If you are a current graduate student, a prospective graduate student, a researcher thinking of applying to a position at my department, or an established researcher interested in a possible collaboration, please read this.
Prospective graduate students
If you are interested in doing a PhD in mathematics at UC Davis, I encourage you to apply to the Mathematics or Applied Mathematics PhD programs. You are welcome to email me if you are interested in my research and/or have questions, but please know that admission decisions are made at the department level and not by individual professors. I don't hire PhD students directly, and emailing me will probably have no effect on your chances of being admitted.
Current graduate students
If you are a current student at the UC Davis Mathematics or Applied Mathematics graduate programs and are interested in talking to me about doing research, you are welcome to email me or drop by my office anytime. I am especially interested in students with strong computer programming skills and an interest in one of the following areas: combinatorics, probability theory, number theory, experimental mathematics. I am also happy to chat informally about any math subject and hear about cool topics you are reading about (or watching lectures or YouTube videos about), a lemma you are struggling with and want to bounce ideas off of someone, etc.
Researchers interested in post-doctoral positions at my department
My department is currently advertising the Krener Assistant Professor positions, which are a combined research and teaching position. Krener Assistant Professors get assigned a faculty mentor with matching research interests. If you plan to apply for the position and work in areas of math that overlap my research interests, please contact me to let me know you are applying. Keep in mind that the positions are departmental positions and I do not make any hiring decisions, but I do have the ability to recommend candidates I am interested in mentoring.
Researchers at other universities who are interested in a research collaboration
I have at various times started remote collaborations with other researchers. Many of these attempted collaborations failed; others succeeded spectacularly, and so I've decided to try to replicate the model and advertise my interest in such collaborations: if you have an exciting research problem that you think I may be able to help with, in any area of math, you are welcome to contact me. Keep in mind I may be too busy to get involved or not interested in the topic, but if I can I will at least try to offer a thought, an idea, or a useful reference, refer you to someone else I know who may be interested, or tell you about a cool problem of my own that your problem reminded me of. Who knows where it might lead?