Welcome! I'm a postdoctoral fellow in the Division of Applied Mathematics at Brown University, working with Kavita Ramanan. I completed my Ph.D. in 2013 in the Department of Mathematics at the University of California, San Diego, under the direction of Ruth J. Williams.
My research interests lie at the interface of dynamics and stochastics. In particular, I am interested in stochastic analysis, large deviations, dynamical systems with delayed dynamics and their applications to engineering and biology.
Click here for my CV (as of December 6, 2016).
I organize the Brown Probability Seminar.
Division of Applied Mathematics
182 George Street, Room 316
david (underscore) lipshutz (at) brown (dot) edu
Publications and preprints:
Large deviations for the empirical measure of a diffusion via weak convergence methods (with P. Dupuis). Preprint.
Pathwise differentiability of reflected diffusions in convex polyhedral domains (with K. Ramanan). Preprint.
On directional derivatives of Skorokhod maps in convex polyhedral domains (with K. Ramanan). To appear in The Annals of Applied Probability.
Existence, uniqueness, and stability of slowly oscillating periodic solutions for delay differential equations with nonnegativity constraints (with R. J. Williams). SIAM Journal on Mathematical Analysis.
I participate in the Math CoOP at Brown, which is a co-operative of students, postdocs and faculty who share a common passion for math outreach and meet monthly to discuss ideas for public outreach. As a participant, I created a presentation for elementary school and middle school students that explains a card "trick'' using De Bruijn sequences, which I first saw in the book Magical Mathematics by Perci Diaconis and Ron Graham. I have also performed the card trick and given the presentation at local elementary schools in Providence, RI.