California Research Training Program in Computational and Applied Mathematics

Andrea Bertozzi, Principal Investigator



The thrust of this Computational and Applied Mathematics program is engaging students starting and finishing the critical transition point from undergraduate to PhD student in high quality university level research. Students experience both the development of independent research projects and the milestones needed to get admitted to and succeed in a top PhD program. They participate in summer research modules on topics such as crime modeling, fluid dynamics experiments and modeling, robotics and control, medical imaging, cancer stem cells, bone growth, remote sensing applications, alcohol biosensors, photovoltaic cells, and algorithm design for microscopy. The program involves faculty from Mathematics in collaboration with faculty in Medicine, Anthropology, Engineering, Chemistry, and other disciplines. The project includes a training program for postdocs and junior faculty to learn how to involve pre-PhD students in publication-level research. The training program is based at UCLA and includes undergraduate and masters student participation from nearby colleges and universities. The program goal is to directly address diversity and access to top level PhD programs in computational and applied mathematics. This program is funded by National Science Foundation Grant DMS-1045536. The program provides:

  • (a) summer fellowships for undergraduates to participate in research in computational and applied mathematics;
  • (b) summer research fellowships for masters students from non-PhD granting institutions;
  • (c) a summer traineeships for faculty from non-PhD granting institutions to gain experience supervising undergraduate research and to collaborate with research faculty based at UCLA;
  • (d) first year PhD fellowships to recruit and train a more diverse group of PhD students
  • (e) postdoctoral traineeships for recent PhDs with an interesting in mentoring undergraduates on research problems;
  • (f) summer research mentorships for postdocs to work with younger students on research modules.

    Mentors, Participants, and Projects Summer 2011

    Schedule Summer 2011

    Project Reports and Presentations Summer 2011

    GRE/MATLAB Boot Camp 2011 Schedule for GRE Math Subject Exam Prep and Matlab Tutorials

    Mentors, Participants, and Projects Summer 2012

    Schedule Summer 2012

    GRE/MATLAB Boot Camp 2012 Schedule for GRE Math Subject Exam Prep and Matlab Tutorials

    Schedule of Final Presentations, Wed. August 8, 2012

    Mentors, Participants, and Projects Summer 2013

    Publications and Preprints from this Program

    From Summer 2012

  • Sorathan Chaturapruek, Jonah Breslau, Daniel Yazdi, Theodore Kolokolnikov and Scott G. McCalla, Crime Modeling with Levy Flights, submitted to SIAM J. Appl. Math, 2012.

    From Summer 2011

  • Jérôme Gilles, Balaji R. Sharma, Will Ferenc, Hannah Kastein, Lauren Lieu, Ryan Wilson, Yuan Rick Huang, Andrea L. Bertozzi, Baisravan HomChaudhuri, Subramanian Ramakrishnan, and Manish Kumar, Robotic Swarming over the Internet, refereed conference proceedings, Proceedings of the 2012 American Control Conference.
  • Timothy Lucas, Garrett Johns, Wancen Jiang, Lucie Yang, A Population Model of Chaparral Vegetation Response to Frequent Wildfires, submitted to Bull. Math. Bio., 2012.
  • Garren R. J. Gaut, Katja Goldring, Francesca Grogan, Cymra Haskell, and Robert J. Sacker, Difference Equations with the Allee Effect and the Periodic Sigmoid Beverton-Holt Equation Revisited, J. Biological Dynamics, 6(2), pp. 1019-1033, 2012. preprint version
  • Yves van Gennip, Blake Hunter, Raymond Ahn, Peter Elliott, Kyle Luh, Megan Halvorson, Shannon Reid, Matt Valasik, James Wo, George E. Tita, Andrea L. Bertozzi, P. Jeffrey Brantingham, Community detection using spectral clustering on sparse geosocial data, to appear in SIAM J. Appl. Math. 2012.

    Conference Presentations

  • Talk at Southern California Conference on Undergraduate Research, Mt. San Antonio College, November 2011
  • Poster at Joint Mathematics Meetings in Boston, MA, January 2012. Outstanding Poster Award Winner
  • Talk at Pacific Coast Undergraduate Mathematics Conference, Cal Poly Pomona, March 2012
  • Talk at Southern California Conference on Undergraduate Research, Cal State Channel Islands, November 2011
  • Poster at Joint Mathematics Meetings in San Diego, CA, January 2013
  • American Physical Society Division of Fluid Dynamics, 2012, Contributed Presentation, Bi-disperse particle-laden flows in the Stokes regime, Gilberto Urdaneta, Saro Meguerdijian, Kali Allison, Thomas Crawford, Wylie Rosenthal, Sungyon Lee, Aliki Mavromoustaki, and Andrea Bertozzi
  • American Physical Society Division of Fluid Dynamics, 2011, Contributed Presentation, An experimental study of gravity-driven thin-film flow with buoyant particles, W. Rosenthal, P. Latterman, S. Hill, P. David, M. Mata, A Mavromoustaki, and A. Bertozzi
  • American Physical Society Division of Fluid Dynamics, 2011, Contributed Presentation, Theoretical challenges in modeling gravity-driven thin-film flow with buoyant particles, P. David, S. Hill, P. Latterman, W. Rosenthal, A. Mavromoustaki, M. Mata, and A. Bertozzi
  • Video Presentation, Gallery of Fluid Motion, APS DFD 2011, Aliki Mavromoustaki, Paul David, Spencer Hill, Paul Latterman, Wylie Rosenthal, Matthew Mata, Andrea Bertozzi