Lecture Notes
Math 7361 (Cohen-Macaulay Modules and Approximations) - Topics in Representation Theory, Fall 2021, taught by Alex Martsinkovsky.
The first part of this course is an introduction to the theory of local rings and to homological methods in commutative algebra. In the next part several constructions of maximal Cohen-Macaulay (mCM) approximations. Including the pitchfork construction of Auslander - Buchweitz. The last third of the course is devoted to various results related to mCM approximations inlcuding: connections with Tate cohomology, homological invariants and characterizations of regular local rings, applications to singularity theory, and group cohomology of groups of finite virtual cohomological dimension.
Other Talks
Nakajima quiver varieties - Learning seminar: Stable envelopes and quantum groups, Northeastern University, February 9 and 16, 2023.
I gave two 2-hour lectures covering the basics of quiver representations (including doubled, and framed represntations) and the GIT construction of Nakajima quiver varieties.
Amenable groups - Arithmetic groups Mini-course, The University of Auckland, December, 2019.
I gave two 75-minute talks covering the basics of amenable groups including the relation with Kazhdan's Property (T) and applications to the construction of expander graphs. The last talk culminated with a 'proof' of the Banach-Tarski paradox
Representations of quivers and dense orbits - Mathematics Students Research Conference, The University of Auckland, June 2019.
Slides from a 30 minute presentation introducing representations of quivers, reflection functors, and an algorithm to detect dense orbits in certain (extended Euclidean) quivers. Based on work done while I was a summer research scholar at Australia National University.