For prospective graduate students

1. Coursework: Before I engage in any capacity with direct supervision, I would expect that you have passed the preliminary exams, taken 202AB and have taken or are intimately comfortable with the material of 206 (also 208 and/or 209 would be ideal). The best possible preparation would be to go through Chapters I through IX in the book ``A Course in Functional Analysis'' by John B. Conway, and independently do all the exercises in them. I expect this to take one summer (could be good to consider after completing the 202AB sequence in your first year). 

2. Disclaimer: While I am interested in taking on new PhD students, it is not always a certainty that I will accept a new student as this may depend on various factors. Also each student various and there is no fixed format or model for supervision that I follow. One common intermediary step which I will likely recommend is to do a reading course on an advanced topic with me. 

3. Seminar: As a student interested in this field, I consider it important to attend the operator algebras research seminar (Tuesdays 3:30PM) weekly, regardless of how advanced you are. 

4. Breadth: Outside of research and reading credits, I strongly advice to take a wide variety of graduate courses in the department (at least one or two every semester), particularly including the following (in no particular order) which are highly relevant to operator algebras: 205, 214, 241, 250AB, 261AB, 240, 229,  215AB, 218AB, 258, 235AB.

My main area of research is in the field of C* and von Neumann algebras, which is a subfield of operator algebras. Jesse Peterson has a substantial collection of resources for books to read in the field. However I isolate two advanced ones below, that are very relevant to my own particular interests. It is essential to obtain these either online or in print, and begin reading them carefully. 

1. ``C*-Algebras and Finite Dimensional Approximations'' by N. Brown and N. Ozawa. 

2. ``An Introduction to II_1 Factors'' by C. Anantharaman and S. Popa. 

Some cornerstone topics that I like include: subfactors, free entropy, deformation rigidity, amenable actions, strong convergence, noncommutative L^p spaces, etc.

Here are some lists containing open problems of interest to me. These may be out of date, so it's best to consult with me or other experts regarding the status of a problem before working on them. 

1. Schafhauser-Tikuisis-White's 99 open problems on the structure of nuclear C*-algebras: https://arxiv.org/pdf/2506.10902

2. My 50 open problem list on ultraproducts of II_1 factors: https://arxiv.org/abs/2511.20377

3. J, Peterson's open problem list in operator algebras: https://math.vanderbilt.edu/peters10/problems.html

4. Hannes Thiel's problem list: http://hannesthiel.org/category/open-problems