☰ George D. Torres

ν: Notes

Below is a collection of notes and survey papers from my undergraduate years to current. Please email me if you find any typos or have corrections.

*Note that, if I make an update to any of the pdfs, it can take up to an hour to be reflected on this page.

◈ Geometric Methods of Data Science (pdf): Lecture notes from M392C Geometric Methods of Data Science at UT Austin, Fall 2021.

◈ Combinatorial Group Theory (pdf): Lecture notes from M392C Combinatorial Group Theory at UT Austin, Spring 2021.

◈ Complex Geometry (pdf): Lecture notes from M392C Complex Geometry at UT Austin, Fall 2020.

◈ Numerical Analysis (pdf): Lecture notes from M387C Numerical Analysis: Algebra and Approximation at UT Austin, Fall 2019.

◈ Tropical Mathematics (pdf): Lecture notes from M394C Tropical Mathematics (Stochastic tropical geometry: theory, applications, and open problems) at UT Austin, Spring 2019.

◈ 4-Manifold Topology (pdf): Lecture notes from M392C 4-Manifolds at UT Austin, Fall 2018.

◈ Gauge Theory and 4 Manifolds (pdf): Lecture notes from M392C Gauge Theory at UT Austin, Spring 2018. A concurrent (and more error checked) version of these notes can be found here on Tim Perutz's page.

◈ Algebraic Number Theory (pdf): Lecture notes from M390C Algebraic Number Theory at UT Austin, Fall 2017.

◈ Contact Topology (pdf): Lecture notes from M392C Contact Topology at UT Austin, Fall 2017.

◈ Differential Topology (pdf): Lecture notes from Math 132 at Harvard, Spring 2015.

◈ Introduction to Category Theory (pdf): A compilation of notes on introductory category theory, with a view towards homological algebra and abelian categories. (in progress)

◈ The Maslov Index and the Poincare-Birkhoff Theorem in Planar Hamiltonian Dynamics (pdf): Undergraduate thesis submitted for the honors requirement of a Bachelor of Arts in Mathematics and Physics, Harvard University. 2017.

◈ The Grothendieck Spectral Sequence in Algebraic Geometry (pdf): Survey paper written as final project for Math 232b at Harvard.

◈ Foundations of Embedded Contact Homology (pdf): Survey paper written as final project for Math 287 at Harvard.

◈ Derived Functors and Homological Dimension (pdf): Survey paper written as final project for Math 221 at Harvard.

◈ Morse Homology (pdf): Survey paper written as final project for Math 231a at Harvard.

◈ Periodic Orbits in Hamiltonian Systems (pdf): Survey paper written as final project for Math 132 at Harvard.

◈ Introduction to Topological K Theory and Bott Periodicity (pdf): Survey paper written as midterm project for Math 231b at Harvard.