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
- 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
- K. Craig, B. Osting, D. Wang, and Y. Xu, Wasserstein Archetypal Analysis, arXiv: 2210.14298
- 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.
- 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).
- 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).
- T. Cai, J. Cheng, K. Craig, and N. Craig, Linearized optimal transport for collider events, arXiv: 2008.08604 Physical Review D., 102 (2020).
- 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).
- 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
- J.A. Carrillo, K. Craig, and Y. Yao, Aggregation-diffusion equations: dynamics, asymptotics, and singular limits, arXiv: 1810.0364, Active Particles, Volume 2, (2019).
- 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).
- 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.
- 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.
- 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.
- K. Craig and I. Topaloglu, Convergence of regularized nonlocal interaction energies, arXiv: 1503.04826, SIAM J. Math. Anal. 48 (2016), no. 1, 34-60.
- K. Craig and A. Bertozzi, A blob method for the aggregation equation, arXiv:1405.6424, Math. Comp. 85 (2016), no. 300, 1681-1717.
- K. Craig, The exponential formula for the Wasserstein metric (thesis)
- K. Craig, The exponential formula for the Wasserstein metric, arXiv:1310.2912, ESAIM COCV 48 (2016), no. 1, 169-187.
- 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
From data archetypes to collider data: two perspectives on the Wasserstein metric as a distance between data distributions
- 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.
- 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
- 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
- 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
- PDE/Applied Math Seminar, Drexel, 1/24/19
- Nonlinear Analysis Seminar, Rutgers, 1/22/19
- Canadian Mathematical Society Winter Meeting, Nonlocal Interaction Models, Vancouver, 12/9/18
- Ki-Net Young Researchers Workshop, 10/22/18, Slides
- Conference in Applied Mathematics, Duke University, 8/20/18
- Computational Applied Mathematics and PDE Seminar, University of Chicago, 5/2/18
- Entropies, the Geometry of Nonlinear Flows, & Applications, Banff International Research Station, 4/9/18, Video
- University of Texas, Analysis Seminar, 2/7/18
- Nonlocal equations in collective behavior, American Institute of Mathematics, San Jose, California, 6/20/18
- AMS Special Session on Metric Geometry and Topology, JMM, San Diego, CA, 1/11/18, Slides
- Optimal Transport and Machine Learning, NIPS, Long Beach, CA, 12/9/17, Slides
- 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.
- SMU Colloquium, 3/27/17
- UCSB Colloquium, 4/14/16
- 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
- Analysis Seminar, UCLA, 5/15/15
- New Trends in Optimal Transport, University of Bonn, 3/6/15.
- 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.
- Numerical Methods for Viscosity Solutions & Applications, SIAM Annual Meeting, Chicago, 7/8/14. Slides
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)