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

Finite Element Exterior Calculus (FEEC) is a powerful framework for developing stable discretizations of partial differential equations, providing a systematic approach to problems in computational electromagnetism and fluid mechanics. This talk explores recent developments in isogeometric versions of FEEC, with a special focus on structure-preserving discretizations for geometries with polar singularities. We will first discuss the construction of hierarchically-refined polar-spline spaces. We will then demonstrate how they form a discrete de Rham complex and provide a mathematically sound foundation for adaptive structure-preserving simulations on polar geometries. The talk is part of the activity of the MUR Excellence Department Project MatMod@TOV (CUP E83C23000330006).

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

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.

This talk addresses Kac’s famous question, “Can one hear the shape of a drum?”—that is, whether the spectrum of the Laplacian on a domain uniquely determines its shape— in the context of convex planar billiard tables. While non-convex counterexamples are known (Gordon–Webb–Wolpert), the problem remains open for strictly convex domains with smooth boundaries. As shown by Anderson, Melrose, and Guillemin, the spectral question is deeply connected to its dynamical analogue: whether the length spectrum—the set of lengths of all periodic billiard trajectories—determines the domain up to isometry. In joint work with Vadim Kaloshin and Alfonso Sorrentino, we show that this is indeed the case for domains that are sufficiently close to a general ellipse and possess dihedral symmetry.
Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023–2027).