Contents
Note: Many of these notes, talks, and articles have been removed for correction and improvement of typesetting. They will all be reposted by….eventually. (I hope by the end of November)
Talks
Research Talks
- Mordell-Weil Groups of Elliptic Curves
- Torsion Subgroups of Rational Elliptic Curves over Nonic Galois Fields (BUGCAT)
- Torsion Subgroups of Rational Elliptic Curves over Nonic Galois Fields (Maine-Québec)
- Torsion Subgroups of Elliptic Curves over (Nonic Galois) Number Fields (Upstate NT)
- Progress in the Classification of Torsion Subgroups of Elliptic Curves
- Torsion of Elliptic Curves over Number Fields of Small Degree
- Torsion of Elliptic Curves over Nonic Galois Fields
- A Foam Model for Bread Development
Expository Talks
- Rational Points on Curves
- Ranks of Elliptic Curves: Why the Rank is (Almost Certainly) Bounded
- To Infinity & Beyond: The Tale of really Big NUMBERS!
- Introduction to Algebraic Number Theory & Arithmetic Geometry
- Hungry, Hungry, Homology (Parts I & II)
- Perfectoid Spaces
- Adic & Perfectoid Spaces
- Analysis on Surreal Numbers
- A Zero Divisor Conjecture for Hopf Algebras
- Elliptic Curves, Galois Representations, and their $L$-functions
- The Critical Thread: The Symmetric Group in Galois Theory, Representation Theory, Representations of Lie Algebras, Combinatorics, and Topology
University & Department Talks
- Welcome to the Mathematics Department: A Guide for the Perplexed (2019)
- Effective Assessment in the Classroom
- Narcissus, An Autobiography: Evaluating Your Teaching
- Supporting Students Across the Spectrum of Academic Preparation
- What they didn’t tell me in orientation: a follow-up workshop for TAs
- Effective Assessment in the Classroom
- Welcome to the Mathematics Department: A Guide for the Perplexed (2018)
- Constructing an Online Teaching Portfolio
- Constructing a Teaching Portfolio
- Revisiting Orientation: A Follow-Up Workshop for TAs
- Integrating Technology in the Classroom
- Underrepresented Groups in Mathematics
- Constructing a Teaching Portfolio
- Revisiting Orientation: A Follow-Up Workshop for TAs
- (Self)Assessment in Teaching
Papers
Expository Papers
- The Sylow Theorems
- Exact Sequences & Homology
- The Binomial Coefficients
- The Isomorphism Theorems
- The Infinitude of the Primes
- On the Sum $1+2+3+\cdots+n$
- Mathematics Reference Tables
- Extending WolframAlpha’s Functionality
Course Notes
- MATH 6370: Algebraic Number Theory
- MAT 682: Numerical Linear Algebra
- MAT 683: Numerical Analysis
- MAT 701: Measure Theory
- MAT 702: Functional Analysis
- MAT 705: Calculus on Manifolds
- MAT 731: Rings & Modules
- MAT 732: Homological Algebra
- MAT 733: Commutative Algebra
- MAT 738: Algebraic Geometry
- MAT 761: Algebraic Topology I
- MAT 762: Algebraic Topology II
- MAT 830: Intersection Theory
- MAT 830: (Co)homology Theories
- MAT 830: Coexeter Groups
- MAT 830: McKay Correspondence
Other Notes
- Rational Points on Curves over Finite Fields, Serre
- AWS 2020: Nonabelian Chabauty
- AWS 2019: Topology and Arithmetic
- AWS 2018: Iwasawa Theory
- AWS 2017: Perfectoid Spaces