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, 34-60.

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

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

6) 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.


In Preparation

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

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


Thesis

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




 
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