• Assistant Professor, UCSB, 2016-present
  • UC President’s Postdoctoral Fellow, UCSB, 2015-2016
  • NSF Postdoctoral Fellow, UCLA, 2014-2015
  • Visiting Researcher, Fields Institute, University of Toronto, September 2014
  • Visiting Researcher, UCLA, February-July 2013

Awards and Grants

  • NSF DMS-2145900, CAREER: Optimal Transport and Dynamics in Machine Learning
  • 2020 Hellman Faculty Fellowship, Optimal Transport and Machine Learning
  • UC Regents' Junior Faculty Fellowship, 2019
  • NSF DMS-1811012, Singular Limits of Gradient Flows: Analysis and Numerics, 2018-2022
  • UC Faculty Research Grant, 2017
  • UC Faculty Enrichment Award, 2016
  • UC President’s Postdoctoral Fellowship, 2015
  • NSF Postdoctoral Fellowship, 2014
  • Rutgers Presidential Fellowship, Rutgers University, 2010-2012
Publications and Preprints
  1. K. Craig, B. Osting, D. Wang, and Y. Xu, Wasserstein Archetypal Analysis, arXiv: 2210.14298
  2. 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.
  3. 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).
  4. 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).
  5. T. Cai, J. Cheng, K. Craig, and N. Craig, Linearized optimal transport for collider events, arXiv: 2008.08604 Physical Review D., 102 (2020).
  6. 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).
  7. 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
  8. J.A. Carrillo, K. Craig, and Y. Yao, Aggregation-diffusion equations: dynamics, asymptotics, and singular limits, arXiv: 1810.0364, Active Particles, Volume 2, (2019).
  9. 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).
  10. 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.
  11. 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.
  12. 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.
  13. K. Craig and I. Topaloglu, Convergence of regularized nonlocal interaction energies, arXiv: 1503.04826, SIAM J. Math. Anal. 48 (2016), no. 1, 34-60.
  14. K. Craig and A. Bertozzi, A blob method for the aggregation equation, arXiv:1405.6424, Math. Comp. 85 (2016), no. 300, 1681-1717.
  15. K. Craig, The exponential formula for the Wasserstein metric (thesis)
  16. K. Craig, The exponential formula for the Wasserstein metric, arXiv:1310.2912, ESAIM COCV 48 (2016), no. 1, 169-187.
  17. 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.


From data archetypes to collider data: two perspectives on the Wasserstein metric as a distance between data distributions

Graph clustering dynamics: from spectral to mean shift via Fokker-Planck

Optimal transport and the geometry of collider data

Wasserstein Gradient Flows and Partial Differential Equations

A blob method for degenerate diffusion and applications to sampling and two layer neural networks.

A Proximal-Gradient Algorithm for Crystal Surface Evolution

  • Nonlinear PDE Seminar, University of California, Irvine, 10/16/20
  • Applied Mathematics and Computation Seminar, University of Massachusetts, Amherst, 9/29/20, slides
  • Variational Methods for Evolution, Oberwolfach, 9/17/20, video

Gradient flows in the Wasserstein metric: From discrete to continuum via regularization

Minimizers and gradient flows in the slow diffusion limit

  • Gradient Flows in PDEs webinar, Institut Camille Jordan (ICJ), Lyon, 10/14/20, slides
  • Nonlocal PDEs: Qualitative Properties and Asymptotic Behaviour, SIAM Annual Meeting, Toronto, 7/6/20


Conference Organization

Other Service

  • NSF panelist, Division of Mathematical Sciences, March 2020, 2021, and 2022
  • Participant, Welcome lunch for UCSB SIMS, a program for high achieving STEM freshmen from underrepresented groups, 8/24/22
  • Invited speaker, Hypatian Seminar, UCSB, 10/12/21
  • Invited speaker, Association for Women in Mathematics, University of Utah, 2/4/20
  • Referee, for Inventiones Mathematicae, Transactions of the AMS, Journal of Differential Equations, Journal of Machine Learning Research, SIAM Journal of Mathematical Analysis, SIAM Journal of Numerical Analysis, Mathematics of Computation, European Journal of Applied Mathematics, and others.

Past Presentations

Minimizers and gradient flows in the slow diffusion limit Gradient flow in the Wasserstein metric A blob method for degenerate diffusion Collective dynamics and optimal transport From slow diffusion to a hard height constraint: characterizing congested aggregation Nonlocal interaction energies and advances in nonconvex Wasserstein gradient flow A blob method for the aggregation equation and convergence of regularized nonlocal interaction energies The exponential formula for the Wasserstein metric

Past Service

  • Organizer, SIAM PDE minisymposium, “Gradient flows and beyond”, December 2019
  • Organizer, Southern California Applied Mathematics Symposium (SOCAMS), UCSB, April 2018.
  • Panelist, UCSB SACNAS Grad Chapter Panel on Securing R1 Faculty Job, October 2018.
  • Participant, UCSB SACNAS Fall Lunch with Faculty, November 2017.
  • Honorable Mention, NSF We Are Mathematics Video Competition, video
  • UCSB Problem Solving for Women to Encourage Research in STEM (POWERS), 3/3/18, photo
  • UCSB GRIT Talk, The math of swarming robots, slime mold, and superconductors, 6/26/17
  • UCSB Public Affairs, Pi Day Video, 3/14/17, video
  • Girls Inc. Curie-osity Project, How math can help you win a car (or goat), 3/1/17, photo
  • Organizer, AMS Special Session, Particle Methods and Nonlocal PDE, 2017, photo
  • Organizer, SIAM PDE minisyposium, Nonlocal Interaction Models: Dynamics, Asymptotics and Applications, 2015
  • Founder and organizer, Math Women’s Tea, Rutgers University, 2011-2012

Recent Teaching

Spring 2022: Math 117 (Real Analysis)
Winter 2022: Math 290J (Optimal Transport)
Spring 2021: Math 117 (Real Analysis)
Winter 2021: Math 6B (Vector Calculus II)
Fall 2020: Math 201a (Measure Theory)