Gérard Besson,  CNRS-Grenoble.  On the intrinsic geometry of horospheres in negative curvature.

Martedì 14 Aprile 2026 ore 14:00 aula 2001

Abstract:   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.

Simon Jubert,  Sorbonne Université.  Yau–Tian–Donaldson correspondence for projective bundles over a curve

Martedì 31 Marzo 2026 ore 16:00 aula 2001

Abstract:   A central question in complex geometry is that of the existence of canonical metrics. In the 1980s, Calabi proposed extremal metrics as candidates, naturally generalizing constant scalar curvature Kähler metrics. In this talk, we will explain that, for projective bundles over a curve, the existence of extremal metrics can be characterized using a notion of stability defined on a certain moment polytope, formulated in terms of convex functions on it. We will try to motivate this stability condition by providing examples where it can be checked effectively. If time permits, we will also give an interpretation of this stability notion in terms of test configurations, that is, one-parameter degenerations of the variety, within the framework of the Yau–Tian–Donaldson conjecture. This is joint work with Chenxi Yin (UQAM). The work was carried out with the support of the ERC project SiGMA.

Samuele Mongodi,  Università di Milano Bicocca.  Sharp subelliptic estimates for the debar-Neumann problem

Martedì 24 Marzo 2026 ore 16:00 aula 2001

Abstract:   I will talk about a joint work with G.M. Dall'Ara (Indam-SNS Pisa) about the problem of determining the optimal gain in regularity in the debar-Neumann problem near a D'Angelo finite type point (wrt the Sobolev scale).  Classical methods developed by Kohn (multiplier ideals) and Catlin (potential theory) do provide some gain in regularity, but fall short in giving optimal results. We introduce a new technique, based on Fourier analysis, a new geometric notion of type for plurisubharmonic functions,  and, by employing an uncertainty principle introduced by Dall'Ara, we are indeed able to obtain sharp subelliptic estimates in a class of low dimensional examples.

Fabrizio Bianchi,  Università di Pisa.  Dynamics of Hénon-like maps

Martedì 17 Marzo 2026 ore 16:00 aula Dal Passo

Abstract:  Hénon-like maps are invertible holomorphic maps, defined on some convex bounded domain of $\mathbb C^k$, that have (non-uniform) expanding behaviour in $p$ directions and contracting behaviour in the remaining $k-p$ directions. They form a large class of dynamical systems in any dimension. In dimension 2, they contain the Hénon maps, which are among the most studied dynamical systems. In this talk, I will give an overview of the main dynamical properties of these maps. In particular, I will focus on how tools from pluripotential theory can allow one to go beyond the algebraic setting of the Hénon maps. The talk is based on joint works with Tien-Cuong Dinh and Karim Rakhimov.

Liviu Ornea,  University of Bucharest.  Non-Kaehler metrics on compact manifolds

Martedì 10 Marzo 2026 ore 16:00 aula 2001

Abstract:  I shall recall the definitions and main properties of several Hermitian non-Kaehler metrics (Gauduchon, puriclosed, balanced, locally conformal Kaehler), then discuss the possibility of their simultaneous existence on the same compact manifold. Based on joint works with Misha Verbitsky.

Anna Miriam Benini,  Università di Parma. Universality in Transcendental Dynamics

Martedì 3 Marzo 2026 ore 16:00 aula 2001

Abstract:  The Mandelbrot set  is a fractal object encoding the dynamical behaviour of the family of quadratic polynomials z^2+c, where c is a parameter varying over the complex plane. It surprisingly appears also in the parameter spaces of all (reasonable) rational maps and in such sense, it also encodes the dynamical behaviour of this much larger class. The explanation is intricate and relies on the concept of renormalization: essentially, renormalization  isolates and extrapolates the behaviour of a rational functions near  its critical values, and brings it back to analogous behaviours for quadratic polynomials.  In this work we present an analogous object for transcendental maps, which arises from a model family  and yet encodes the dynamical behaviour of all  (reasonable) families of transcendental meromorphic maps.

This is joint work with M. Astorg and N. Fagella.

Pouriya Torkinejad Ziarati,  Université Paul Sabatier Toulouse. Examples of critically cyclic functions in the Dirichlet spaces of the ball

Martedì 27 Gennaio 2026 ore 16:00 aula D'Antoni

Abstract: 

In this work, we construct examples of holomorphic functions in the Dirichlet space of the ball in C^2, for which there exists an index a in [1/2,2] such that the function is cyclic in b-Dirichlet space if and only if b is bounded above by a. To this end, we use the notion of interpolation sets in smooth ball algebras, as studied by Bruna-Ortega and Chaumat-Chollet.

Alberto Saracco, Università di Parma. On transcendental Hénon maps with escaping Fatou components

Martedì 18 Novembre 2025 ore 16:15 aula D'Antoni

Abstract: 

The dynamics of holomorphic maps in several variables in much richer than that in one variable and has yet to be fully understood.

An easier setting is that of functions of "one and a half" variable, i.e. functions from C^2 to C^2 of some easier form that makes them look more similar to functions of one single variable. One kind of such functions is that of Henon maps, automorphisms of C^2 of the form: F(z,w)= (f(z)-aw,z).

We investigate the case where f(z) is trascendental and find example of (1) escaping Fatou components admitting different limit functions (joint work with Miriam Benini and Michela Zedda) and (2) escaping Fatou components with disjoint hyperbolic limit sets (joint work with Veronica Beltrami and Miriam Benini).

Javad Mashreghi, Laval University. Polynomial Approximation: Old Foundations and New Frontiers

Martedì 28 Ottobre 2025 ore 16:15 aula D'Antoni

Abstract: 

In this presentation, we explore polynomial approximation schemes within function spaces. While Taylor polynomials are fundamental in polynomial approximation theory, there are instances where they may not be the most suitable candidates. Without entering into technical details, we will discuss some summation methods, with a particular emphasis on the well-known Cesaro means. Our focus remains primarily on Hardy and Dirichlet spaces, although other function spaces also make appearances in the discussion. Moreover, within the broader context of super-harmonically weighted Dirichlet spaces, we establish that Fejer polynomials and de la Vallee Poussin polynomials serve as appropriate approximation schemes.

This work has evolved over an extended period and is the result of collaborative efforts with O. El-Fallah, E. Fricain, K. Kellay, H. Klaja, M. Nasri, P. Parisé, M. Shirazi, W. Verreault, T. Ransford, and M. Withanachchi in various combinations.

Yifan Chen, UC Berkeley. When singular Kahler-Einstein metrics are Kahler currents

Martedì 7 Ottobre 2025 ore 16:00 aula D'Antoni

Abstract: 

We show that a general class of singular Kähler metrics with Ricci curvature bounded below define Kähler currents. In particular the result applies to singular Kähler-Einstein metrics on klt pairs. This is a joint work with Shih-Kai Chiu, Max Hallgren, Gabor Szekelyhidi, Tat Dat To, and Freid Tong.

Tjaša Vrhovnik, University of Granada. Every nonflat conformal minimal surface is homotopic to a proper one

Martedì 30 Settembre 2025 ore 16:00 aula D'Antoni

Abstract: 

Given an open Riemann surface $M$, we prove that every nonflat conformal minimal immersion $M\to\R^n$ ($n\geq 3$) is homotopic through nonflat conformal minimal immersions $M\to\R^n$ to a proper one. If $n\geq5$, it may be chosen in addition injective, hence a proper conformal minimal embedding. Prescribing its flux, as a consequence, every nonflat conformal minimal immersion $M\to\R^n$ is homotopic to the real part of a proper holomorphic null embedding $M\to\C^n$. We also obtain a result for a more general family of holomorphic immersions from an open Riemann surface into $\C^n$ directed by Oka cones in $\C^n$.