Research:

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
• Connor Marrs, UCSB graduate student

Former students:

• Haoqing Yu, UCSB undergraduate student
• 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

Teaching:

Spring 2025: Math CS117: Methods of Analysis

Courses on Optimal Transport: In winter 2025, I taught an graduate topics course on Optimal Transport. Notes from the course are available on the course website. In Summer 2023, we also held a learning seminar on connections between optimal transport and particle physics.

Publications and Preprints

1. T. Cai, N. Craig, K. Craig, X. Lin, Multi-scale Optimal Transport for Complete Collider Events, arXiv: 2501.10681
2. K. Craig and H. Yu, Wavelet s-Wasserstein distances for 0 < s <= 1, arXiv: 2411.12153
3. K. Craig, K. Elamvazhuthi, and H. Lee, A blob method for mean field control with terminal constraints, arXiv: 2402.10124, ESAIM: Control, Optimisation and Calculus of Variations, Volume 31 (2025).
4. K. Craig, M. Jacobs, and O. Turanova, Nonlocal approximation of slow and fast diffusion, arXiv: 2312.11438, Journal of Differential Equations, Volume 42 (2025).
5. K. Craig, B. Osting, D. Wang, and Y. Xu, Wasserstein Archetypal Analysis, arXiv: 2210.14298, Applied Mathematics and Optimisation, 90 (2024).
6. 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).
7. 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).
8. 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).
9. T. Cai, J. Cheng, K. Craig, and N. Craig, Linearized optimal transport for collider events, arXiv: 2008.08604 Physical Review D., 102 (2020).
10. 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).
11. 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
12. J.A. Carrillo, K. Craig, and Y. Yao, Aggregation-diffusion equations: dynamics, asymptotics, and singular limits, arXiv: 1810.0364, Active Particles, Volume 2, (2019).
13. 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).
14. 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.
15. 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.
16. 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.
17. K. Craig and I. Topaloglu, Convergence of regularized nonlocal interaction energies, arXiv: 1503.04826, SIAM J. Math. Anal. 48 (2016), no. 1, 34-60.
18. K. Craig and A. Bertozzi, A blob method for the aggregation equation, arXiv:1405.6424, Math. Comp. 85 (2016), no. 300, 1681-1717.
19. K. Craig, The exponential formula for the Wasserstein metric, arXiv:1310.2912, ESAIM COCV 48 (2016), no. 1, 169-187.
20. K. Craig, The exponential formula for the Wasserstein metric (thesis)
21. 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.