Daniel Eceizabarrena will defend his doctoral thesis on Wednesday, July 8th

• Due to the restrictions caused by the COVID-19 pandemic, the defense will be held online and users will be able to follow it live

Daniel Eceizabarrena obtained a Bachelor’s Degree in Mathematics from the University of the Basque Country in 2015 and a Master's Degree in Mathematics and Applications from the Autonomous University of Madrid in 2016. He was awarded with the Extraordinary End of Degree Award in Mathematics (2014/2015) by the UPV/EHU and with the National End-of-Career Award (2014/2015) by the Spanish Ministry of Education and Vocational Training.

In 2016, he joined the Basque Center for Applied Mathematics as a PhD student (FPU MECD 2015) within the Linear and Non-Linear Waves research line. During this period, he also spent three months at Laboratoire Jacques-Louis Lions (LJLL), Sorbonne Université (France) under Prof. Valeria Banica.

His PhD thesis, A geometric and physical study of Riemann's non-differentiable function, has been directed by Prof. Luis Vega (BCAM-UPV/EHU).

Due to the COVID-19 pandemic, the defense will be held online, through the platform BBCollaborate. It will take place on Wednesday, July 8^th at 11:30 am, and users will be able to follow it live using the following link: https://eu.bbcollab.com/guest/9e0250062259445aa7637cb95223684c

On behalf of all BCAM members, we would like to wish Daniel the best of luck in his upcoming thesis defense. 

PhD thesis Title: A geometric and physical study of Riemann's non-differentiable function

Abstract:

Riemann’s non-differentiable function is a classic example of a continuous but almost nowhere differentiable function, whose analytic regularity has been widely studied since it was proposed in the second half of the 19th century. But recently, strong evidence has been found that one of its generalisation to the complex plane can be regarded as the trajectory of a particle in the context of the evolution of vortex filaments. It can, thus, be given a physical and geometric interpretation, and many questions arise in these settings accordingly.

It is the purpose of this dissertation to describe, study and prove geometrically and physically motivated properties of Riemann’s non-differentiable function. In this direction, a geometric analysis of concepts such as the Hausdorff dimension, geometric differentiability and tangents will be carried out, and the relationship with physical phenomena such as the Talbot effect, turbulence, intermittency and multifractality will be explained.