# My students past and present

One of the best things about doing mathematics is getting to work with highly motivated students. I have been involved in mentoring students in mathematics research at three different levels: advanced high school students, undergraduate, and graduate students. I am very proud of all of them!

## Ph.D. students

I am currently supervising three Ph.D. students here in Edinburgh: Juliet Cooke and Tim Weelinck started in Fall 2015, and both are working on aspects of factorization homology. Anna Mrktchyan started in Fall 2016, and is jointly supervised by myself and Catharina Stroppel, at University of Bonn.

In addition to my own Ph.D students here in Edinburgh, I have worked with a handful of graduate students during my time at the University of Texas and at the University of Edinburgh, though I have learned at least as much from them as they from me!

- With
**Hendrik Orem**, a Ph.D. student of David Ben-Zvi, we studied algebro-geometric structures present in the lower central series of NC-complete algebras. This led to the paper, An algebro-geometric constructino of lower central series quotients. - With
**Iordan Ganev**, a Ph.D. student of David Ben-Zvi, we studied the quantization of multiplicative hypertoric varieties, via algebras of $q$-difference operators and their quantum Hamiltonian reduction. Iordan is now a post-doc with Tamas Hausel, in Vienna. - With
**Pavel Safronov**, a Ph.D. student of David Ben-Zvi, we are studying the symplectic stack $BG$ and its quantizations. Pavel Safronov was a post-doc at University of Oxford, and now Max Planck Institute for Mathematics in Bonn. - With
**Noah White**, a Ph.D. student of Iain Gordon, we are studying the center of the reflection equation algebra for $GL_n$, and certain quantum deformations of the characteristic polynomial there. Noah is now a post-doc with Raphael Rouquier, at UCLA.

## Undergraduate students

I have mentored undergraduate research projects at the Summer Program in Undergraduate Research (SPUR) and Undergraduate Research OPportunities (UROP) program at MIT, an M.Math dissertation and through the London Mathematical Society Research Bursary program at the Univeristy of Edinburgh.

- In 2009, I mentored
**Asilata Bapat**in the SPUR program. Her project with me, published as Lower central series of free algebras in symmetric tensor categories, won us a Hartley Rogers prize for best research paper at SPUR. Asilata is currently a Ph.D. student at the University of Chicago, and a beloved mentor at Canada/USA Math Camp. - In 2010, I mentored
**Ben Bond**in the UROP program. His project with me, The lower central series of the symplectic quotient of a free associative algebra was published in the Journal of Algebra. Ben is currently a mathematics graduate student at Stanford University. - In the schoolyear 2013-2014, I supervised the MMath dissertation of
**Sam Moore**, an exposition of various constructions of Ramanujan expander graphs using group theory and number theory. Sam is starting a graduate program in statistical and applied mathematics at the University of Bath.

## High School Students

I was a mentor at the Research Science Institute (RSI) and the Program for Research in Mathematics, Engineering and Science (PRIMES), at MIT. These were programs for bright high school students to conduct mathematics research in a rigorous and challenging environment.-
**Susan Zhang**and**Sana Raoof**were my first RSI students. Susan Zhang studied optimization problems around quantum computing gates, went on to study math at Princeton, and now works as a data scientist. Sana won the International Science and Engineering Fair in 2008 for her project with me about connections between knot theory and DNA. She is currently an MD/Ph.D student at Harvard. -
**Noah Arbesfeld**and**Eric Larson**were my next two RSI students. Noah's project with me, published as New results on the lower central series of a free associative algebra, won Noah 6th place nationally at the Intel Science Talent Search in 2009. Eric's project with me, published as On the classification of certain fusion categories won Eric 2nd place in the Siemens Competition, and 1st place at Intel Science Talent Search in 2009. They both shook hands with President Obama! Noah majored in mathematics at MIT and is now a Ph.D. student at Columbia University, with a handful of papers on the arXiv. Eric majored in mathematics at Harvard, and is currently a Hertz Fellow and Ph.D. student at MIT. Eric also has a handful of papers on the arXiv. - In 2011 I was a PRIMES mentor to
**Surya Bhupatiraju, Yongyi Chen, William Kuszmaul, Jason Li, Michael Zhang**. Their work with me led to the papers Lower central series of associative algebras over the integers and finite fields and Poisson traces in positive characteristic. Surya and William each went on to participate in the RSI program the next year; William was an Intel/STS finalist.

## Mentors

I have been extremely lucky to have excellent research mentors at every stage of my education and early resarch. Arkady Vaintrob advised my undergraduate thesis, and taught me about representation theory and its interactions with low-dimensional topology. I did my Ph.D. under the expert guidance of Pavel Etingof, whose mathematical impact on me has been tremendous. Kobi Kremnizer served as an excellent informal second adviser to me, and in particular proposed my thesis problem. I was a post-doc with David Ben-Zvi, who was about the best post-doc mentor one could ask for!