November 12, 2024

A Glimpse into Cauchy Problems Describing Pseudospherical Surfaces

It is well known that solutions of certain integrable equations can define abstract surfaces with negative and constant Gaussian curvature, commonly referred to as pseudospherical surfaces. Many of these equations are viewed as evolution equations and have been extensively studied, particularly regarding the existence and uniqueness of solutions. In this talk, we will explore the connections between Cauchy problems and pseudospherical surfaces, with a particular focus on the Camassa-Holm and Degasperis-Procesi equations.

About the speaker

Igor Leite Freire is currently an Associate Professor at the Department of Mathematics, Federal University of São Carlos (UFSCar), Brazil. Before joining UFSCar, he was an Associate Professor at the Federal University of ABC (Brazil), where he served as Vice-Provost for Research. He was a visiting professor at the Silesian University in Opava (Czech Republic), a Residential Fellow of the Institute of Advanced Studies at Loughborough University (UK), and an academic visitor to the Department of Mathematical Sciences at Loughborough University (UK). He currently serves as academic editor for Advances in Mathematical Physics and the International Journal of Differential Equations, both published by Wiley. His research interests include the connections between integrable systems, the geometry of surfaces, and Cauchy problems, with an emphasis on Camassa- Holm type equations.