I am always happy to hear from students who are interested in mathematics research! But I get more requests to advise students than I can reasonably accommodate. If you think you might be interested in joining my lab, please consider the following information.
Math research is quite different from coursework. In a typical college course, the professor gives you a set of problems they know students can solve in a reasonable amount of time. Research is more open ended. We often find some interesting phenomenon and spend months thinking about it until we make some progress, and oftentimes this progress doesn't even mean that we solve the original problem we sought out to solve.
Enjoying a course I taught is not necessarily correlated with a successful research partnership. My courses are designed to be accessible and support students with a wide range of mathematical backgrounds. Research, by contrast, requires independent learning, constant revision, and sitting with unresolved problems for weeks.
I primarily focus on numerical analysis, usually applied to PDEs on metric graphs (networks). That means that I develop algorithms to solve complicated mathematical problems that otherwise do not have a nice analytical solution. The complicated parts of Math 452/552 are similar to my work, but imagine many Runge-Kutta or Linear Multistep Methods coupled together in time and space in a complex system. The two most important features of an algorithm for me are efficiency and consistency (e.g. is the code as optimized as it can be, and can we be sure it's solving the equation we think it is). For this reason, students who rely primarily on AI-generated code are not a good fit for my research group. AI tools may be used as screening and brainstorming aids, but students are responsible for fully understanding their code, testing it, editing it, and defending every part of the code they submit.
Once we have a working code infrastructure, we can start to observe patterns and make conjectures. Often, interesting patterns emerge and we get to act as math detectives to figure out what causes them. For a mostly student-accessible introduction to some of my research, you can look through my 2022 dissertation.
Really consider: are you asking me because you need to fulfil a credit/honors requirement and you either did well in my course or "like my vibe?" I love making math accessible and fun, but I have found that it's not a solid foundation for a collaboration.
Have you read mathematics outside of assigned classes?
Do you enjoy coding? How do you feel about spending weeks debugging code?
Are you ok with the possibility that a project might not work out as cleanly as you envisioned?
Are you excited (not just willing, but excited) to put in the effort necessary to produce a high quality research paper? In particular, are you prepared to spend substantial time revising work? Are you open to constructive feedback? Will you be willing to redo your figures and rerun your code multiple times?
Do you want to learn numerical PDEs, or is your interest actually in a different area of mathematics?
Beginning a research project does not guarantee completion of an honors thesis, master's thesis, publication, or other final product.
Research is inherently uncertain. Projects sometimes take unexpected directions, require substantially more background than anticipated, or do not produce results suitable for a thesis (in these cases, we might change direction but that takes time). In other cases, a student's level of engagement or the quality of the work may not meet the standards required for successful completion.
My responsibility as a mentor is to help students learn mathematics and conduct research to the best of their ability. Successful completion of a thesis depends on sustained effort, professional standards, and the quality of the resulting work, not simply on enrolling in a research project.