Appointments

  • 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

  • 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, 2018-2021
  • 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, 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, 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 (thesis)
  13. K. Craig, The exponential formula for the Wasserstein metric, arXiv:1310.2912, ESAIM COCV 48 (2016), no. 1, 169-187.
  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.

Presentations

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.


Service

Organizer, Geometric Methods in Optimization and Sampling, Simons Institute for ToC, UC Berkeley, Fall 2021
NSF panelist, Division of Mathematical Sciences, March 2021
Lead organizer, MSRI Conference on Optimal Transport and Machine Learning, May 2020
NSF panelist, Division of Mathematical Sciences, March 2020
Co-organizer, SIAM Conference on Partial Differential Equations, December 2019
Co-organizer, SIAM PDE minisymposium, “Gradient flows and beyond”, December 2019
Panelist, UCSB SACNAS Grad Chapter Panel on Securing R1 Faculty Job, October 2018.
Co-organizer, Southern California Applied Mathematics Symposium (SOCAMS), UCSB, April 2018.
Participant, UCSB SACNAS Fall Lunch with Faculty, November 2017.
Co-organizer, AMS Special Session, Particle Methods and Nonlocal PDE, 2017, photo
Co-organizer, SIAM PDE minisyposium, Nonlocal Interaction Models: Dynamics, Asymptotics and Applications, 2015
Co-organizer, UCLA Special Seminar in Kinetic Theory, 2015
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


Teaching

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


Outreach

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