In this talk I will present a recent construction of equilibrium states at positive temperature, with and without Bose-Einstein condensation, for a non-relativistic Bosonic QFT (gas of Bose particles) in the infinite volume limit, interacting through a localised two body interaction. In order to obtain this result, we use methods of quantum field theory in the algebraic formulation and of quantum statistical mechanics in the operator algebraic setting. The convergence of the interacting correlation functions is obtained constructing an equivalent perturbative series expansion introducing an auxiliary stochastic Gaussian field which mediates the interaction. Limits where the localisation of the two-body interaction is removed are eventually discussed in combination with other regimes. This talk is based on a collaboration with Nicola Pinamonti.

We present some recent results on optimal control/differential games in cases where the state equation is a stochastic delay differential equation (SDDE) with delay in the state and/or in the control. We look at two possible approaches: one based on partial smoothing properties of the transition semigroup associated with the uncontrolled SDDE (papers on optimal control , mean field control, mean field games without common noise with G. Bolli, F. Masiero, M. Ricciardi, M. Rosestolato), one based on regularization of viscosity solutions (paper with F. De Feo, A. Swiech, L. Wessels, on mean field control with only common noise).
NB: This talk is part of the activity of the MUR Excellence Department Project MATH@TOV CUP E83C23000330006

Motivated by the Green-Griffiths and Lang-Vojta conjectures, it is expected that the algebraic exceptional set of a log-surface $(X,B)$ of log-general type - which parametrizes rational curves on $X$ meeting $B$ in at most two points - is finite. In this talk, I will discuss recent results on this set for the cases where $X$ is the projective plane or a Hirzebruch surface, and is a curve with three irreducible components. This talk is based on [arXiv.2507.13280] and work in 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

I will introduce Lp spectral triples and give an overview of their properties. I will also discuss spectral triple isometries. On a different note, I will introduce twisted crossed products of Lp and Banach algebras by locally compact groups and outline some of their properties.
Time permitting, I will present a generalization of the so-called Packer-Raeburn trick to the Lp setting.

We start by reviewing the classical spectral theory of the Dirichlet-Laplacian, on a general open set. It is well-known that the spectrum may fail to be purely discrete, in this generality. We then turn our attention to a nonlinear variant of this problem, by considering the case of the $p-$Laplacian with Dirichlet homogeneous conditions. More precisely, we analyze the minmax levels of the constrained $p-$Dirichlet integral: we show that, whenever one of these levels lies below the threshold given by the $L^p$ Poincar\'e constant ''at infinity'', it actually defines an eigenvalue. We also prove a quantitative exponential fall-off at infinity for the relevant eigenfunctions: this can be seen as a generalization of v{S}nol-Simon--type estimates to the nonlinear case. Some of the results presented have been obtained in collaboration with Luca Briani (TUM Monaco) and Francesca Prinari (Pisa). <br> <b>NB</b>: <i> This talk is part of the activity of the MUR Excellence Department Project MATH@TOV CUP E83C23000330006 </i>

È ben noto grazie a un lavoro di Ein del 1988 che le intersezioni complete molto generali di multigrado $(d_1,...,d_c)$ nello spazio proiettivo di dimensione $n$ non contengono curve razionali non appena $d_1+...+d_c geq 2n-c-1 $. Questo risultato è stato reso ottimale ed esteso nel caso delle ipersuperfici grazie a un metodo introdotto da Voisin che ha ispirato lavori ulteriori di Clemens, Ran e miei. Nonostante lavori più recenti di Coskun, Riedl e Yang sempre nel caso delle ipersuperfici, il risultato di Ein è rimasto l’unico disponibile per intersezioni complete di codimensione arbitraria. Nel seminario parlerò di un lavoro in collaborazione con Francesco Bastianelli in cui estendiamo il lavoro di Ein, mescolando l’approccio di Voisin con quello di Coskun, Riedl e Yang.
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 argument shift method is a simple but efficient way to produce a commutative subalgebra in a Poisson algebra, in particular in the symmetric algebra of a Lie group. Its main ingredient is an operator on the Poisson algebra that generates the elements of the commutative subalgebra by acting on its center. In my talk I will describe an analogous operator on the universal enveloping algebra of gl(d), and show why it satisfies a similar property.
  N.B.: this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006)

&nbsp; The full symmetric Toda system is a Hamilton system on the space of real symmetric matrices, given by the Lax equation <em>L'</em> = [<em>M</em>(<em>L</em>),<em>L</em>] , where <em>M</em>(<em>L</em>) is the na&iuml;ve antisymmetrisation of the symmetric matrix <em>L</em> (deleting the diagonal and inverting the sign of the lower-triangular half). This system turns out to be Liouville-integrable and even super-integrable. In my talk I will prove that it satisfies one more integrability criterion, the Lie-Bianchi criterion, based on the study of its symmetries. <br> &nbsp; <em><small><small> <strong><u>N.B.</u>:</strong> this talk is part of the activity of the MIUR Excellence Department Project MatMod@TOV (CUP E83C23000330006) </small></small></em>

We introduce the concept of horospherical billiard in the universal covering of a compact surface without focal points and prove some rigidity results assuming the existence of some geometric first integrals.
Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023–2027).

Exponential sums over finite fields are essential ingredients in the solution of many arithmetic problems. Their study often relies on algebraic geometry, and especially on Deligne's Riemann Hypothesis over finite fields, which reveals deep structural features of these sums. In turn, one can exploit these to construct some remarkable combinatorial objects. The talk will provide a survey of these various aspects. (Joint works with A. Forey, J. Fresán and Y. Wigderson) <em> Note: </em> 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