Research:

Interests: nonlinear PDE, optimal transport, calculus of variations, and numerical analysis.

Projects:

Current students:

Information for prospective students

Slides from recent talks: can be found on my curriculum vitae.

Academic Bio: 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.

Teaching:

Spring 2021: Math 117 (Methods of Analysis)

Optimal Transport: In spring 2020, I taught an online graduate topics course on Optimal Transport. Notes from the course are available on the course website, and the password to access videos of lectures is available by request. A sample video on the topology of the Wasserstein metric and absolutely continuous curves is publicly available.

Publications and Preprints

  1. K. Craig, N. García Trillos, and D. Slepčev, Clustering dynamics on graphs: from spectral clustering to mean shift through Fokker-Planck interpolation, submitted.
  2. T. Cai, J. Cheng, K. Craig, and N. Craig, Linearized optimal transport for collider events, arXiv: 2008.08604 Physical Review D., 102 (2020).
  3. K. Craig, J.-G. Liu, J. Lu, J. L. Marzuola, and L. Wang, A Proximal-Gradient Algorithm for Crystal Surface Evolution , submitted.
  4. J.A. Carrillo, K. Craig, L. Wang, and C. Wei, Primal dual methods for Wasserstein gradient flows, arxiv: 1901.08081, Foundations of Computational Mathematics (2021), 1-55. Videos
  5. J.A. Carrillo, K. Craig, and Y. Yao, Aggregation-diffusion equations: dynamics, asymptotics, and singular limits, arXiv: 1810.0364, Active Particles, Volume 2, (2019).
  6. K. Craig and I. Topaloglu, Aggregation-diffusion to constrained interaction: minimizers & gradient flows in the slow diffusion limit, arXiv: 1806.07415, Annales de l'Insitut Henri Poincare C, Analyse non linear, vol. 37, no. 2, (2020).
  7. J.A. Carrillo, K. Craig, and F.S. Patacchini, A blob method for diffusion, arxiv: 1709.09195 , Calculus of Variations and Partial Differential Equations 58 (2019), no. 2.
  8. 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.
  9. 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.
  10. K. Craig and I. Topaloglu, Convergence of regularized nonlocal interaction energies, arXiv: 1503.04826, SIAM J. Math. Anal. 48 (2016), no. 1, 34-60.
  11. K. Craig and A. Bertozzi, A blob method for the aggregation equation, arXiv:1405.6424, Math. Comp. 85 (2016), no. 300, 1681-1717.
  12. K. Craig, The exponential formula for the Wasserstein metric, arXiv:1310.2912, ESAIM COCV 48 (2016), no. 1, 169-187.
  13. K. Craig, The exponential formula for the Wasserstein metric (thesis)
  14. 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.