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
- AMS Student Chapter Award for Research Excellence, Rutgers University, 2014
- Rutgers Presidential Fellowship, Rutgers University, 2010-2012

- 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, L. Wang, A proximal-gradient algorithm for crystal surface evolution, submitted.
- 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

Graph Clustering Dynamics: From Spectral to Mean Shift via Fokker-Planck

- 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

- 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, 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

- 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
- 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

A blob method for degenerate diffusion

• 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

• 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

Conference Organization

- Lead organizer, Dynamics & Discretization: PDEs, 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

- Co-organizer, SIAM Conference on Partial Differential Equations, December 2019

- Co-organizer, SIAM PDE minisymposium, “Gradient flows and beyond”, December 2019

- Co-organizer, Southern California Applied Mathematics Symposium (SOCAMS), UCSB, April 2018.

- 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

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

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

Collective dynamics and optimal transport

• 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

• 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