The European Journal of Applied Mathematics will run a special issue on "Evolution Equations on Graphs".
Email me ASAP if you would like to submit an article. Please share widely!


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

Projects: NSF DMS-2145900, CAREER: Optimal Transport and Dynamics in Machine Learning

PDF of curriculum vitae: here (updated 10/12/22)

Slides from recent talks: can be found here.

Current students:

  • Đorđe Nikolić, UCSB graduate student
  • Claire Murphy, UCSB graduate student
  • Haoqing Yu, UCSB undergraduate student

Former students:

  • Ben Faktor, UCSB undergraduate student, now pursuing PhD in math at UCLA
  • Emily Lopez, UCSB undergraduate and McNair scholar, now pursuing PhD in applied math at University of Minnesota

Information for prospective students

Which Springer GTM book I would be


Spring 2024: CCS Math 117: Real Analysis

Winter 2024: Math 117: Real Analysis

Courses on Optimal Transport: In winter 2022, I taught an hybrid 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 curves in the space of probability measures is publicly available. In Summer 2023, we also held a learning seminar on connections between optimal transport and particle physics.

Publications and Preprints

  1. K. Craig, K. Elamvazhuthi, and H. Lee, A blob method for mean field control with terminal constraints, arXiv: 2402.10124
  2. K. Craig, M. Jacobs, and O. Turanova, Nonlocal approximation of slow and fast diffusion, arXiv: 2312.11438.
  3. K. Craig, B. Osting, D. Wang, and Y. Xu, Wasserstein Archetypal Analysis, arXiv: 2210.14298.
  4. K. Craig, K. Elamvazhuthi, M. Haberland, and O. Turanova, A blob method for inhomogeneous diffusion with applications to multi-agent control and sampling, arXiv: 2202.12927, Mathematics of Computation, Volume 29 (2023).
  5. T. Cai, J. Cheng, K. Craig, and N. Craig, Which Metric on the Space of Collider Events?, arXiv: 2111.03670, Physical Review D., 105 (2022).
  6. K. Craig, N. García Trillos, and D. Slepčev, Clustering dynamics on graphs: from spectral clustering to mean shift through Fokker-Planck interpolation, arXiv: 2108.08687, Active Particles, Volume 3, (2022).
  7. T. Cai, J. Cheng, K. Craig, and N. Craig, Linearized optimal transport for collider events, arXiv: 2008.08604 Physical Review D., 102 (2020).
  8. K. Craig, J.-G. Liu, J. Lu, J. L. Marzuola, and L. Wang, A Proximal-Gradient Algorithm for Crystal Surface Evolution, arXiv 2006.12528, Numerische Mathematik (2022).
  9. 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
  10. J.A. Carrillo, K. Craig, and Y. Yao, Aggregation-diffusion equations: dynamics, asymptotics, and singular limits, arXiv: 1810.0364, Active Particles, Volume 2, (2019).
  11. 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).
  12. 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.
  13. 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.
  14. 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.
  15. K. Craig and I. Topaloglu, Convergence of regularized nonlocal interaction energies, arXiv: 1503.04826, SIAM J. Math. Anal. 48 (2016), no. 1, 34-60.
  16. K. Craig and A. Bertozzi, A blob method for the aggregation equation, arXiv:1405.6424, Math. Comp. 85 (2016), no. 300, 1681-1717.
  17. K. Craig, The exponential formula for the Wasserstein metric, arXiv:1310.2912, ESAIM COCV 48 (2016), no. 1, 169-187.
  18. K. Craig, The exponential formula for the Wasserstein metric (thesis)
  19. 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.