I am a Postdoctoral Teaching Scholar 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.
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
. Now at TTU, I am collaborating
alongside Professor Magdalena Toda
Other research collaborators are: Professors Manuel Barros
, Anthony Gruber
, Emilio Musso
, and Changhwa Woo