Katy Craig         Curriculum Vitae

 
 

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 Honors

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) J.A. Carrillo, K. Craig, and F.S. Patacchini, A blob method for diffusion.

2) K. Craig, I. Kim, and Y. Yao, Congested aggregation via Newtonian interaction, arXiv: 1603.03790, accepted to Archive for Rational Mechanics and Analysis.

3) 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.

4) K. Craig and I. Topaloglu, Convergence of regularized nonlocal interaction energies, arXiv: 1503.04826, SIAM J. Math. Anal. 48 (2016), no. 1, 34-60.

5) K. Craig and A. Bertozzi, A blob method for the aggregation equation, arXiv:1405.6424, Math. Comp. 85 (2016), no. 300, 1681-1717.

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

7) 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.


Thesis

  1. K.Craig, The exponential formula for the Wasserstein metric



Presentations

Gradient flow in the Wasserstein metric

  1. 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

  1. 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

  1. SMU Colloquium, 3/27/17

  2. UCSB Colloquium, 4/14/16


From slow diffusion to a hard height constraint: characterizing congested aggregation

  1. 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: from Geometric Optics to Economics, Banff International Research Station, 4/12/17. Video, Slides
    Analysis and applied math seminar , Duke, 2/22/17, Slides

  2. Ki-net: Mean-field modeling and multiscale methods, UCSB, 10/31/16

  3. PIMS Workshop on Nonlocal Variational Problems and PDEs, 6/15/16

  4. SIAM PDE, Numerical Methods for PDE and Applications in Computational and Data Science, 12/8/15

  5. Midwest PDE Seminar, Michigan State University, 11/22/15

  6. Analysis Seminar, UCLA, 10/23/15


Nonlocal interaction energies and advances in nonconvex Wasserstein gradient flow

  1. Analysis Seminar, UCLA, 5/15/15

  2. 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

  1. Summer School on Quantum and Kinetic Theory for Complex Systems, UCSB, 6/17/16

  2. SIAM PDE, PDE Models and Control of Swarm Dynamics, 12/8/15

  3. Swarming and Collective Behavior, Equadiff, 7/6/15

  4. Session on Fractional Calculus and Nonlocal Operators, AMS Central Spring Sectional Meeting, Michigan State University, 3/14/15

  5. Applied Math/PDE Seminar, UCSB, 10/10/14. Slides: BlobBeamer_100814.pdf

  6. Variational Problems Members Seminar, Fields Institute, 9/3/14.                                                                          

  7. Entropy Methods, PDEs, Functional Inequalities, and Applications, Banff International Research Station, 7/1/14. Video

  8. Applied Math Colloquium, UCLA, 4/30/14.

  9. Applied Math Colloquium, Penn State, 4/21/14.

  10. SIAM PDE, Orlando, 12/9/13.


The exponential formula for the Wasserstein metric

  1. Numerical Methods for Viscosity Solutions & Applications, SIAM Annual Meeting, Chicago, 7/8/14. Slides: ExpFormBeamer_062814.pdf

  2. Probability/PDE Seminar, Rutgers University, 4/11/14.

  3. Analysis Seminar, University of Pennsylvania, 2/18/14.

  4. Introductory Workshop on Optimal Transport, MSRI, 8/28/13.



Service

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

Professor for Math 117: Real Analysis, UCSB, Spring 2017

Professor for Math 117: Real Analysis, UCSB, Fall 2016

Instructor for Math 164: Optimization, UCLA, Spring 2015

Instructor for Math 134: Dynamical Systems, UCLA, Winter 2015

Instructor for Math 164: Optimization, UCLA, Fall 2014


Introductory Lectures

The math of swarming robots, slime mold, and superconductors

  1. • UCSB REU, 7/24/17

  2. Collective dynamics and optimal transport

    1. • UCSB Graduate Student Colloquium, 3/2/17
      • UCSB Graduate Student Colloquium, 11/5/15

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

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


    Outreach

    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