Dipartimento di Matematica -UTV-

Date	Type	Start	End	Room	Speaker	From	Title
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) Abstract We investigate discrete thin objects which are described by a subset $X$ of $mathbb{Z}^d imes {0,dots, M-1 }^k$, 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 discrete-to-continuum and dimension-reduction 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 dimension-lowering coarse-graining process and a discrete version of the p-connectedness 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. Abstract Given an algebraic variety X, the Brauer group of X is the group of Azumaya algebras over X, or equivalently the group of Severi-Brauer 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 prime-to-char(k) part in positive characteristic. It turns out that the Brauer group of the non-compact 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 Brauer-Severi 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 non-trivial 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 non-compact 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 Chaotic-like transfers of energy in Hamiltonian PDEs (MS Teams link for the streaming at the end of the abstract) 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 chaotic-like transfers of energy for the nonlinear cubic Wave, the Hartree and the nonlinear cubic Beam equation on the 2-dimensional 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. Abstract 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 Abstract 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) Abstract We provide an elementary introduction to Elias-Williamson’s Soergel diagrammatics and p-Kazhdan-Lusztig theory and discuss the applications in representation theory. In particular we will discuss the recent proof of (generalised versions of) Libedinsky-Patimo’s conjecture, which states that certain simple characters of affine Hecke algebras are given in terms of p-Kazhdan-Lusztig polynomials and of Berkesch-Griffeth-Sam’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. 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 half-line, 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 half-line 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 point-like defect characterised by a unitary scattering matrix, that allows both reflection and transmission. Microsoft Teams Link
26/10/21	Seminario	14:30	15:30	1201 Dal Passo	Amos Turchet	University of Roma Tre	Geometry Seminar Campana’s program and special varieties Abstract Campana proposed a series of conjectures relating algebro-geometric and complex-analytic properties of algebraic varieties and their arithmetic. The main ingredient is the definition of the class of special varieties, which is the key for a new functorial classification of algebraic varieties, that is more suitable to answer arithmetic questions. In the talk we will review the main conjectures and constructions, and we will discuss some recent results that give evidence for some of these conjectures. This is joint work with E. Rousseau and J. Wang.
20/10/21	Seminario	16:00	17:00	1201 Dal Passo	Jean-Luc Sauvageot	Institut de Mathématiques de Jussieu	Misurabilità, densità spettrali e tracce residuali in geometria non commutativa Abstract We introduce, in the dual Macaev ideal of compact operators of a Hilbert space, the spectral weight rho(L) of a positive, self-adjoint operator L having discrete spectrum away from zero. We provide criteria for its measurability and unitarity of its Dixmier traces ( rho(L) is then called a spectral density) in terms of the growth of the spectral multiplicities of L and in terms of the asymptotic continuity of the eigenvalue counting function NL. Existence of meromorphic extensions and residues of the zeta-function zeta L of a spectral density are provided, under summability conditions on the spectral multiplicities. The hypertrace property of the states Omega L(·) = Tr omega(· rho(L)) on the norm closure of the Lipschitz algebra AL follows if the relative multiplicities of L vanish faster then its spectral gaps or if, at least, NL is asymptotically regular.
19/10/21	Seminario	14:30	15:30	1201 Dal Passo	Laura Pertusi	University of Milano	Geometry Seminar Serre-invariant stability conditions and cubic threefolds Abstract Stability conditions on the Kuznetsov component of a Fano threefold of Picard rank 1, index 1 and 2 have been constructed by Bayer, Lahoz, Macrì and Stellari, making possible to study moduli spaces of stable objects and their geometric properties. In this talk we investigate the action of the Serre functor on these stability conditions. In the index 2 case and in the case of GM threefolds, we show that they are Serre-invariant. Then we prove a general criterion which ensures the existence of a unique Serre-invariant stability condition and applies to some of these Fano threefolds. Finally, we apply these results to the study of moduli spaces in the case of a cubic threefold X. In particular, we prove the smoothness of moduli spaces of stable objects in the Kuznetsov component of X and the irreducibility of the moduli space of stable Ulrich bundles on X. These results come from joint works with Song Yang and with Soheyla Feyzbakhsh and in preparation with Ethan Robinett. These talks are part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006.