I am an Assistant Professor at the Department of Mathematics and Statistics of Texas Tech University (TTU) in Lubbock.
My main mathematical research interests are in the area of Differential Geometry
. More specifically,
I am interested in theoretical problems related to the Geometric Calculus of Variations
for curves and surfaces, including, but
not limited to classical elastic curves
, constant mean curvature surfaces
, Willmore surfaces
, biharmonic surfaces
, and their multiple
generalizations, immersed in several ambient spaces: Riemannian and Lorentzian space forms
, Bianchi-Cartan-Vranceanu spaces
, and Killing submersions
. Although the spirit of my research is
primarily theoretical, I continually seek out potential applications of it to other fields, such as, Physics, Engineering, Biology, and Image Reconstruction, to mention a few.
I received my PhD from the University of the Basque Country (UPV/EHU) in Bilbao, Spain, in October 2018. My thesis,
"Invariant Surfaces with Generalized
Elastic Profile Curves"
, was written under the supervision of Professors Óscar J. Garay
and Josu Arroyo
and was declared "Sobresaliente Cum Laude", which represents
the foremost qualification. My dissertation was also honored with "Extraordinary Prize of PhD". Additionally, as an undergraduate student, I completed the End of Degree Project
"Geodésicas en Variedades de Riemann"
and, as a master's student, the
End of Master Project "Teorema Fundamental de Superficies y Aplicaciones"
. Both projects were also awarded the foremost qualification "Matrícula de Honor".
During my time as a PhD student, I spent one week at the University of Granada (Spain) collaborating with Professor Rafael López
. I also spent three months for a predoctoral stay at the
University of Cagliari (Italy) under the supervision of Professor Stefano Montaldo
Subsequently, I spent two years as a Visiting Postdoctoral Researcher at Idaho State University (ISU) in Pocatello working with Professor Bennnett Palmer
. Then at TTU, as a Postdoctoral Teaching Scholar, I collaborated
with Professor Magdalena Toda
Other research collaborators are: Professors Manuel Barros
, Anthony Gruber
, Emilio Musso
, and Changhwa Woo