Information for Prospective Students

**Undergraduate students:**

- I have positions for 1-2 undergraduate students per year, working on research projects in optimal transport and machine learning. Research stipends are available.
- I prefer students who commit to work on a project for a minimum of one year, beginning with a one quarter trial period.
- Recommended preparatory coursework includes introductory analysis (e.g. math 117) and programming in either matlab, python, or julia. Coursework in optimization, differential equations, and advanced analysis would also be useful.
- Interested students should email me a CV, unofficial transcript, and a short summary of their academic/career goals (1 paragraph).
- Surprisingly, I receive a lot of "junk" email from students who mass-email all professors asking to work with them. To let me know that you are a real person, please mention your favorite dessert. My favorite dessert is sweet potato pie :).
- Due to the limited number of open positions, very few students will be selected. Applications from a diverse range of students (racial/cultural/intellectual/etc.) are highly encouraged, since approaching unsolved problems with new perspectives is key to progress.

**Graduate students:**

- I have positions for 1-2 graduate students per year, working on research projects at the intersection of partial differential equations and optimal transport, with applications to mathematical biology, fluid dynamics, materials science, and machine learning. Research assistantships are available.
- I enjoy beginning to work with graduate students relatively early in their PhD, preferably toward the end of their first year or during their second year.
- I prefer to begin with a one quarter/summer trial period, during which we read and discuss relevant papers and try our hand at some warmup problems. At the end of this trial period, either of us can decide to stop working together, with no hard feelings. Compatibility is very important in a research relationship, and it can sometimes take a few tries to find the right fit.
- Recommended preparatory coursework includes an undergraduate degree in mathematics (including a year of real analysis, a semester of abstract algebra, and a semester of linear algebra), graduate real analysis, and programming in either matlab, python, or julia. Coursework in ordinary differential equations, partial differential equations, numerical analysis, optimization, and calculus of variations would also be useful.
- Interested students should email me a CV, unofficial transcript, and a short summary of their academic/career goals (1 paragraph).
- Surprisingly, I receive a lot of "junk" email from students who mass-email all professors asking to work with them. To let me know that you are a real person, please mention your favorite dessert. My favorite dessert is sweet potato pie :).
- Applications from a diverse range of students (racial/cultural/intellectual/etc.) are highly encouraged, since approaching unsolved problems with new perspectives is key to progress.

** Recommended References:**

- Real Analysis:

Folland,*Real Analysis: Modern Techniques and Their Applications*, second edition

Lieb and Loss,*Analysis*, second edition - Functional Analysis:

Brezis,*Functional Analysis, Sobolev Spaces and Partial Differential Equations*, - Convex Analysis:

Combettes, "Monotone operator theory in convex optimization" Bauschke and Combettes,*Convex Analysis and Monotone Operator Theory in Hilbert Spaces*, - Fluid Mechanics and PDEs:

Chorin and Marsden,*A Mathematical Introduction to Fluid Mechanics*, - Optimal Transport:

Villani,*Topics in Optimal Transportation*,

Santambrogio,*Optimal Transport for Applied Mathematicians*,

Figalli, Glaudo,*An Invitation to Optimal Transport*, (I have a copy you can borrow)

Ambrosio, Brué,Semola*Lectures on Optimal Transport*,

- Gradient Flows:

Ambrosio, Gigli, Savaré,*Gradient Flows in Metric Spaces and in the Space of Probability Measures*,

Ambrosio and Savaré,*Gradient Flows of Probability Measures*,

Santambrogio,*{Euclidean, metric, and Wasserstein} gradient flows*,

- Computational Optimal Transport:

Peyré and Cuturi,*Computational Optimal Transport*,