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 $\C^n$.