• 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
  • AMS Student Chapter Award for Research Excellence, Rutgers University, 2014
  • Rutgers Presidential Fellowship, Rutgers University, 2010-2012
Publications and Preprints
  1. 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.
  2. 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).
  3. 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).
  4. T. Cai, J. Cheng, K. Craig, and N. Craig, Linearized optimal transport for collider events, arXiv: 2008.08604 Physical Review D., 102 (2020).
  5. K. Craig, J.-G. Liu, J. Lu, J. L. Marzuola, L. Wang, A proximal-gradient algorithm for crystal surface evolution, submitted.
  6. 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
  7. J.A. Carrillo, K. Craig, and Y. Yao, Aggregation-diffusion equations: dynamics, asymptotics, and singular limits, arXiv: 1810.0364, Active Particles, Volume 2, (2019).
  8. 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).
  9. 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.
  10. 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.
  11. 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.
  12. K. Craig and I. Topaloglu, Convergence of regularized nonlocal interaction energies, arXiv: 1503.04826, SIAM J. Math. Anal. 48 (2016), no. 1, 34-60.
  13. K. Craig and A. Bertozzi, A blob method for the aggregation equation, arXiv:1405.6424, Math. Comp. 85 (2016), no. 300, 1681-1717.
  14. K. Craig, The exponential formula for the Wasserstein metric (thesis)
  15. K. Craig, The exponential formula for the Wasserstein metric, arXiv:1310.2912, ESAIM COCV 48 (2016), no. 1, 169-187.
  16. 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.


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 flow in the Wasserstein metric

A blob method for degenerate diffusion

AMS Fall Western Sectional Meeting, Stochastic & Multi-scale Models in Math Biology, UC Riverside, 11/4/17
Aggregation-Diffusion PDEs, Anacapri, Italy, 7/12/17
Collaboratory on Mathematics for Mesoscopic Modeling of Materials (CM4), Webinar, 5/15/17
Optimal Transport meets Probability, Statistics and Machine Learning, Casa Matemática Oaxaca, 5/2/17.

Collective dynamics and optimal transport

• SMU Colloquium, 3/27/17
UCSB Colloquium, 4/14/16

From slow diffusion to a hard height constraint: characterizing congested aggregation
• SIAM Special Session on Quasilinear Dispersive PDE, JMM, San Diego, CA, 1/13/18
AMS Fall Western Sectional Meeting, Particle Methods & Nonlocal PDEs, UC Riverside, 11/5/17
Center for Nonlinear Analysis Seminar, Carnegie Mellon University, 8/31/17
Generated Jacobian Equations, Banff International Research Station, 4/12/17. Video, Slides
Analysis and applied math seminar , Duke, 2/22/17, Slides
Ki-net: Mean-field modeling and multiscale methods, UCSB, 10/31/16
PIMS Workshop on Nonlocal Variational Problems and PDEs, 6/15/16
• SIAM PDE, Numerical Methods for PDE and Applications in Computational and Data Science, 12/8/15
Midwest PDE Seminar , Michigan State University, 11/22/15
Analysis Seminar, UCLA, 10/23/15

Nonlocal interaction energies and advances in nonconvex Wasserstein gradient flow
Analysis Seminar, UCLA, 5/15/15
New Trends in Optimal Transport, University of Bonn, 3/6/15.

A blob method for the aggregation equation and convergence of regularized nonlocal interaction energies
Summer School on Quantum and Kinetic Theory for Complex Systems, UCSB, 6/17/16
• SIAM PDE, PDE Models and Control of Swarm Dynamics, 12/8/15
Swarming and Collective Behavior, Equadiff, 7/6/15
Session on Fractional Calculus and Nonlocal Operators, AMS Sectional Meeting, Michigan State University, 3/14/15
• Applied Math/PDE Seminar, UCSB, 10/10/14. Slides: BlobBeamer_100814.pdf
Variational Problems Members Seminar, Fields Institute, 9/3/14.
Entropy Methods, PDEs, Functional Inequalities, and Applications, Banff International Research Station, 7/1/14. Video
Applied Math Colloquium , UCLA, 4/30/14.
Applied Math Colloquium, Penn State, 4/21/14.
SIAM PDE, Orlando, 12/9/13.

The exponential formula for the Wasserstein metric
Numerical Methods for Viscosity Solutions & Applications, SIAM Annual Meeting, Chicago, 7/8/14. Slides
• Probability/PDE Seminar, Rutgers University, 4/11/14.
Analysis Seminar, University of Pennsylvania, 2/18/14.
Introductory Workshop on Optimal Transport, MSRI, 8/28/13.


Conference Organization

Other Service

  • NSF panelist, Division of Mathematical Sciences, March 2021
  • NSF panelist, Division of Mathematical Sciences, March 2020
  • Panelist, UCSB SACNAS Grad Chapter Panel on Securing R1 Faculty Job, October 2018.
  • Participant, UCSB SACNAS Fall Lunch with Faculty, November 2017.
  • Member, UCLA Math Women’s Group, 2015
  • Founder and organizer, Math Women’s Tea, Rutgers University, 2011-2012
  • Referee for Inventiones Mathematicae, SIAM Journal of Mathematical Analysis, Mathematics of Computation, European Journal of Applied Mathematics, and Journal of Mathematical Analysis


Spring 2020: Math 290J (Optimal Transport)
Fall 2018: Math 117 (Real Analysis) and Math 119a (ODEs and Dynamical Systems)
Spring 2017: Math 117 (Real Analysis)
Spring 2016: Math 117 (Real Analysis)
Spring 2015: UCLA Math 164 (Optimization)
Winter 2015: UCLA Math 134 (Optimization)
Fall 2014: UCLA Math 164 (Optimization)

Introductory Lectures

PDE meets optimization: optimal transport and machine learning

  • UCSB Graduate Student Colloquium, 4/22/21 slides

The math of swarming robots, slime mold, and superconductors

• UCSB REU, 7/24/17

Collective dynamics and optimal transport

• UCSB Graduate Student Colloquium, 2/7/19
• UCSB Graduate Student Colloquium, 3/1/18
• UCSB Graduate Student Colloquium, 3/2/17
• UCSB Graduate Student Colloquium, 11/5/15

The math of swarming robots, slime mold, and college admissions

• UCSB Association for Women in Mathematics, 2/8/17
• UCLA Undergraduate Mathematics Students Association, 2/11/15


Invited speaker, Hypatian Seminar, UCSB, 10/12/21
Invited speaker, Association for Women in Mathematics, University of Utah, 2/4/20
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