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.

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

Note that I am not the sole author.

Professor: Igor Rapinchuk

Professor: Igor Rapinchuk

Professor: Rajesh Kulkarni

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.

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.

Professor: Aaron Levin

Professor: Igor Rapinchuck

Professor: George Pappas

Textbooks: *Commutative Algebra*, Atiyah-MacDonald.

Professor: Peter Maygar

Textbooks: *Modern Graph Theory*, Béla Bollobás and *Graph Theory*, Reinhard Diestel

Professor: Michael Shapiro

Textbook: *Quiver Representations*, Ralf Schiffler

Professor: Matthew Hedden

Textbook: *Algebraic Topology*, Allen Hatcher

Professor: Jonathan Hall

Professor: Michael Shapiro

Textbook: *Representation Theory: A First Course*, William Fulton and Joe Harris

Professor: Jeff Schenker

Textbook: *Complex Function Theory*, Donald Sarason

Professor: Rajesh Kulkarni

Textbook: *Algebra*, Serge Lang

Professor: Matt Hedden

Textbook: *Algebraic Topology*, Allen Hatcher

Professor: Alexander Volberg

Textbook: *Real Analysis: Measure Theory, Integration, and Hilbert Spaces*, Elias Stein and Rami Shakarchi

Professor: Rajesh Kulkarni

Textbook:*Algebra*, Serge Lang

Professor: Xiaodong Wang

Textbook: *Introduction to Smooth Manifolds*, John Lee

Advisor: Christopher Moseley

Textbook: *Introduction to Lie Algebras*, Karin Erdmann and Mark Wildon