Andrea Bertozzi Research Group

Current Postdocs (Former Postdocs)

• Alethea Barbaro - crime models and swarming
• Thomas Laurent - aggregation equations and applied analysis
• Mario Micheli - image analysis and understanding
• George Mohler - pattern forming systems and stochastic differential equations
• Nebo Murisic - thin films and fluid interfaces
• Martin Short - crime models
• Todd Wittman - image processing

Current Ph.D. Students   (Former Students)

• Alexander Chen (UCLA Mathematics)
  Hyperspectral Image Processing
• Julia Dobrosotksaya (UCLA Mathematics)
  Image processing using PDEs and wavelets
• Wenhua Gao (UCLA Mathematics)
  Image inpainting and medical imaging
• Yifei Lou (joint with S. Soatto)
  Nonlocal imaging methods
• Matthew Mata (UCLA Mathematics)
  Particle Laden Flow
• Nancy Rodriguez (UCLA Mathematics)
  Crime models
• Wen Yang (Shanghai)
  Visiting PhD student in Control Theory

Undergraduate researchers (Former undergraduate researchers)

• See web page of Todd Wittman for current REU projects in Imaging
• See web page of Thomas Ward for current REU projects in Fluids

  Current Projects

• Fluid interfaces and moving contact lines . We work on modeling of microfluidic devices and have some ongoing experiments on thin film slurry flow in the Applied Math Lab. Mathematical models include phase field methods and hyperbolic conservation laws.
• Cooperative motion and swarming We are interested in modeling both biological swarms and artificial swarms. We study the mathematical properties of collective groups and the large scale dynamics that ensues from small scale motion.
• Image processing We are interested in hyperspectral imagery, road inpainting, and imaging through turbulence.
  1. The work on cooperative motion and image processing includes a joint research project with USC, Brown, and Univ. of IL on Nonlinear Tracking click here to access the web page
  2. Los Angeles Multi-Band Data Analysis (LAMBDA) group is a project on hyperspectral imagery that I am involved with.
• Crime Hot Spots is funded by the NSF and the DoD and includes collaborations with Jeff Brantingham in Anthropology and with Lincoln Chayes.

Current Research Grants

1. ONR grant N000140810363 Geometry Based Image Analysis and Understanding, 1/08-12/10
2. NGA grant HM1582-06-1-2034 Novel Segmentation, Reconstruction, and Learning Models for Hyperspectral Image Processing and Analysis, 9/06-9/09, joint with Stan Osher.
3. NSF grant DMS-0601395 Research Training Group in Applied Differential Equations and Scientific Computing, 6/06-5/11, (EMSW21 Workforce Grant for training REU students and first year Ph. D. students).
4. ARO MURI grant 50363-MA-MUR, Spatio-temporal event pattern recognition, subcontract from USC/Brown, Boris Rozovsky, PI. UCLA portion involves T. Chan and P. J. Brantigham, 5/06-4/09.
5. NSF grant BCS-0527388, DHB: Mathematical and Simulation Modeling of Crime Hot Spots, P. Jeffrey Brantigham (PI), also with L. Chayes and G. Tita (UCI), 1/06-12/08.
6. ONR grant N000140610059 Pattern formation and control of distributed swarming vehicles, 10/05-10/08, joint grant with Ira Schwartz, Naval Research Lab.
7. ONR grant N000140710431, Fundamental Problems in Microfluidic Mixing and Multiphase Flows, 10/06-9/09
8. NSF grant ACI-0321917 9/03-8/08, Collaborative Research-ITR-High Order Partial Differential Equations: Theory, Computational Tools, and Applications in Image Processing, Computer Graphics, Biology, and Fluids (total project includes S. Osher (UCLA), G. Sapiro (UMN), A. Hosoi (MIT), and R. Fedkiw (Stanford)).

Other Research Funding

Additional research support comes from the Department of Defense and Industry, through short term contracts directly related to our research projects.

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UCLA * Department of Mathematics *