Education

• Ph.D. in Mathematics, University of California, Santa Barbara (December 2009)
  • Dissertation: Hex Structures on Singular Euclidean Surfaces with Conical Singularities.
• Certificate in College and University Teaching, University of California, Santa Barbara (December 2009)
• Summer Teaching Institute for Associates Certificate, University of California, Santa Barbara (Summer 2007)
• Master's Degree in Mathematics, University of California, Santa Barbara (December 2005)
• Bachelor's Degree in Mathematics, University of Guanajuato and Center for Mathematical Research (CIMAT), Mexico (August 2003)

Research Interests/Scholastic Profile

• I am interested in low-dimensional topology and geometry, especially in geometric structures on 2- and 3-manifolds. Currently, I have been using a geometric complexity function to study topological and Riemann surfaces as branched covers of the Riemann sphere. I am also interested in exploring the connections of that complexity function to the classical Hurwitz problem.

Courses Taught at Texas Wesleyan 

• MAT-1302: College Algebra
• MAT-1303: Precalculus
• MAT-1305: Advanced Foundations of Mathematics for Teachers
• MAT-1310: Mathematics for Business and Economic Analysis
• MAT-1324: Calculus I
• MAT-1325: Calculus II
• MAT-2331: Calculus III

Publications

• Generalizations of Hyperbolic Area for Topological Surfaces. Rev. Un. Mat. Argentina  59 (2018) 431–441.
• An elementary upper bound for the number of generic quadrisecants of polygonal knots (with T. Ramirez-Rosas.) Appl. Math. E-Notes, 17 (2017) 157–163.
• The Complexity of Riemann Surfaces and the Hurwitz Existence Problem (with T. Ramirez-Rosas.) Bull. Austral. Math. Soc. 87 (2013) 131–138.
• Classifying Voronoi graphs of hex spheres. Topology Appl. 159 (2012) 1210–1218.
• The Moduli Space of Hex Spheres. Algebr. Geom. Topol. 11 (2011) 1323--1343.
• Hex Structures on Singular Euclidean Surfaces with Conical Singularities. Ph.D. Thesis, University of California, Santa Barbara, 2009.

Presentations

• An Introduction to Persistent Homology and the Shape of Data (July 2017), MathFest, Chicago, IL.
• An Introduction to Persistent Homology (Sep 2016), Texas Christian University, Fort Worth, TX.
• The Topological Complexity of a Surface (Jan 2016), Joint Mathematics Meetings, Seattle, WA.
• Finding Formulas for the Complexity of Riemann Surfaces (Aug 2013), Mathematical Congress of the Americas, Guanajuato, Mexico.
• The Complexity of Riemann Surfaces and the Hurwitz Problem (Mar 2012), The 46th Spring Topology and Dynamics Conference, Mexico City, Mexico.
• The Complexity of Riemann Surfaces (Jan 2012), AMS-MAA Joint Mathematics Meetings.
• Classifying Voronoi Graphs of Hex Spheres (Jan 2011), AMS-MAA Joint Mathematics Meetings.
• Classifying Hex Spheres (Sept 2010), International Conference Japan-Mexico on Topology and its Applications, Colima, Mexico.
• The Moduli Space of Hex Spheres (Aug 2010), International Congress of Mathematicians, Hyderabad, India.
• El Espacio Moduli de Esferas Hexagonales (The Moduli Space of Hex Spheres) (Jun 2010), Mathematics Institute, National University of Mexico.
• Hex Structures on Spheres (Jan 2010), AMS-MAA Joint Mathematics Meetings.