My current mathematical interests are in group cohomology, Brauer groups, algebraic K-theory, Chevalley groups, and algebraic groups. This page contains an assortment of my mathematical writing, including seminar talk notes, homework sets, and other things.

Various seminar talks

The "sample" links in the scale theory beamer slides don't work, sorry.


Note that I am not the sole author.


Expository papers

Derived categories - Fall 2020

Professor: Igor Rapinchuk

Homological algebra and sheaf cohomology - Fall 2019

Professor: Igor Rapinchuk

Algebraic Groups - Summer 2019

Professor: Rajesh Kulkarni

Comprehensive exam materials - Spring 2019

The following are various resources I created for myself in preparation for my comprehensive exam in Spring 2019. The topics of the exam were group cohomology, Brauer groups, algebraic K-theory, and some algebraic number theory.

Seminar on Galois cohomology, Brauer groups, and local class field theory - Spring 2019

These are notes for a student seminar that I ran with the help of Nick Rekuski and Suo Jun (Stan) Tan at Michigan State University during spring of 2019. Of the notes below, Stan wrote notes and presented for weeks 4, 5, 12, and 13, and Nick wrote notes and presented weeks 2, 8, and part of 9. The rest (1,3,6,7,9,10,11) are my own notes.

Algebraic Number Theory 2 - Spring 2019

Professor: Aaron Levin

Algebraic Number Theory 1 - Fall 2018

Professor: Igor Rapinchuck

Commutative Algebra - Fall 2018

Professor: George Pappas
Textbooks: Commutative Algebra, Atiyah-MacDonald.

Graph Theory - Spring 2018

Professor: Peter Maygar
Textbooks: Modern Graph Theory, Béla Bollobás and Graph Theory, Reinhard Diestel

Quiver Representations - Spring 2018

Professor: Michael Shapiro
Textbook: Quiver Representations, Ralf Schiffler

Algebraic Topology 2 - Fall 2017

Professor: Matthew Hedden
Textbook: Algebraic Topology, Allen Hatcher

Lie Algebras - Fall 2017

Professor: Jonathan Hall

Representation Theory - Fall 2017

Professor: Michael Shapiro
Textbook: Representation Theory: A First Course, William Fulton and Joe Harris

Complex Analysis - Spring 2017

Professor: Jeff Schenker
Textbook: Complex Function Theory, Donald Sarason

Algebra - Spring 2017

Professor: Rajesh Kulkarni
Textbook: Algebra, Serge Lang

Algebraic Topology - Spring 2017

Professor: Matt Hedden
Textbook: Algebraic Topology, Allen Hatcher

Real Analysis - Fall 2016

Professor: Alexander Volberg
Textbook: Real Analysis: Measure Theory, Integration, and Hilbert Spaces, Elias Stein and Rami Shakarchi

Algebra - Fall 2016

Professor: Rajesh Kulkarni
Textbook:Algebra, Serge Lang

Differential Geometry - Fall 2016

Professor: Xiaodong Wang
Textbook: Introduction to Smooth Manifolds, John Lee

Undergraduate Thesis

Advisor: Christopher Moseley
Textbook: Introduction to Lie Algebras, Karin Erdmann and Mark Wildon