Research

I am interested in nonlinear PDE, optimal transport, calculus of variations, and numerical analysis.
On my curriculum vitae, I link to slides from recent talks I have given.

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.

Publications and Preprints

  1. K. Craig and I. Topaloglu, Aggregation-diffusion to constrained interaction: minimizers & gradient flows in the slow diffusion limit, submitted.
  2. J.A. Carrillo, K. Craig, and F.S. Patacchini, A blob method for diffusion.
  3. K. Craig, I. Kim, and Y. Yao, Congested aggregation via Newtonian interaction, arXiv: 1603.03790, Archive for Rational Mechanics and Analysis (2018), no. 1, 1-67.
  4. 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.
  5. K. Craig and I. Topaloglu, Convergence of regularized nonlocal interaction energies, arXiv: 1503.04826, SIAM J. Math. Anal. 48 (2016), no. 1, 34-60.
  6. K. Craig and A. Bertozzi, A blob method for the aggregation equation, arXiv:1405.6424, Math. Comp. 85 (2016), no. 300, 1681-1717.
  7. K. Craig, The exponential formula for the Wasserstein metric, arXiv:1310.2912, ESAIM COCV 48 (2016), no. 1, 169-187.
  8. 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

K. Craig, The exponential formula for the Wasserstein metric