05/11/24  Seminario  15:00  16:00  1200 Biblioteca Storica  Stefano Serra Capizzano  University of Insubria  Updating the GLT analysis, new tools, and beyond
The class of Generalized Locally Toeplitz (GLT) sequences has been introduced as a generalization both of classical Toeplitz sequences and of variable coefficient differential operators and, for every sequence of the class, under mild assumptions it has been demonstrated that it is possible to give a rigorous description of the asymptotic spectrum in terms of a function (the symbol) that can be easily identified.
The GLT class has nice algebraic properties and indeed it has been proven that it is stable under linear combinations, products, and inversion when the sequence which is inverted shows a sparsely vanishing symbol (sparsely vanishing symbol = a symbol which vanishes at most in a set of zero Lebesgue measure). Furthermore, the GLT class virtually includes any approximation of partial differential equations (PDEs), fractional differential equations (FDEs), integrodifferential equations (IDEs) by local methods (Finite Difference, Finite Element, Isogeometric Analysis etc).
In the present talk, we discuss the foundations of the theory and its impact with special attention to new tools and to new directions as those based on symmetrization tricks, on the extradimensional approach, and on blocking operations, blocking structures. 
05/11/24  Seminario  14:30  16:00  1101 D'Antoni  Doug Ulmer  University of Arizona  Geometry Seminar ptorsion of curves in characteristic p
Note:
This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (20232027)
The Torelli locus  the image of the moduli space of curves (M_g) in the moduli space of abelian varieties (A_g)  is muchstudied but still mysterious. In characteristic p, A_g has a beautiful stratification by the isomorphism type of A[p], and examples show that Mg is far from transverse to this stratification. In an ongoing project, we develop tools to understand (and perhaps make principled conjectures about) which strata of A_g meet M_g. In this talk, we explain some of the structures involved and give new results about them. Parts of this are joint work with Bryden Cais and Rachel Pries. 
05/11/24  Seminario  14:30  15:30  1201 Dal Passo  Anna Doubova  Universidad de Sevilla  Seminario di Equazioni Differenziali
Inverse problems in 1D fluidsolid interaction model
In this talk we consider inverse problems for the partial differential equations describing the behavior of certain fluids. Our focus will be on the fluidstructure interaction problem and the objective is to determine the moving domain where the equations are satisfied, based on external measurements. We concentrate on a onedimensional fluidsolid interaction problem for the Burgers equation, and we will prove uniqueness and conditional stability results. This work is in collaboration with J. Apraiz, E. FernandezCara and M. Yamamoto [1].
[1] J. Apraiz, A. Doubova, E. FernandezCara, M. Yamamoto, "Inverse problems for onedimensional fluidsolid interaction models", Communications on Applied Mathematics and Computation, https://doi.org/10.1007/s42967024004373
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C23000330006

29/10/24  Seminario  14:30  15:30  1201 Dal Passo  Fabiana Leoni  Università di Roma "La Sapienza"  Radial singular solutions of fully nonlinear equations in punctured balls
We consider radial solutions of fully nonlinear, uniformly elliptic equations posed in punctured balls, in presence of radial singular quadratic potentials. We discuss both the principal eigenvalues problem and the case of equations having also absorbing superlinear zero order terms: for the former problem, we explicitly compute the principal eigenvalues, thus obtaining an extension in the fully nonlinear framework of the HardySobolev constant; for the latter case, we provide a complete classification of solutions based on their asymptotic behavior near the singularity. The results are based on joint papers with I. Birindelli and F. Demengel. 
29/10/24  Seminario  14:30  16:00  1101 D'Antoni  Sam Molcho  Università Sapienza di Roma  Geometry Seminar Integration on compactified Jacobians
Note:
This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (20232027)
The tautological ring is a certain subring of the Chow ring of the moduli space of curves. It is generated by the algebraic cycles that arise from the modular nature of the moduli space, and is one of the most studied objects in enumerative geometry. In this talk, I will explain that any semi stable family of algebraic varieties  in particular the compactified Jacobians over the moduli space of curves gives rise to a tautological ring, and discuss the relationship between the tautological rings of compactified Jacobians and the usual tautological ring of the moduli space of curves. 
25/10/24  Seminario  16:00  17:00  1201 Dal Passo  Anne MOREAU  Université ParisSaclay 
Algebra & Representation Theory Seminar (ARTS)
"On a series of simple affine VOAs arising from rank one 4D SCFTs"
N.B.: this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)
It is known by the works of Adamović and Perše that the affine simple vertex algebras associated with G_{2} and B_{3} at level 2 can be conformally embedded into L_{2}(D_{4}).
In this talk, I will present a join work with Tomoyuki Arakawa, Xuanzhong Dai, Justine Fasquel, Bohan Li on the classification to the irreducible highest weight modules of these vertex algebras.
I will also describe their associated varieties: the associated variety of that corresponding to G_{2} is the orbifold of the associated variety of that corresponding to D_{4} by the symmetric group of degree 3 which is the Dynkin diagram automorphism group of D_{4}. This provides new interesting examples in the context of orbifold vertex algebras. These vertex algebra also appear as the vertex operator algebras corresponding to rank one ArgyresDouglas theories in four dimension with flavour symmetry G_{2} and B_{3}.
N.B.: this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)

25/10/24  Seminario  14:30  15:30  1201 Dal Passo  Linda HOYER  RWTH Aachen University 
Algebra & Representation Theory Seminar (ARTS)
"Orthogonal Determinants of Finite Groups"
N.B.: this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)
Let G be a finite group. It is not hard to see that for any representation ρ : G ⟶ GL(V) for V a real vector space, there exists a Ginvariant bilinear form β on V, i.e., a nondegenerate bilinear form such that β(ρ(gv,ρ(g)w) = β(v,w) for all g ∈ G, v, w ∈ V. If ρ is "orthogonally stable" (so it is a sum of evendimensional irreducible real representations) then the square class of the determinant of the Gram matrix for any basis (the "orthogonal determinant") does not depend on the choice of β, giving us interesting invariants of our group G. Richard Parker conjectured that these orthogonal determinants are always "odd", for any finite group. We will see that the conjecture holds for the symmetric groups, as well as the general linear groups GL(q) for q a power of an odd prime. In the discussion, important concepts like (standard) Young tableaux and IwahoriHecke algebras will come up. This talk has the additional purpose of giving a small introduction (with many examples) into the representation theory of finite groups. As such, no previous knowledge in that area will be assumed.
N.B.: this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)

22/10/24  Seminario  14:30  16:00  1101 D'Antoni  Taro Sano  Kobe University  Geometry Seminar Delta invariants of Fano weighted hypersurfaces
Note:
This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (20232027)
Kstability (or existence of KählerEinstein metrics) of explicit Fano varieties has been studied for a long time. Delta invariants (stability thresholds) detect the Kstability of Fano varieties. Moreover, AbbanZhuang developed a powerful method to compute the delta invariants by adjunctions.
In this talk, I will explain our recent results on the Kstability of some Fano weighted hypersurfaces via the AbbanZhuang method.
This is based on joint work with Luca Tasin. 
22/10/24  Seminario  14:30  15:30  1201 Dal Passo  Valerio Assenza  IMPA, Rio de Janeiro  Seminario di Equazioni Differenziali
Magnetic curvature and one application to the existence of closed magnetic geodesic
Magnetic systems are the natural toy model for the motion of a charged particle moving on a Riemannian manifold under the influence of a (static) magnetic force. In this talk we introduce a curvature operator called magnetic curvature which encodes the information of the classical Riemannian curvature together with terms of perturbation due to the magnetic interaction. In a variational setting, we use this new notion of curvature to approach the problem of finding closed trajectories for small energy levels.
Note:
This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (20232027) 
16/10/24  Colloquium  15:00  16:00  1201 Dal Passo  Silvia Pappalardi  University of Cologne  Colloquium LeviCivita
Free probability approaches to quantum manybody dynamics
Note: this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006).
Understanding how to characterize quantum chaotic dynamics is a longstanding question. The universality of chaotic manybody dynamics has long been identified by random matrix theory, which led to the wellestablished framework of the Eigenstate Thermalization Hypothesis. In this talk, I will discuss recent developments that identify Free
Probability  a generalization of probability theory to noncommuting
objects  as a unifying mathematical framework to describe correlations
of chaotic manybody systems. I will show how the full version of the
Eigenstate Thermalization Hypothesis, which encompasses all the
correlations, can be rationalized and simplified using the language of
Free Probability. This approach uncovers unexpected connections between
quantum chaos and concepts in quantum information theory, such as
unitary designs. 