Dia: Dimecres 29 de gener de 2025
Lloc: Aula S03, Facultat de Matemàtiques i Estadística, UPC. Pau Gargallo,14 BCN.
A càrrec de: Sabyasachi Mukherjee (Tata Institute for Fundamental Research, India)
Títol: Topology and geometry of quadrature domains via holomorphic dynamics
Resum: A domain in the complex plane is called a quadrature domain if it admits a Schwarz reflection map; i.e., a meromorphic map that extends continuously to the boundary as the identity map. Quadrature domains have important connections with statistical physics, fluid dynamics, and diverse areas of analysis. We will discuss how classical Riemann surface theory and dynamics of Schwarz reflection maps can be exploited to study the topology and singularities of quadrature domains. We will review earlier works of Gustafsson, Lee, and Makarov in this direction, and introduce classical ideas from holomorphic dynamics to provide sharp upper bounds on the connectivity and number of double points of quadrature domains. Time permitting, we will mention connections between Schwarz reflection dynamics and combination theorems for antiholomorphic polynomials and reflection groups.
A càrrec de: Maciej Capiński (AGH University of Kraków)
Títol: Arnold Diffusion in the Full Three Body Problem
Resum: We will present a geometric mechanism which leads to Arnold Diffusion in the three body problem. As an application of our method we will consider the Neptune-Triton-asteroid system, with the mass of the asteroid playing the role of the perturbation parameter. The proof is computer assisted.
This is joint work with Marian Gidea.
Last updated: Thu Jan 30 11:27:02 2025