Mercoledì 10 Giugno 2026, dalle ore 14:00 in Aula U9-11 (Edificio U9 - Viale dell’Innovazione 10, Milano), Davide Furchì (Università degli Studi dell'Insubria) e Paolo Grossi (Università di Pavia) terranno i seguenti interventi
Relatore: Davide Furchì
Titolo: The Hermitian Killing form and the Hermitian Distance degree
Abstract: In this talk, I will discuss the Hermitian distance problem, specifically I am interested in knowing the number of critical points of the induced differentiable real-valued function. I will first briefly consider polynomials with conjugate variables (sometimes polyanalytic polynomials), which characterize the Hermitian distance problem, and present two methods to count their zeros, with an application to harmonic polynomials. I will then introduce the concept of Hermitian Distance degree, which is the set of naturals indicating the possible number of critical points of the Hermitian distance from a generic position in the ambient space to an algebraic variety. I will discuss properties and present examples and results.
Relatore: Paolo Grossi
Titolo: Galois closure and Lagrangian surfaces
Abstract: Given a 2n-dimensional smooth complex variety equipped with a nondegenerate holomorphic 2 form, an n-dimensional subvariety is called Lagrangian if the form vanishes identically on it. This seminar is devoted to a joint work with Federico Moretti concerning a class of surfaces that are Lagrangian in their Albanese variety and arise as Galois closures of rational maps from very general (1,6) abelian surfaces to the projective plane. These surfaces share some relevant properties and have relatively low invariants: K^2 = 24, p_g = 6 and q =4. As a secondary result, we proved the existence of a unique genus 6 hyperelliptic curve in the linear system of the polarization of a very general (1,6) abelian surface. The construction of hyperelliptic curves in the linear system of other (1,d) polarizations is the subject of an ongoing collaboration with Paweł Borówka and Anatoli Shatsila.
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