| 24/10/25 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Antonio Miti | U Roma La Sapienza |
Algebra & Representation Theory Seminar (ARTS)
Construction and Reduction of the Lie infinity Algebra of Observables associated with a BV-Module
Multisymplectic manifolds generalize symplectic manifolds by featuring a closed nondegenerate differential form of degree higher than 2. Such structures are natural candidates for a geometric formalization of classical field theories. In this context, Rogers (2010) showed that just as a symplectic manifold yields a Poisson algebra of functions, an n-plectic manifold yields an n-terms Lie infinity algebra of observables. The remarkable aspect of Rogers' construction is that it is essentially algebraic and relies only on the axioms of Cartan calculus, suggesting that this higher version of the "observable Poisson algebra" can be generalized beyond the realm of manifolds. In this talk, we propose such a generalization in the setting of Gerstenhaber algebras and Batalin–Vilkovisky (BV) modules, which provide an algebraic formulation of Cartan calculus of interests in the context of non-commutative geometry. This framework allows us to construct Lie infinity algebras of observables in a purely algebraic way, without reference to an underlying manifold. As an application, we turn to the problem of reducing multisymplectic observables in the presence of constraints or symmetries. Building on the work of Dippel, Esposito, and Waldmann, who introduced the notion of a "constraint triple" as a categorical package for coisotropic reduction, we adapt this formalism to our BV-module context and the associated Lie infinity algebras. This construction provides a conceptual framework for the algebraic reduction procedure of multisymplectic observables, as developed in our recent joint work with Casey Blacker (SIGMA 2024). The results presented here are part of a collaboration with Leonid Ryvkin, published in Differential Geometry and its Applications (2025).
This talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006) |
| 22/10/25 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | Gandalf Lechner | FAU Erlangen-Nürnberg |
Operator Algebras Seminar
Inclusions of Standard Subspaces
Note:This talk is part of the activity of the MUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)
Standard subspaces are closed real subspaces of a complex Hilbert space that appear naturally in Tomita–Takesaki modular theory and have many applications to quantum field theory. In this talk, standard subspaces are considered as a subject of interest in their own right (independently of von Neumann algebras). A particular focus are inclusions of standard subspaces, which have similarities to subfactors, and several new methods for investigating the relative symplectic complement of an inclusion will be discussed. A particular class of examples that arises from the fundamental irreducible building block of a conformal field theory on the line is analyzed in detail.
Joint work with Ricardo Correa da Silva, see https://link.springer.com/article/10.1007/s00220-025-05458-4. |
| 21/10/25 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Mattia Galeotti | Università di Bologna |
Seminario di Equazioni Differenziali
The Benamou-Brenier formulation of optimal transport on sub-Riemannian manifolds
The dynamical formulation of optimal transport between two probability measures $\mu_0,\mu_1$ on a (sub)Riemannian manifold $M$, aims at minimizing the square integral of a Borel family of vector fields
$$
\int_0^1\int_M||v_t||^2dmu_t dt,
$$
where the narrowly continuous curve of probabilities $\mu_t$ and $v_t$ must respect the continuity equation.
The equivalence between this Benamou-Brenier formulation and the Kantorovich formulation of optimal transport, is well known in Riemannian context, but still open in sub-Riemannian manifolds (in the SR case, $v_t$ is a family of {em horizontal} vector fields).
I will present some recent advancements in this problem and a joint work (with Giovanna Citti and Andrea Pinamonti), proving the equivalence under general regularity assumptions
in the case of a sub-Riemannian manifold with no non-trivial abnormal geodesics. The key idea is the formulation of a relaxed version of the dynamical problem that hinges the other two versions, and allows to prove the equivalence of the Kantorovich formulation with the relaxed and the original Benamou-Brenier formulation.
NB:This talk is part of the activity of the MUR Excellence Department Project MATH@TOV CUP E83C23000330006 |
| 15/10/25 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | Roberto Conti | Sapienza University of Rome |
Operator Algebras Seminar
Automorphisms of the Cuntz algebras: small subgroups of outer reduced Weyl groups
Weyl groups for the Cuntz algebras were introduced implicitly by Cuntz at the end of the seventies. However, they remained largely ignored probably because of computational difficulties until about 30 years later, when the breakthrough work by Conti and Szymanski allowed to determine explicitly a huge number of their elements by a sophisticated condition with a clear combinatorial flavour. In recent times, Brenti, Conti and Nenashev pushed the boundaries of the involved combinatorial structures, obtaining for instance the first enumerative results (at the moment, only for cycles).
In this talk I will report on recent work joint with F. Brenti and G. Nenashev (in preparation) where, building on the combinatorial machinery developed over the last few years, we construct certain subgroups of outer automorphisms of O_n. In particular, we are able to describe in detail the 46 distinct finite groups of outer automorphisms of O_4 lying in the outer reduced Weyl group and maximal at level 2, which were first determined by Szymanski and collaborators by clever computer-assisted methods. The notion of bicompatible subgroup of the permutations of a square grid will play a role in the discussion.
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| 14/10/25 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Bruno Premoselli | Université Libre de Bruxelles | Seminario di Equazioni Differenziali
Extremising eigenvalues of the GJMS operators in a fixed conformal class
Let $(M,g)$ be a closed Riemannian manifold of dimension $n ge 3$ and $P_g$ be a conformally-covariant operator on $(M,g)$. We consider in this talk two problem at the crossroads of conformal geometry and spectral theory: 1) determining the extremal value that the renormalized eigenvalues of $P_g$ take as $g$ runs through a fixed conformal class and 2) determining whether these extremal values are attained at an extremal metric. Examples of such operators $P_g$ include the famous conformal Laplacian of the Yamabe problem, $P_g = Delta_g + c_n S_g$, but also its higher-order generalisations such as the GJMS operators of order $2k$ for any positive integer $k$.
NB:This talk is part of the activity of the MUR Excellence Department Project MATH@TOV CUP E83C23000330006
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| 14/10/25 | Seminario | 14:30 | 16:00 | 1101 D'Antoni | Oscar Kivinien | University of Nottingham | Geometry Seminar
On the Betti numbers of compactified Jacobians
We prove a conjecture of Cherednik describing the Betti
numbers of compactified Jacobians of unibranch planar curves via
superpolynomials of algebraic knots. The methods of the proof use the
theory of orbital integrals and affine Springer theory. No prior
knowledge about any of these will be assumed.
Note:
This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023-2027) and the PRIN 2022 Moduli Spaces and Birational Geometry and Prin PNRR 2022 Mathematical Primitives for Post Quantum Digital Signatures |
| 10/10/25 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | Jiefeng LIU | Northeast Normal University, Changchun |
Algebra & Representation Theory Seminar (ARTS)
"Cohomology of restricted Poisson algebras in characteristic 2"
N.B.: this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)
In this talk, I will introduce restricted Poisson algebras in characteristic 2 and explore their connection with restricted Lie–Rinehart algebras. For the latter, a cohomology theory is deve-loped and abelian extensions are investigated. I will also construct a cohomology complex for restricted Poisson algebras in characteristic 2 that controls formal deformations. This complex is shown to be isomorphic to the cohomology complex of a suitable restricted Lie–Rinehart algebra. Several examples are provided to illustrate the constructions.
This is a joint work with Sofiane Bouarroudj and Quentin Ehret.
N.B.: this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006) |
| 10/10/25 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Luca CASARIN | "Sapienza" Università di Roma |
Algebra & Representation Theory Seminar (ARTS)
"The factorizable Feigin-Frenkel center"
N.B.: this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)
Given a simple finite Lie algebra over the complex numbers, we can consider two other Lie algebras attached to it: its Langlands dual Lie algebra and the affine algebra at the critical level. It is a theorem of the nineties, by Feigin and Frenkel, that the center of the completed enveloping algebra of the affine algebra at the critical level is canonically isomorphic to the algebra of functions on the space of Opers on the pointed disk for the Langlands dual Lie algebra. These objects are actually pointwise instances of a more general picture: the space of opers for example enhances to a space which lives over an arbitrary smooth curve that is equipped with a natural factorization structure. This structure is fundamental for the Geometric Langlands community: factorization patterns allow for local to global arguments. In this talk I will explain the construction of the objects mentioned above and elaborate on a joint work with Andrea Maffei in which we prove the factorizable version of the Feigin-Frenkel theorem.
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<em> <strong><u>N.B.</u>:</strong> this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006) </em>
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| 07/10/25 | Seminario | 14:30 | 16:00 | 1101 D'Antoni | Ulrich Derenthal | Leibniz Universität Hannover | Geometry Seminar
Rational points of bounded height on the chordal cubic fourfold
Cubic hypersurfaces over the rational numbers often contain infinitely many rational points. In this situation, the asymptotic behavior of the number of rational points of bounded height is predicted by conjectures of Manin and Peyre. After reviewing previous results, we discuss the chordal cubic fourfold, which is the secant variety of the Veronese surface. Since it is isomorphic to the symmetric square of the projective plane, a result of W. M. Schmidt for quadratic points on the projective plane can be applied. We prove that this is compatible with the conjectures of Manin and Peyre once a thin subset with exceptionally many rational points is excluded from the count.
Note:
This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023-2027) and the PRIN 2022 Moduli Spaces and Birational Geometry and Prin PNRR 2022 Mathematical Primitives for Post Quantum Digital Signatures |
| 30/09/25 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Gianmichele Di Matteo | Scuola Superiore Meridionale - Napoli | Seminario di Equazioni Differenziali
Energy identity for a higher dimensional Sacks-Uhlenbeck approximation
In this talk, we introduce a family of functionals approximating the conformally invariant Dirichlet n-energy of maps between two Riemannian manifolds (M^n,g) and (N,h), which admit critical points. Along the approximation process, these critical points may incur a bubbling phenomenon, due to the conformal invariance of the limit Dirichlet n-energy. We prove an energy identity result for this approximation, ensuring that no energy gets lost along the formation of bubbles, under a Struwe type entropy bound assumption. We then show that min-max problems for the n-energy are always solved by a "bubble tree" of n-harmonic maps. This is a joint work with T. Lamm.<br>
<b>NB</b>:<i>This talk is part of the activity of the MUR Excellence Department Project MATH@TOV CUP E83C23000330006</i> |