Information For Students

Recommendation Letters for Undergraduates

Ideally, ask me at least one month in advance. I will need the following materials:

resume/CV,
academic transcript,
and any statements or other materials you would like to share.

If there is something particular you would like me to address in the letter, please say so.

(Keep in mind that, even if you have done well in my course and talked with me during office hours, it is likely that I do not know you that well, so any extra information which you think might help me write the letter is welcome.)

I welcome reminder emails as the due date approaches!

Undergraduate Research

I do sometimes supervise undergraduate research. I recommend that you take Math 519 (Ordinary Differential Equations), with honors, ideally with me, and express to me your interest in undergraduate research. Other relevant courses include

[primary] Math 619 (Partial Differential Equations), Math 514 (Numerical Analysis), Math 521/522 (Analysis I & II);
[secondary] Math 616 (Data-Driven Dynamical Systems), Math 629 (Measure and Integration), Math 415 (Applied Dynamical Systems, Chaos and Modeling, significant overlap with Math 519);
and graduate courses.

Unfortunately, I do not always have time to supervise undergraduate research, so I may have to say no to some requests.

See MXM, Directed Reading Program, list of math REUs (see also references therein), and SROP. This outreach page links to the Math Club and Putnam Club.

Graduate Advising (Masters and PhD)

It is my pleasure to work with motivated graduate students. I currently have 5 PhD students (updated: 8/25/2025).

To work with me, you should already be enrolled at the University of Wisconsin-Madison. I strongly recommend you to have already taken Math 719 (Graduate PDE I) or an equivalent course. If you think you might want me to serve as your advisor, please ask me about a reading course.

Coursework

For working with me, the following courses are important:

Math 719/720 (Graduate PDE I/II). The graduate analysis courses are not a prerequisite -- they can be taken concurrently with PDEs! If you are interested in PDEs, I recommend to take this course right away. Deep knowledge of measure theory and functional analysis are not strictly necessary for this course.
Math 821 (Topics in PDE)
Math 716 (Ordinary Differential Equations)
Math 721/725 (Analysis I & II) and Math 722 (Complex Analysis, though this is less overtly relevant)

The following "applied" courses are also important:

Math 703/704 (Applied Math I & II)
Math 705 (Mathematical Fluid Dynamics)

Long term, it is useful to have some familiarity with harmonic analysis, geometry, numerics, physics...