Disclaimer: I composed most of the following notes to improve my own understanding of various topics as I was learning them, so they should not be considered authoritative, especially the unfinished notes. Please email me at enikitop [at] umich [dot] edu with typos/questions/suggestions. (In particular, please do not email any of the listed professors about these notes.) Also, the notes below do not include the notes I have written for any of my presentations; please click here for those.
More or Less Finished Notes
These are notes I am not likely to change very much, except to fix typos.Here are some notes about stochastic integration/differential equations. They are based on a Fall 2018 UCSD course given by Todd Kemp. They were also revamped (through Lecture 25) and used as the main text for the 2022 iteration of the course. Lectures after 25 have not yet been edited and fixed up. The document was last updated on November 8, 2022.
Here are some notes I wrote about free products of noncommutative probability spaces. I may add material on the C* and W* cases at some point as well. This document was last updated on May 15, 2019.
Unfinished Notes
These are some incomplete notes from courses I took before graduate school. I am not sure I will ever get around to filling in the missing portions, but I would like to leave them up in case the added exposition about the topics that are there is helpful to anyone.Here are some notes about Riemannian geometry. They are based on an AY 2017–2018 ELTE course of Balázs Csikós, but I have added a large amount of background material. I did not get around to writing about the last topic of the course: geodesics and Jacobi fields. This document was last updated on December 21, 2017.
Here are some notes about ergodic theory. They are based on a Spring 2018 ELTE course given by Zoltán Buczolich. I did not get around to writing about the last topic of the course: entropy. This document was last updated on May 8, 2018.