Dia: Dimecres 15 de juliol de 2026
Lloc: Aula S02, Facultat de Matemàtiques i Estadística, UPC. Pau Gargallo,14 BCN.
A càrrec de: Álvaro Fernández-Mora (Monash University)
Títol: Computer-assisted approach for the Infinitesimal Hilbert 16th problem
Resum: The infinitesimal Hilbert's 16th problem asks for a uniform upper bound on the number of limit cycles in polynomial Hamiltonian vector fields under polynomial perturbations. Let Z(n) denote this maximum number of limit cycles, where n is the degree of the perturbation and n+1 is the degree of the Hamiltonian. Upper bounds for Z(n) remain largely unknown even for low degrees. In this work, we present novel computer-assisted techniques to approach this classical problem. We apply our framework to construct an alternative proof of the celebrated result Z(2)=2. While the quadratic case is one of the few cases that has been fully solved, our primary objective is to build a scalable toolkit capable of overcoming the algebraic complexity that currently limits the study of Z(n) for large n.
Last updated: Thu Jul 9 23:18:36 2026