teaching and service
I'm not currently teaching anything. In the fall 2016 semester, I taught Calculus III at Columbia. Here is the courseworks website. Next semester, I'll teach a topics course on deformation theory. A preliminary description: This course will be an introduction to deformation theory, focusing heavily on applications. Recommended textbooks are Hartshorne's "Deformation Theory" and "FGA Explained," but neither are necessary -- and we will rapidly move away from the material in those sources towards more recent work. Topics may include the Tian-Todorov theorem (on unobstructedness of Calabi-Yau manifolds), infinitesimal Torelli theorems and infinitesimal variations of Hodge structure, the cotangent complex with applications to deformations of group schemes, liftability of K3 surfaces, and many others.
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. 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 summer I'm mentoring 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)
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.