She earned her bachelor's and master's degrees from Princeton University, followed by her PhD from Princeton in 1991;[3] her dissertation was titled Existence, Uniqueness, and a Characterization of Solutions to the Contour Dynamics Equation.[1][4] Prior to joining UCLA in 2003, Bertozzi was an L. E. Dickson Instructor at the University of Chicago, and then Professor of Mathematics and Physics at Duke University.[5] She spent one year at Argonne National Laboratory as the Maria Goeppert-Mayer Distinguished Scholar.[1]
Bertozzi has contributed to many areas of applied mathematics, including the theory of swarming behavior, aggregation equations and their solution in general dimension, the theory of particle-laden flows in liquids with free surfaces, data analysis/image analysis at the micro and nano scales, and the mathematics of crime.[6] Her earlier fundamental work in fluids led to novel applications in image processing, most notably image inpainting, swarming models, and data clustering on graphs.[7]
Bertozzi coauthored the book Vorticity and Incompressible Flow, which was published in 2000 and remains one of her most cited works.[1]
Bertozzi now has over 200 publications on Web of Science, covering a range of topics including fluid dynamics, image processing, social sciences, and cooperative motion.[8] Bertozzi's publications include over 100 collaborators in a wide range of disciplines including Mathematics, Applied Mathematics, Statistics, Computer Science, Chemistry, Physics, Mechanical and Aerospace Engineering, Medicine, Anthropology, Economics, Politics, and Criminology.[9]
Between 2010 and 2020, Bertozzi has been granted multiple patents related to her research, which center on image inpainting, data fusion mapping estimation, and most recently, on determining fluid reservoir connectivity using nanowire probes.[10]
Bertozzi has developed numerous novel mathematical theories throughout her career. While a Dickson Instructor at Univ. of Chicago, she developed the mathematical theory of thin film equations, fourth order degenerate parabolic equations that are used to describe lubrication theory for coating flows.[11] She has also worked with Jeffrey Brantingham and other colleagues to apply mathematics to the patterns of urban crime, research which was the cover feature in the March 2, 2010 issue of Proceedings of the National Academy of Sciences.[12] Bertozzi also spoke about the mathematics of crime at the 2010 annual meeting of the American Association for the Advancement of Science.[12] Since 2017, Bertozzi has been developing new mathematics related to microfluidic technologies as part of her Simons Math + X investigator program joint with UCLA's Department of Mechanical and Aerospace Engineering and the California NanoSystems Institute. That work includes the theory of transient growth for linear stability of driven contact lines and the theory of undercompressive shocks in driven films with nonconvex fluxes. In 2020, she applied these ideas to discover a new class of undercompressive shock solutions in the "tears of wine" problem.[13]
Bertozzi has also published academic works regarding the 2020 pandemic, the most significant of which is an article on the difficulties of forecasting the spread of COVID-19.[14] She has continued making contributions to the scientific community throughout the pandemic, including a talk on epidemic modeling and a study on the increase in domestic violence reports during stay-at-home restrictions.[15][16]
^Bertozzi, Andrea Louise (1991). Existence, uniqueness, and a characterization of solutions to the contour dynamics equation (Ph.D. thesis). Princeton University. OCLC23826740. ProQuest303962634.
^Bertozzi, Andrea (1996). "The lubrication approximation for thin viscous films: Regularity and long-time behavior of weak solutions". Communications on Pure and Applied Mathematics. 49 (2): 85–123. doi:10.1002/(SICI)1097-0312(199602)49:2<85::AID-CPA1>3.0.CO;2-2.