Appointments

• Associate Professor, UCSB, 2023-Present
• Assistant Professor, UCSB, 2016-2023
• 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

• Mochizuki Memorial Fund Award for outstanding achievement as a professor of mathematics, 2023
• 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

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

Colloquium, MIT, Applied Math ``Nonlocal particle approximation of optimal transport and diffusion,'' 9/23/24

Tutorial, Optimal Transport and Applications in Particle Physics and Machine Learning

• SIAM Annual Meeting, Spokane, Washington, 7/11/24

Blob methods for nonlinear diffusion and mean field control

• Minisymposium on Optimal Transport, SIAM Annual Meeting, Spokane, Washington, 7/12/24
• Workshop on Particle Systems in Dynamics, Optimization, and Learning, Lagrange Center, Paris, 3/6/24

Colloquium, Cal Tech, Applied Math ``Nonlocal particle approximation of optimal transport and diffusion,'' 1/29/24

Colloquium, UConn, Probability and Data Science ``Nonlocal particle approximation of optimal transport and diffusion,'' 12/14/23

Nonlocal particle approximation of optimal transport and diffusion

• Workshop on Measure Transport, Diffusion Processes and Sampling Workshop, Flatiron Institute, 12/5/23
• Workshop on New Trends in Kinetic and Optimal Transport, University of Minnesota, 10/26/23

Blob methods for transport and degenerate diffusion, with applications to sampling

• Minisymposium on different perspectives in non-linear and non-local PDEs, ICIAM, Tokyo, Japan, 08/21/23
• Workshop on New Trends in Fluids and Collective Dynamics, Banff, 07/25/23

Colloquium, Michigan State University, ``Optimal Transport in Machine Learning and Partial Differential Equations,'' 3/2/23

Colloquium, Purdue University, ``Optimal Transport in Machine Learning and Partial Differential Equations,'' 2/28/23

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

• Workshop on Optimal Transport, Mean-Field Models, and Machine Learning, Munich, Germany 5/11/22
• Pacific Rim Mathematical Association Congress, Vancouver, Canada, 12/6/22

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

• Online seminar on mathematics in imaging, data and optimization, Rochester Polytechnic Institute, 10/19/22. video
• Applied math seminar, University of Utah, 9/19/22.
• SIAM PDE minisymposium on "The Geometry of PDEs on Graphs: Analysis and Applications," 3/15/22.
• Data Science Seminar, Johns Hopkins University, 3/2/22.
• Data Science Seminar, Institute for Mathematics and Applications, University of Minnesota, 2/15/22. slides

Optimal transport and the geometry of collider data

• Minisymposium on geometric distances and robust data analysis, SIAM Data Science, San Diego, 9/28/22.
• ML and Science Forum, Berkeley Institute for Data Science, UC Berkeley, 12/07/21. slides

Wasserstein Gradient Flows and Partial Differential Equations

• Bootcamp on Geometric Methods in Sampling and Optimization, Simons Center for Theory of Computing, UC Berkeley, 9/02/21. notes

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

• Caltech-UCLA-USC Analysis Seminar, University of California, Los Angeles, Analysis Seminar, 2/21/23
• University of California, Santa Cruz, Baskin School of Engineering Applied Mathematics, 4/25/22
• University of California, San Diego, Center for Computational Mathematics Seminar, 4/19/22
• University of Bonn SFB-Seminar, Analysis and Differential Equations, 1/11/22
• Columbia University Applied Math Colloquium, 11/9/21 slides
• Geometry & Learning from Data, Centro Matematica Oaxaca, 10/27/21
• Sampling Algorithms and Geometries on Probability Distributions, Simons Center for Theory of Computing, 9/29/21
• BIRS New Trends in Nonlinear Diffusion, Centro Matematica Oaxaca, 9/9/21, video
• Monte Carlo Methods 2021, University of Mannheim, 8/18/21
• Entropic Regularization of Optimal Transport and Applications, Banff International Research Station, 6/25/21
• PDE and Applied Math Seminar , UC Riverside, 1/13/21
• Optimal Transport and Applications, Canadian Mathematical Society Winter Meeting, Montreal, 12/6/20

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

• Plenary Lecture, Southern California Applied Mathematics Symposium, 5/21/22
• Operations Research Seminar, Stanford University, 11/4/20, slides , video
• Optimal Transport, Topological Data Analysis and Applications to Shape and Machine Learning, Mathematical Biosciences Institute, The Ohio State University, 7/28/20, slides
• Optimal Transport, Regularization, and Applications, Department of Statistics, Columbia University, 7/7/20, Video

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

Service

Conference Organization

• Lead organizer, PDE Methods in Machine Learning, BIRS-IMAG, Granada, Spain, June 2024
• Organizer, Interacting Particle Systems, ICERM, Providence, Rhode Island, May 2024
• Lead organizer, Women in Optimal Transport , University of British Columbia, April 2024
• Organizer, Nonlinear diffusion and nonlocal interaction , BIRS-IMAG, Granada, Spain, May 2023
• Lead organizer, Dynamics & Discretization: PDE, Sampling, Optim., Simons Institute for ToC, UC Berkeley, October 2021, photo
• Organizer, Geometric Methods in Optimization and Sampling, Simons Institute for ToC, UC Berkeley, Fall 2021
  
• Lead organizer, MSRI Conference on Optimal Transport and Machine Learning, May 2020
  
• Organizer, SIAM Conference on Partial Differential Equations, December 2019
  

Other Service

• Mentor, Association for Women in Mathematics Mentoring Lunch, SIAM Annual Meeting, 7/11/24
  
• Guest Editor, European Journal of Applied Mathematics Special Issue on Evolution Equations on Graphs, 2024
• Invited speaker, UCSB Association for Women in Math, 5/26/23
• Panelist, UCSB Association for Women in Math, International Day of Women in Math, 2023
• 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.

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)