Expository Papers and Talk Slides

Here are some of the expository papers and sets of notes that I've written, a single Youtube video of a lecture I gave, and some slides for slide talks that I've given.

• An Introduction to Sheaf Theory, a Youtube video of an introductory talk I gave on an introduction to sheaves and Grothendieck topologies. The video quality is low, so beware!
• Descent Theory, a set of notes going through descent theory and fibrations for the purpose of doing algebraic geoemtric representation theory. These are under construction and unfinished! However, I think the development of descent for sites that are not induced by a pretopology is new and not done elsewhere in the way it's done here, if it's done at all.
• An Introduction to Sheaves and Sites, an expository paper that introduces the theory of sheaves and sites on categories.
• FMCS 2019 talk on geometrizing quasicharacters of p-adic schemes.
• An Introduction to the Local Class Field Theory of Serre and Hazewinkel, a set of notes that I wrote to modernize some of the exposition and show that it gives a geoemtric perspective for the proof of the Local Langlands Correspondence for p-adic GL(1).
• Pontryagin Duality, a set of companion notes that I wrote for a talk that I gave introducing the theory for the purpose of understanding Tate's Thesis.
• Introduction to Model Categories, a set of introductory notes that I wrote for a course in homotopy type theory that I took in my undergrad.
• An Introduction to Infinity Categories through Simplicial Sets, a set of introductory notes for the course in homotopy type theory above that I took in my undergrad.
• The Mitchell-Freyd Embedding Theorem, a term paper for a grad course in category theory I took in my undergrad.
• Intro to p-adic numbers slides, a set of slides that I did for an introductory general talk on p-adic numbers and ultrametric spaces.
• Intro to division rings slides, a set of slides that I wrote for a general talk on constructing and giving examples of (noncommutative) division rings.
• The Galois Cohomology Funtime Hour, a set of slides that I wrote for a talk that I gave in a graduate course in Advanced Galois Theory that I took in my undergrad. I was pranked when the slides were compiled, so there is a picture of Kim Jong Un on the last slide.
• Fubini's Theorem, Basic Measure Theory, and Convolution, a set of  slides that I used in a talk for a course in harmonic analysis that I took in my undergrad.
• The Fourier Transform and Distributions, a set of slides that I used in a talk in the same harmonic analysis course that I took in my undergrad. There is a slight error in one of the slides; readers beware! The error can be easily repaired, but  I never did fix it.