ is a connected graph and periodic in the first $d$directions. We consider quadratic energies on $X$ and we perform a discretetocontinuum and dimensionreduction process for such energies. We show that, upon scaling of the domain and of the energies by a small parameter $varepsilon$, the scaled energies $Gamma$converges to a $d$dimensional functional. The main technical points are a dimensionlowering coarsegraining process and a discrete version of the pconnectedness approach by Zhikov. This is a joint work with A. Braides.
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

09/11/21  Seminario  14:30  15:30  1201 Dal Passo  Roberto Pirisi  Sapienza  Geometry Seminar
Brauer groups of moduli of hyperelliptic curves and their compactifications.
Given an algebraic variety X, the Brauer group of X is the group of Azumaya algebras over X, or equivalently the group of SeveriBrauer varieties over X. While the Brauer group has been widely studied for schemes, computations at the level of moduli stacks are relatively recent, the most prominent of them being the computations by Antieau and Meier of the Brauer group of the moduli stack of elliptic curves over a variety of bases, including Z, Q, and finite fields. In a recent series of joint works with A. Di Lorenzo, we use the theory of cohomological invariants, and its extension to algebraic stacks, to completely describe the Brauer group of the moduli stacks of hyperelliptic curves, and their compactifications, over fields of characteristic zero, and the primetochar(k) part in positive characteristic. It turns out that the Brauer group of the noncompact stack is generated by elements coming from the base field, cyclic algebras, an element coming from a map to the classifying stack of étale algebras of degree 2g+2, and when g is odd by the BrauerSeveri fibration induced by taking the quotient of the universal curve by the hyperelliptic involution. This paints a richer picture than in the case of elliptic curves, where all nontrivial elements come from cyclic algebras. Regarding the compactifications, there are two natural ones, the first obtained by taking stable hyperelliptic curves and the second by taking admissible covers. It turns out that the Brauer group of the former is trivial, while for the latter it is almost as large as in the noncompact case, a somewhat surprising difference as the two stacks are projective, smooth and birational, which would force their Brauer groups to be equal if they were schemes. 
02/11/21  Seminario  16:00  17:00  1201 Dal Passo  Stefano Pasquali  Lund University, Sweden  Seminario di Equazioni Differenziali
Chaoticlike transfers of energy in Hamiltonian PDEs
(MS Teams link for the streaming at the end of the abstract)
A fundamental problem in nonlinear Hamiltonian PDEs on compact manifolds is understanding how solutions can exchange energy among Fourier modes. I will present a recent result which shows a new type of chaoticlike transfers of energy for the nonlinear cubic Wave, the Hartree and the nonlinear cubic Beam equation on the 2dimensional torus by combining techniques from dynamical systems and PDEs .
This mechanism is based on the existence of heteroclinic connections between invariant manifolds and on the construction of symbolic dynamics (Smale horseshoe) for the Birkhoff Normal Form truncation of those equations.
This is a joint work with F. Giuliani, M. Guardia and P. Martin (UPC, Barcelona).
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

02/11/21  Seminario  14:30  15:30  1201 Dal Passo  Peter Stevenhagen  University of Leiden  Geometry Seminar
Elliptic curves and primes of cyclic reduction.
Let E be an elliptic curve defined over a number field K. Then for every prime p of K for which E has good reduction, the point group of E modulo p is a finite abelian group on at most 2 generators. If it is cyclic, we call p a prime of cyclic reduction for E. We will answer basic questions for the set of primes of cyclic reduction of E: is this set infinite, does it have a density, and can such a density be computed explicitly from the Galois representation associated to E? This is joint work with Francesco Campagna (MPIM Bonn). 
29/10/21  Seminario  16:00  17:00  1201 Dal Passo  Michele D'ADDERIO  Université Libre de Bruxelles 
Algebra & Representation Theory Seminar (ARTS)
"Partial and global representations of finite groups"
 in live & streaming mode 
(see the instructions in the abstract)
N.B.: this talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006
The notions of partial actions and partial representations have been extensively studied in several algebraic contexts in the last 25 years. In this talk we introduce these concepts and give a short overview of the results known for finite groups.
We will briefly show how this theory extends naturally the classical global theory, in particular in the important case of the symmetric group.
This is joint work with William Hautekiet, Paolo Saracco and Joost Vercruysse.
N.B.: please click HERE to attend the talk in streaming 
29/10/21  Seminario  14:30  15:30  1201 Dal Passo  Chris BOWMAN  University of York 
Algebra & Representation Theory Seminar (ARTS)
"Soergel diagrammatics in modular representation theory"
 in live & streaming mode 
(see the instructions in the abstract)
We provide an elementary introduction to EliasWilliamson’s Soergel diagrammatics and pKazhdanLusztig theory and discuss the applications in representation theory. In particular we will discuss the recent proof of (generalised versions of) LibedinskyPatimo’s conjecture, which states that certain simple characters of affine Hecke algebras are given in terms of pKazhdanLusztig polynomials and of BerkeschGriffethSam’s conjecture which states that the unitary representations admit cohomological constructions via BGG resolutions.
This is joint work with Anton Cox, Amit Hazi, Emily Norton, and Jose Simental.
N.B.: please click HERE to attend the talk in streaming

27/10/21  Seminario  14:00  14:59  1201 Dal Passo  Erik Tonni  SISSA  Modular Hamiltonians for the massless Dirac field in the presence of a boundary or of a defect
 in blended mode  Microsoft Teams link in the abstract.
The reduced density matrix of a spatial subsystem can be written as the exponential of the modular Hamiltonian, hence this operator contains a lot of information about the entanglement of the corresponding spatial bipartition. First we consider the massless Dirac field on the halfline, imposing the most general boundary conditions that ensure the global energy conservation. This leads to two inequivalent phases where either the vector or the axial symmetry is preserved. In these two phases, we discuss the analytic expressions for the modular Hamiltonians of an interval on the halfline when the system is in its ground state, for the corresponding modular flows of the Dirac field and for the corresponding modular correlators. The method allows to obtain analytic expressions also for the modular Hamiltonians, the modular flows and the modular correlators for two disjoint equal intervals at the same distance from a pointlike defect characterised by a unitary scattering matrix, that allows both reflection and transmission.
Microsoft Teams Link
