note to prospective students

I plan to recruit one PhD student to join my group at Penn State in Fall 2027. I am looking for students who enjoy mathematical thinking and want to develop the foundations of scientific machine learning.

mentoring approach

My goal as an advisor is to help students become independent researchers who can identify meaningful questions, develop sound arguments, and communicate their ideas clearly. I encourage building intuition through simple examples and connecting mathematical reasoning with computational experiments. Mathematical maturity develops throughout the PhD, through sustained practice, discussion, and feedback.

research fit

My current research spans spectral operator learning, probabilistic and generative modeling, and uncertainty quantification. I am particularly interested in understanding why methods work, where they fail, and how to develop algorithms with sound mathematical and statistical foundations.

Please read my research overview and explore my papers. You should be able to explain how your interests connect to at least one of these directions.

what I look for

  • Mathematical preparation: A solid foundation in linear algebra, probability, and multivariable calculus is required. Experience with analysis, optimization, or statistics is also useful.
  • Mathematical curiosity and maturity: An interest in working through proofs and derivations, examining assumptions, and formulating precise questions. You should be willing to spend time on difficult ideas and learn unfamiliar mathematics.
  • Research initiative: A willingness to explore ideas independently, discuss uncertainty openly, and explain your reasoning clearly. I value thoughtful questions and sustained effort.

getting in touch

If this sounds like a good fit, please email me with:

  1. A brief introduction to your background, relevant mathematical preparation, and research interests.
  2. One of my papers that interests you, with its title or link and a short paragraph explaining what caught your attention and how it connects to your interests. A specific question, limitation, or possible extension is welcome.
  3. Your CV and, if available, links to relevant research, projects, or writing.

You do not need to understand every detail of the paper. Explain what you understood and what you would like to understand better, in your own words. A few focused paragraphs are enough.

Please include cockatoo in your email subject to indicate that you have read this page. For example: PhD Fall 2027 — cockatoo — Your Name.

applying

Please follow the Penn State CSE graduate application instructions for current requirements and deadlines. In your statement of purpose, mention my name and explain your research interests. Contacting me and submitting the formal PhD application are separate steps.