Benjamín Venegas

I’m an incoming DPhil student in Mathematics at the University of Oxford (Pembroke College), under the supervision of Prof. Kaibo Hu. You can find my institutional page here.

Previously, I graduated from Civil Mathematical Engineering at Universidad de Concepción (UdeC), Chile. I wrote my undergraduate dissertation under the supervision of Prof. Snorre Christiansen, titled “On the discretization of Dirac equations in the framework of Finite Element Systems”.

During the final three years of my undergraduate studies, I was trained as a Numerical Analyst. Throughout this period, I was lucky to be mentored by Prof. Gabriel N. Gatica in the art of Mixed Finite Element Methods, especially for Banach space-based formulations of nonlinear multiphysics problems arising in fluid flow models in porous media.

Nowadays, my work consists mainly in combining tools from this traditional method with tools from other areas of mathematics, such as algebraic topology and differential geometry, to obtain so-called structure-preserving discretisations, such as those derived from Arnold’s Finite Element Exterior Calculus and Christiansen’s Finite Element Systems.

On a broader level, I’m deeply interested in the interplay between Numerical Analysis, Differential Geometry, Functional Analysis and PDEs, as they study similar phenomena from fundamentally different viewpoints, which I believe to be complementary.