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. Her earlier fundamental work in fluids led to novel applications in image processing, most notably image inpainting, swarming models, and data clustering on graphs. Bertozzi coauthored the book
Vorticity and Incompressible Flow, which was published in 2000 and remains one of her most cited works. 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. 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. 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. 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. Bertozzi also spoke about the mathematics of crime at the 2010 annual meeting of the
American Association for the Advancement of Science. 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. 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. ==Personal life==