In Kähler geometry, the Calabi-Yau theorem establishes the existence and uniqueness of Kähler metrics with prescribed volume form. In this talk, I will present a non-Archimedean version of this theorem for general Kähler manifolds, extending a theorem of Boucksom-Jonsson from the projective setting. This is joint work with David Witt Nyström.
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

The Weyl energy on four-manifolds is a geometric functional related to the Chern-Gauss-Bonnet formula. Similarly to Willmore’s functional for surfaces embedded in the three-dimensional Euclidean space, it enjoys conformal invariance properties. We are interested in the interaction of the Weyl’s functionals of two manifolds under the operation of connected sum, showing conditions that decrease the total energy. Such estimates might be useful in understanding compactness properties of minimizing or critical families of metrics. This is joint work with F.Malizia
NB: This talk is part of the activity of the MUR Excellence Department Project MATH@TOV CUP E83C23000330006

In this seminar, I will present the problem of the propagation of singularities for differential equations and the corresponding problem of propagation of polarization for systems of differential equations. The problem has been solved for operators of principal type, but the theory is still incomplete for more general operators. Finally, I would like to present an example of an extremely degenerate operator that does not fall within the classical theory, yet for which propagation phenomena still occur. This example arises from differential geometry and concerns certain systems of PDEs related to the curvature tensors of a Riemannian or Lorentzian metric. N.B.: this talk is part of the activity of the MIUR Excellence Department Project Mat-Mod@TOV (CUP E83C23000330006).

In his seminal classification paper from 1976, Connes remarked that every separable tracial von Neumann algebra ought to be embeddable into an ultrapower of the hyperfinite type II_1 factor, or, in other words, be approximable by matrices. Over the following decades, the Connes Embedding Problem (CEP) remained unsolved, but many interesting and deep reformulations were discovered. Prominently, Kirchberg proved in his famous 1991 Inventiones paper that CEP is equivalent to several questions concerning C*-algebras and their tensor product, including his QWEP conjecture. He also showed that CEP holds if and only if there is a unique C*-norm of the tensor product of two copies of the full group C*-algebra of the free group. The latter was shown (by several authors) to be equivalent to Tsirelson’s conjecture about quantum correlations. CEP also relates to the open problems in group theory if all infinite discrete groups are sofic. Recently, Ji-Natarajan-Vidick-Wright-Yuen announced a negative solution to Tsirelson’s conjecture, and hence also a negative answer to CEP by proving that two complexity classes are the same

The YTD conjecture predicts that the existence of "canonical" Kähler metrics on a polarized projective manifold is governed by a purely algebro-geometric notion known as K-stability. Recently, solutions to (variants of) this conjecture have been proposed, and the purpose of this talk is to review this recent progress.
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

We are interested in climate models introduced by Sellers in 1969 which takes the form of some nonlinear parabolic equation with a degenerate diffusion coefficient. We investigate here some inverse problem issue that consists in recovering the so-called insolation function. We not only solve the uniqueness question but also provide some strong stability result, more precisely unconditional Lipschitz stability.
NB: This talk is part of the activity of the MUR Excellence Department Project MATH@TOV CUP E83C23000330006

&nbsp; Given a Coxeter group and a standard parabolic subgroup, Deodhar constructed a module over the Iwahori-Hecke algebra of the Coxeter group, giving rise to the so-called parabolic Kazhdan-Lusztig polynomials. <br> &nbsp; There is no general theory of "Coxeter subgroups" of Coxeter groups, but several families of subgroups of Coxeter groups themselves admit a canonical structure of Coxeter group. <br> &nbsp; We explain how to generalize Deodhar's construction to subgroups obtained as fixed points of an automorphism of order at most two of a standard parabolic subgroup of an arbitrary Coxeter group. This is joint work with P.-E. Chaput and L. Fresse, relying on properties of elements of minimal length in cosets modulo such subgroups obtained in a joint work with N. Chapelier. <br> &nbsp; <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>

&nbsp; This talk revolves around generating functions enumerating linear orbits and conjugacy classes of unipotent groups. We will study these generating functions by means of their linearised siblings ("ask zeta functions") obtained by averaging over sizes of kernels in modules of matrices. The study of the latter functions involves a happy blend of algebra, combinatorics, and geometry. <br> &nbsp; <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>

I am going to discuss a certain characterization of Birkhoff Billiards inside discs which is related to the expansion of the formal Lazutkin conjugacy at the boundary. Based on the joint work with Jacopo De Simoi, Andrew Gad and Marco Poon.
Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023–2027).

Noncommutative function theory and dilation theory for semigroups of completely positive maps have led to an interesting class of algebras generalizing Cuntz and Cuntz-Pimsner algebras. While formally they are defined in a familiar way, using creation operators on Fock-type spaces, what makes them difficult to study is that it is not clear how to obtain mixed commutation relations between the creation and annihilation operators. As a result until recently these algebras have been understood only in a few special cases, and there are still no general methods of obtaining relations in them, analyzing the ideal structure or computing the K-theory. Some of these algebras admit large quantum symmetries, and quantum groups provide then tools to analyze them, which are not accessible from a more classical point of view. The talk will review some results, examples and open problems in this area.