Postdoctoral position: Outstanding candidates for postpoc positions are always welcome! If you email me, then please enclose a vita, a brief description of your research interests, links to a couple of your best manuscripts, and ideally contact information for one or two senior researchers who could tell me more about you.
Let me also encourage anyone interested in working with me to apply for the Peter O’Donnell Jr. Postdoc Fellowship at the Oden Institute. More information here. Additionally, the Bing Instructorships in the Department of Mathematics offer another excellent way to come to UT-Austin. If you apply for either of these opportunities and are interested in working with me, then please write me to give me a heads-up!
Doctoral students: I for the most part take on only students who are already enrolled in a doctoral program at the University of Texas. The best fit is likely to be with students in the CSEM program in the Oden Institute, or in the applied mathematics track in the mathematics department. I am certainly happy to work with students from other programs as well, provided this would be permissible by the home department.
If you are interested in working with me, but are not yet at the University of Texas, then I would be very happy to hear from you. However, it is unlikely that I would commit to anything as I think it is typically best for students to pick a program rather than a specific adviser. This is not a strict rule, and exceptions can be made, in particular for students who are further along in their studies (having, say, already completed a master's degree elsewhere).
Summer internships: No funded openings at this time.