| 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)
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.
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 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.
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
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
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
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.
|
| 15/10/21 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | Giovanni CERULLI IRELLI | “Sapienza” Università di Roma |
Algebra & Representation Theory Seminar (ARTS)
"On degeneration and extensions of
symplectic and orthogonal quiver representations"
- in live & streaming mode -
(see the instructions in the abstract)
Motivated by linear degenerations of flag varieties, and the study of 2-nilpotent B-orbits for classical groups, I will review the representation theory of symmetric quivers, initiated by Derksen and Weyman in 2002. I will then focus on the problem of describing the orbit closures in this context and how to relate it to the orbit closures for the underlying quivers. In collaboration with M. Boos we have recently given an answer to this problem for symmetric quivers of finite type. I believe that this result is a very special case of a much deeper and general result that I will mention in the form of conjectures and open problems.
The talk is based on the preprint version of my paper with Boos available on the arXiv as 2106.08666.
N.B.: please click HERE to attend the talk in streaming
|
| 15/10/21 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Lorenzo GUERRA | Scuola Normale Superiore - Pisa |
Algebra & Representation Theory Seminar (ARTS)
"Symmetric groups, tensor powers and extended powers of a topological space"
- in live & streaming mode -
(see the instructions in the abstract)
The n-th cohomology of the symmetric group Sn on n objects with coefficients in the n-th tensor power of a vector space V on a field k, is endowed with an extremely rich algebraic structure. Indeed, their direct sum for all n ∈ N is an example of what goes under the name of "Hopf ring".
First I will recall and review the definition of Hopf ring, then I will explicitly describe the cohomology algebras above, and finally I will briefly discuss the link with extended powers and other topological spaces interesting for homotopy theorists.
The content of this talk stems from an ongoing collaboration with Paolo Salvatore and Dev Sinha.
N.B.: please click HERE to attend the talk in streaming
|