My main interests are Random Matrix Theory, Algebraic Geometry and Number Theory.
Theses
- Undergrad: The Prime Number Theorem
- Master: Rational Tetrahedra
- Ph.D.: Colored Triangulations
Some Documents I Have Written:
- 2011: Exercises in Algebraic Geometry complementing Andreas Gathmann's online notes
- 2011: Complex Square Roots
- 2011: Intersection Theory on Smooth Surfaces
- 2011: The relation between the 27 Lines on a cubic surface and the 28 bitangents of a quartic curve
- 2011: Four Lines in Sapce: A set of exercises
- 2011: Notes on Quadratic Forms
- 2011: The Tangent Space to a Scheme
- 2010: The Group Law on a Cubic Curve
- 2008: Ranks of Quadratic Twists of Elliptic Curves over Function Fields
- 2008: The Topology of Curves
- 2008: Parameter Spaces of Curves and hypersurfaces
- 2006: Defining the Integers Inside the Rational Number Field (Spanish)
Recent Programs:
- 2009:
PerturbedKeplerOrbitSimulator
Written in Python, uses Pylab. It simulates the trajectory of a massless particle under the simultaneous influence a sun and a planet revolving around the sun.
Slides
- The Genus Expansion
- The Moduli Space of Stable Genus Zero Curves Part I Part II
- The Math Behind Escher's Print Gallery
- Lines on Cubic Surfaces and a Simpler version for undergrads
- Ordinals and Cardinals Part I Part II and a high-school version Cardinales y ordinales
- Ranks of Quadratic Twists of Elliptic Curves
- Rational Tetrahedra (Spanish)
- Defining the Integers Inside the Rational Numbers (Spanish)
More information about my mathematical background and teaching experience can be found in my CV, available by request.