There are classical results showing that if a negatively closed manifold has its horospheres of constant mean curvature then it is locally symmetric. Here we shall present a rigidity result involving the intrinsic Riemannian structure of these horospheres. More precisely if one of them is flat than the closed manifold is locally real hyperbolic. Several questions arose from the approach that we will discuss, in particular concerning replacing the hypothesis on the curvature by the assumption that there is no conjugate points. This is based on a joint work with G. Courtois and S. Hersonsky.

Cercherò di dare un’idea di alcuni dei risultati contenuti nel preprint ArXiv 2508.05105.
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 give necessary and sufficient conditions for the connectedness of some degeneracy loci. In the special case of Ulrich bundles, these degeneracy loci are called Ulrich subvarieties and we will see that they are always connected with a few exceptions. Joint work with V. Buttinelli and R. Vacca.
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

This presentation explores the emergence of Strange Non-Chaotic Attractors (SNAs) within quasiperiodically forced dynamical systems. We examine two distinct methodologies to rigorously prove the existence of these unique mathematical structures, focusing on recent results. In this work, we analyse a two-parameter family of quasiperiodically forced maps acting on the cylinder. We establish the existence of a continuous bifurcation curve, along which the system undergoes a nonsmooth period-doubling bifurcation. Furthermore, we demonstrate that at this critical parameter value, the closure of the associated attractor possesses a positive two-dimensional Lebesgue measure. We characterize the resulting fractalization by the divergence of the Lipschitz constant of the attracting invariant curve. N.B.: This talk is part of the activity of the MIUR Excellence Department Project Mat-Mod@TOV (CUP E83C23000330006).

This presentation explores the emergence of Strange Non-Chaotic Attractors (SNAs) within quasiperiodically forced dynamical systems. We examine two distinct methodologies to rigorously prove the existence of these unique mathematical structures, focusing on recent results. In this work, we analyse a two-parameter family of quasiperiodically forced maps acting on the cylinder. We establish the existence of a continuous bifurcation curve, along which the system undergoes a nonsmooth period-doubling bifurcation. Furthermore, we demonstrate that at this critical parameter value, the closure of the associated attractor possesses a positive two-dimensional Lebesgue measure. We characterize the resulting fractalization by the divergence of the Lipschitz constant of the attracting invariant curve. N.B.: This talk is part of the activity of the MIUR Excellence Department Project Mat-Mod@TOV (CUP E83C23000330006).

Le superoscillazioni sono un fenomeno che nasce dalla teoria dei misuramenti deboli di Aharonov ma che trovano inaspettate applicazioni in microscopia (superrisoluzione) ed in teoria dei numeri. Da un punto di vista matematico danno origine ad un fenomeno, detto supershift, che imita il comportamento delle funzioni analitiche. La precisa relazione tra queste due nozioni è più complessa di quanto ci si possa aspettare. In questo seminario darò le nozioni di base sulle funzioni superoscillanti e discuterò brevemente le loro applicazioni alla microscopia e alla teoria dei numeri. Concluderò discutendo la nozione di supershift e la sua relazione con il concetto di analiticità.
NB: This talk is part of the activity of the MUR Excellence Department Project MATH@TOV CUP E83C23000330006

I will study the Kodaira dimension of $A_6$, i.e., the moduli space of principally polarized Abelian $g$-folds, and of $X_g^n$, i.e., the space of Kuga $n$-fold varieties on these spaces. I will then use the results on the slope of Siegel modular forms to determine the Kodaira dimension for all Kuga varieties and $A_g (g eq 6)$. I will report the results for the case $g=6$. If I have time, I will report the results on the moving slope of $A_g$. These results were obtained in collaboration with: Dittmann, Scheithauer, Poon, Sankaran, Grushevsky, Ibukiyama, and Mondello.
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

&nbsp; Parabolic Kazhdan-Lusztig polynomials are ubiquitous across representation theory, geometry, and Lie theory. This raises two questions: can the (often strictly combinatorial) methods used to compute them be enriched to shed light on algebraic and geometric structures? Furthermore, if two a priori distinct structures are governed by the same polynomials, does this imply a deeper equivalence? <br> &nbsp; In this talk, we address these questions for parabolic Kazhdan-Lusztig polynomials of type (<em>D_n</em> , <em>A</em>_<em>n</em>-1) . By enriching the combinatorial methods to calculate these polynomials, we give a new presentation of the structure for the basic algebra of the anti-spherical Hecke category of isotropic Grassmannians. We then use this enriched structure to prove that it is isomorphic to the type <em>D</em> Khovanov arc algebra. <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>

  The homotopy groups of CW complexes and of the mapping spaces between them are notoriously difficult to compute. However, if one disregards torsion, rational homotopy theory becomes very effective and can easily solve such problems. Moreover, it produces efficient invariants of homotopy classes of maps, called Maurer-Cartan elements, which encode the rational type of path components. I will give a couple of examples and then explain how this extends to embedding spaces.
  Based on joint work with Benoit Fresse and Thomas Willwacher.
  N.B.: this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)

Assuming g_1, g_2, ..., g_k are measure preserving transformations on a probability space X, we require that a function f from X to a measurable space Y satisfies that f(x) is in F(x, f(g_1 x), .... f(g_k x) ) almost everywhere for an upper semi continuous correspondence F defined on X x Y^k. If there exists such functions however NONE of them are measurable with respect to any finitely additive extension of the probability measure for which the g_i are still measure preserving, we say that the correspondence F is paradoxical. We demonstrate some paradoxical correspondences that are also convex valued and nowhere empty. We are curious if there are applications beyond optimization and economics.