Below is some information about my mentoring philosophy that might be useful to graduate students who are considering working with me.
General philosophy about our potential mentoring relationship: My goal would be to help you achieve your own goals. These could be anything from becoming a professor at a research-intensive or teaching-focused university to working in industry or, who knows, opening a bakery (which is what I'm doing in some parallel universe).
Your goals may change, mine will not.
This is a relationship that will involve substantial support from me for a number years as you build your career. I will take this responsibility with the seriousness it deserves.
Mathematically: My goal will be to help you become an independent researcher. Toward that end, I want to meet you where you are, whether you already have questions you'd like to investigate or you would like some direction from me to help catalyze the process of developing a research program. However this works out, we'll be exploring some untread mathematical territory together before you head off into the wider world. This process is part of what makes (mathematical) research so wonderful.
Professionally: The process from starting as a graduate student to achieving your eventual goals will involve any number of possible paths. I will help with this process however I can.
Personally: Mathematics is a human endeavor. I will seek to recognize and affirm your full humanity in our mentoring relationship, as well as support you in whatever way I can as you navigate our department and the wider mathematical community.
My expectations of you: In general, I will expect you to mirror the above ideas in your own interactions with me. Beyond that, I will expect the following of you:
To be as fully engaged as possible in developing your research program;
To keep an open channel of communication with me about your mathematical, professional, and (when appropriate) personal concerns.
To be unwaveringly honest with me, as I will endeavor to be with you.
Possible directions of research: My research is mainly in geometric group theory and its connections to objects arising naturally in low-dimensional topology. Specifically:
The geometry of spaces with coarse non-positive curvature features, including:
Mapping class groups of finite type
Hierarchically hyperbolic spaces, more generally
CAT(0) spaces, including CAT(0) cubical geometry, median spaces, injective spaces, etc.
Convex cocompactness, subgroup stability, and their generalizations
Morse and sublinear-Morse boundaries, and their generalizations
Teichmüller geometry, surface bundles, and singular flat geometry
Big mapping class groups and surfaces of infinite type
I will be happy to provide you with any number of papers to start your investigations.