Teaching
During fall quarter 2016, I taught Math 117, Methods of Analysis.
Research
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) K. Craig, I. Kim, and Y. Yao, Congested aggregation via Newtonian interaction, arXiv: 1603.03790, submitted to Archive for Rational Mechanics and Analysis.
2) K. Craig, Nonconvex gradient flow in the Wasserstein metric and applications to constrained nonlocal interactions, arXiv:1512.07255, accepted to Proceedings of the London Mathematical Society.
3) K. Craig and I. Topaloglu, Convergence of regularized nonlocal interaction energies, arXiv: 1503.04826, SIAM J. Math. Anal. 48 (2016), no. 1, 3460.
4) K. Craig and A. Bertozzi, A blob method for the aggregation equation, arXiv:1405.6424, Math. Comp. 85 (2016), no. 300, 16811717.
5) K. Craig, The exponential formula for the Wasserstein metric, arXiv:1310.2912, ESAIM COCV 48 (2016), no. 1, 169187.
6) E. Carlen and K. Craig, Contraction of the proximal map and generalized convexity of the MoreauYosida regularization in the 2Wasserstein metric, arXiv: 1205.6565, Math. and Mech. of Complex Systems 1 (2013), no. 1, 3365.
In Preparation

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

2)K. Craig and I. Topaloglu, A numerical method for height constrained aggregation, with applications to nonlocal shape optimization.
Thesis