Teaching

During spring quarter 2017, I am teaching Math 117, Methods of Analysis.
Congratulations to the winners of the extra credit math movie competition!
You can find links to their excellent videos here: 1st place, 2nd place, 3rd place, honorable mention.

On my curriculum vitae, I link to material from recent courses I have taught.


Research Program

I am interested in nonlinear PDE, optimal transport, calculus of variations, and numerical analysis.

I received my Ph.D. at Rutgers University, where my advisor was Eric Carlen. I spent the first year of my NSF postdoc at UCLA, where my postdoctoral mentor was Andrea Bertozzi. I then spent a year at UCSB as a UC President’s Postdoctoral Fellow, under the mentorship of Bjorn Birnir. I am now an assistant professor at UCSB.

On my curriculum vitae, I link to slides from recent talks I have given.


Publications and Preprints

1) J.A. Carrillo, K. Craig, and F.S. Patacchini, A blob method for diffusion.

2) K. Craig, I. Kim, and Y. Yao, Congested aggregation via Newtonian interaction, arXiv: 1603.03790, accepted to Archive for Rational Mechanics and Analysis.

3) K. Craig, Nonconvex gradient flow in the Wasserstein metric and applications to constrained nonlocal interactions, arXiv:1512.07255, Proc. London Math. Soc., (2017), no. 114, 60–102.

4) K. Craig and I. Topaloglu, Convergence of regularized nonlocal interaction energies, arXiv: 1503.04826, SIAM J. Math. Anal. 48 (2016), no. 1, 34-60.

5) K. Craig and A. Bertozzi, A blob method for the aggregation equation, arXiv:1405.6424, Math. Comp. 85 (2016), no. 300, 1681-1717.

6) K. Craig, The exponential formula for the Wasserstein metric, arXiv:1310.2912, ESAIM COCV 48 (2016), no. 1, 169-187.

7) E. Carlen and K. Craig, Contraction of the proximal map and generalized convexity of the Moreau-Yosida regularization in the 2-Wasserstein metric, arXiv: 1205.6565, Math. and Mech. of Complex Systems 1 (2013), no. 1, 33-65.


Thesis

  1. K.Craig, The exponential formula for the Wasserstein metric