Colloquio De Giorgi

       8 October 2025 ore 4:00 pm

     Aula Dini, Palazzo del Castelletto, via del Castelletto, Pisa

Prof. SERGE CANTAT

Université de Rennes

Title: Degree Growth

Abstract : Consider a polynomial transformation f of a vector space V and iterate f; that is, compose f with itself, and then with f again, etc. Doing so, one gets a sequence of polynomial transformations f^n. Computing the degree of the formulas defining f^n, one obtains a sequence of integers deg(f^n). The problem I will discuss is : what type of sequences do we obtain in this way?
For instance, in dimension 2, the degree of f(x,y)=(y,xy) is 2, then the degree of f^2(x,y)=(xy, xy^2) is 3, then f^3(x,y)=(xy^2,x^2y^3) has degree 5, … and the degree of f^n is given by a sequence which is well known in Pisa.
The question is related to dynamical systems, basic algebraic geometry, and some number theory.

No previous knowledge will be assumed.

Web site: https://crmdegiorgi.sns.it/evento/colloquio-de-giorgi-2024-2025/

The event will take place in person.

Those who are unable to be physically present may attend the talk via zoom by following the link:

https://us02web.zoom.us/j/81126340951?pwd=cUQ2SldDK0xKU3hqdENEU3FiUXNkUT09

Luisa Ferrini

Centro di Ricerca Matematica
Ennio De Giorgi
Palazzo Puteano
Piazza dei Cavalieri 3
56126 PISA