teaching and service
This semester I am teaching a topics course in deformation theory. Here is the website.
In the fall 2016 semester, I taught Calculus III at Columbia. Here is the courseworks website.
I believe that lecture is an important component of college-level math courses, but it is not the only component. Especially in an introductory course like Calculus, students must read the assigned section of the book, and do the assigned problems as independently as possible. In any course, you must take the initiative to understand the material -- if you don't understand something in lecture, speak up! You should also try some more independent diagnostics -- if you are having trouble with a problem, really try to have an honest dialogue with yourself about what concepts you are not understanding. Of course, you should feel free to come to office hours or the math help room and discuss these issues with me or with a graduate student (for example, your TA).
I am currently supervising an undergraduate research project aimed at understanding some subtle aspects of representation theory of general linear groups in positive characteristic; I'm also mentoring a student working on certain computational aspects of the inverse Galois problem. This past summer I also mentored a group of undergrads in the Columbia REU program with Dave Hansen, in a project about applications of Lie algebra representation theory to combinatorics. (Problem sets: I, II). Last summer I mentored a group of undergrads in the Columbia REU program with Daniel Halpern-Leistner.
In the past, I've been a mentor for Columbia's Summer Undergraduate Research program and a similar program at Stanford, and I regularly give talks aimed at undergraduates or younger students. I've spoken at the Columbia undergraduate math society, the Stanford undergraduate math organization, both MIT and Stanford SPLASH, as well as various math circles.
If you are undergraduate and are interested in working on a project with me (for example, if you would like me to supervise your senior thesis), please take a look at my research and see if you find it interesting before coming to speak with me. You might also want to look at Ravi Vakil's advice to potential students, in particular the section on general advice.