Added section about the cancellation of her Noether Lecture at the 2021 JMM. |
Tritesprite (talk | contribs) Someone has been repeatedly deleting Bertozzi's extensive contributions. I am merely restoring what was deleted. Tags: Reverted possible unreferenced addition to BLP Visual edit |
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==Contributions== |
==Contributions== |
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Bertozzi coauthored the book ''Vorticity and Incompressible Flow'', which was published in 2000. |
Bertozzi's scientific contributions center around nonlinear partial differential equations, both rigorous theory and and applications. She has over 250 published works in a wide range of research areas. Her PhD thesis was on the regularity of the boundary of a vortex patch, a special solution of the inviscid Euler equations in two dimensions. Bertozzi coauthored the book ''Vorticity and Incompressible Flow'', which was published in 2000. |
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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. Mathematically this area is challenging because the degeneracy leads to odd behavior of solutions not seen in second order degenerate parabolic equations. Her work in this area of research includes both sharp results for regularity of weak solutions and analytical and numerical results on finite time singularities, including second-kind similarity solutions. She has also developed the theory of transient growth for for linear stability of driven contact lines and the theory of undercompressive shocks in driven films with nonconvex fluxes. Very recently she applied those ideas to discover a new class of undercompressive shock solutions in the "tears of wine" problem. |
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Starting around 2000 Bertozzi began working on problems in data science - starting with geometric methods for image processing. Her first paper in this area shows a connection between the Navier-Stokes equations and the geometry of image inpainting - bringing methods from computational fluid dynamics into image processing. Her work in this area connects ideas from physical sciences to problems in imaging. Another such example is the use of the Cahn-Hilliard equation, introduced in the mid 1900s for problems in materials science, for fast image inpainting. Bertozzi holds a patent for this technology. More recently she has spearheaded research in high dimensional data analysis, also using diffuse interface methods and threshold dynamics to classify data using similarity graphs. With Arjuna Flenner, she won a SIAM 2014 Outstanding paper prize for this seminal work that has led to applications in hyperspectral imaging and network science. |
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Also around 2001 Bertozzi began working on modeling swarm dynamics, both in biology and via artificial control of robotic systems. Her work in that area was the subject of her 2009 SIAM Sonia Kovalevskaya lecture. She developed shape well-posedness theory of aggregation equations in all space dimensions, proving that an Osgood condition on the interaction kernel is a necessary and sufficient condition for global well-posedness of smooth solutions. The same condition also holds for Lp weak solutions. At the same time she built a robotics testbed at UCLA where engineering students and math students worked together on implementing interacting controls for robots. |
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Starting in 2003 Bertozzi began studying particle laden flow. This problem lacked good quantitative physical models that would reproduce experimental results. With A. E. Hosoi's group at MIT, Bertozzi developed a shock theory for particles mixed with a viscous fluid on an incline. That work led to an experimental design at UCLA where her students were able to compare mathematical models directly with data. In 2008 her PhD student Ben Cook showed that a simple balance between shear-induced migration of particles and hindered settling led to a theory that quantitatively matched earlier experiments in Hosoi's lab. It predicted quite accurately an observed bifurcation in the dynamics of the experiment - between particles settling to the substrate with clear fluid flowing ahead vs. particles accumulating at the contact line. Through a series of experiments at UCLA her team was able to verify this analysis resulting in the first quantitative dynamic model for particle laden flow - published in the Journal of Fluid Dynamics in 2013. Her team was able to extend that work to mixtures of particles with two different densities and also to spiral separator technology used in the mining industry. |
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Since 2005 she has worked with social scientists to apply mathematics to human activity patterns. This includes urban crime, social network dynamics and social media. One of her papers in this area 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]]. |
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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 Dept of Mechanical and Aerospace Engineering and the California NanoSystems Institute. That work includes fiber coating technology for desalination and microencapsulation technology for biological assays. |
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Bertozzi has 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. |
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Bertozzi coauthored the book ''Vorticity and Incompressible Flow'', which was published in 2000.<ref name="google1" /> |
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She has 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 of the United States of America|Proceedings of the National Academy of Sciences]].<ref name="redorbit1">{{cite web|url=http://www.redorbit.com/news/science/1826185/can_math_and_science_help_solve_crimes/ |title=Can Math And Science Help Solve Crimes? - Science News |publisher=redOrbit |date=2010-02-22 |accessdate=2012-10-30}}</ref> Bertozzi also spoke about the mathematics of crime at the 2010 annual meeting of the [[American Association for the Advancement of Science]].<ref name="redorbit1"/> |
She has 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 of the United States of America|Proceedings of the National Academy of Sciences]].<ref name="redorbit1">{{cite web|url=http://www.redorbit.com/news/science/1826185/can_math_and_science_help_solve_crimes/ |title=Can Math And Science Help Solve Crimes? - Science News |publisher=redOrbit |date=2010-02-22 |accessdate=2012-10-30}}</ref> Bertozzi also spoke about the mathematics of crime at the 2010 annual meeting of the [[American Association for the Advancement of Science]].<ref name="redorbit1"/> |
Revision as of 18:02, 18 October 2020
Andrea Bertozzi | |
---|---|
Born | 1965 (age 58–59) |
Nationality | American |
Alma mater | Princeton University |
Scientific career | |
Fields | Mathematics |
Institutions | University of California, Los Angeles Duke University Argonne National Laboratory University of Chicago |
Doctoral advisor | Andrew Majda |
Andrea Louise Bertozzi (born 1965) is an American mathematician.[1] Her research interests are in non-linear partial differential equations and applied mathematics.[2]
Education and career
She earned her bachelor's and master's degrees from Princeton University, followed by her PhD from Princeton in 1991; her dissertation was titled Existence, Uniqueness, and a Characterization of Solutions to the Contour Dynamics Equation.[1] 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.[3] She spent one year at Argonne National Laboratory as the Maria Goeppert-Mayer Distinguished Scholar.[1]
She is a member of the faculty of the University of California, Los Angeles, as a Professor of Mathematics (since 2003) and Mechanical and Aerospace Engineering (since 2018) and Director of Applied Mathematics (since 2005).[3] She is a member of the California NanoSystems Institute.
Contributions
Bertozzi's scientific contributions center around nonlinear partial differential equations, both rigorous theory and and applications. She has over 250 published works in a wide range of research areas. Her PhD thesis was on the regularity of the boundary of a vortex patch, a special solution of the inviscid Euler equations in two dimensions. Bertozzi coauthored the book Vorticity and Incompressible Flow, which was published in 2000.
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. Mathematically this area is challenging because the degeneracy leads to odd behavior of solutions not seen in second order degenerate parabolic equations. Her work in this area of research includes both sharp results for regularity of weak solutions and analytical and numerical results on finite time singularities, including second-kind similarity solutions. She has also developed the theory of transient growth for for linear stability of driven contact lines and the theory of undercompressive shocks in driven films with nonconvex fluxes. Very recently she applied those ideas to discover a new class of undercompressive shock solutions in the "tears of wine" problem.
Starting around 2000 Bertozzi began working on problems in data science - starting with geometric methods for image processing. Her first paper in this area shows a connection between the Navier-Stokes equations and the geometry of image inpainting - bringing methods from computational fluid dynamics into image processing. Her work in this area connects ideas from physical sciences to problems in imaging. Another such example is the use of the Cahn-Hilliard equation, introduced in the mid 1900s for problems in materials science, for fast image inpainting. Bertozzi holds a patent for this technology. More recently she has spearheaded research in high dimensional data analysis, also using diffuse interface methods and threshold dynamics to classify data using similarity graphs. With Arjuna Flenner, she won a SIAM 2014 Outstanding paper prize for this seminal work that has led to applications in hyperspectral imaging and network science.
Also around 2001 Bertozzi began working on modeling swarm dynamics, both in biology and via artificial control of robotic systems. Her work in that area was the subject of her 2009 SIAM Sonia Kovalevskaya lecture. She developed shape well-posedness theory of aggregation equations in all space dimensions, proving that an Osgood condition on the interaction kernel is a necessary and sufficient condition for global well-posedness of smooth solutions. The same condition also holds for Lp weak solutions. At the same time she built a robotics testbed at UCLA where engineering students and math students worked together on implementing interacting controls for robots.
Starting in 2003 Bertozzi began studying particle laden flow. This problem lacked good quantitative physical models that would reproduce experimental results. With A. E. Hosoi's group at MIT, Bertozzi developed a shock theory for particles mixed with a viscous fluid on an incline. That work led to an experimental design at UCLA where her students were able to compare mathematical models directly with data. In 2008 her PhD student Ben Cook showed that a simple balance between shear-induced migration of particles and hindered settling led to a theory that quantitatively matched earlier experiments in Hosoi's lab. It predicted quite accurately an observed bifurcation in the dynamics of the experiment - between particles settling to the substrate with clear fluid flowing ahead vs. particles accumulating at the contact line. Through a series of experiments at UCLA her team was able to verify this analysis resulting in the first quantitative dynamic model for particle laden flow - published in the Journal of Fluid Dynamics in 2013. Her team was able to extend that work to mixtures of particles with two different densities and also to spiral separator technology used in the mining industry.
Since 2005 she has worked with social scientists to apply mathematics to human activity patterns. This includes urban crime, social network dynamics and social media. One of her papers in this area 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.
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 Dept of Mechanical and Aerospace Engineering and the California NanoSystems Institute. That work includes fiber coating technology for desalination and microencapsulation technology for biological assays.
Bertozzi has 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.
Bertozzi coauthored the book Vorticity and Incompressible Flow, which was published in 2000.[1]
She has 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.[4] Bertozzi also spoke about the mathematics of crime at the 2010 annual meeting of the American Association for the Advancement of Science.[4]
Personal life
She is the older sister of the chemist Carolyn Bertozzi.[5] Her father, William Bertozzi, was a professor of physics at the Massachusetts Institute of Technology.
Recognition
In 1995 Bertozzi received a research fellowship from the Sloan Foundation.[1] In 1996 she received the Presidential Early Career Award for Scientists and Engineers from the U.S. Office of Naval Research.[1][6] She was also awarded the 2009 Association for Women in Mathematics-Society for Industrial and Applied Mathematics Sonia Kovalevsky Lecture, and was elected a Society for Industrial and Applied Mathematics Fellow in 2010.[3]
In 2010 she was elected to the American Academy of Arts and Sciences. In 2012 she became a fellow of the American Mathematical Society.[7] In 2013 she was named the Betsy Wood Knapp Chair for Innovation and Creativity at UCLA.[8] In 2014 she won a SIAM Outstanding Paper Prize (joint with Arjuna Flenner).[citation needed] In 2016 she became a Fellow of the American Physical Society.[9] In 2015 and 2016 she was named a Thomson-Reuters/Clarivate Analytics 'highly cited' researcher.[citation needed] In 2017 she became a Simons Investigator.[10] In 2018 she was elected to the US National Academy of Sciences.[citation needed] In 2019 she was awarded SIAM's Kleinman Prize.[citation needed]
Cancellation of Noether Lecture
The Noether Lecture to have been given by Bertozzi at the at the 2021 Joint Mathematics Meetings was cancelled over connections to policing. This announcement was posted at https://science.clemson.edu/dinamics/noether-lecture-cancelled-over-connections-to-policing/
References
- ^ a b c d e f Oakes, Elizabeth H. (2007). Encyclopedia of World Scientists - Elizabeth H. Oakes - Google Books. ISBN 9781438118826. Retrieved 2012-10-30.
- ^ "Personal Webpage of Andrea L. Bertozzi".
- ^ a b c "List of Visiting Speakers: Andrea L. Bertozzi". SIAM. Archived from the original on 2012-10-18. Retrieved 2012-10-30.
- ^ a b "Can Math And Science Help Solve Crimes? - Science News". redOrbit. 2010-02-22. Retrieved 2012-10-30.
- ^ "UCLA Math Department Faculty". Retrieved 4 June 2012.
- ^ Oakes, Elizabeth H. (2007). Encyclopedia of World Scientists - Elizabeth H. Oakes - Google Boeken. ISBN 9781438118826. Retrieved 2012-10-30.
- ^ List of Fellows of the American Mathematical Society, retrieved 2012-11-10.
- ^ "Andrea Bertozzi named to UCLA's Betsy Wood Knapp Chair for Innovation and Creativity". Archived from the original on 2013-07-23. Retrieved 2013-06-25.
- ^ APS Fellowship, American Physical Society
- ^ Simons Investigators Awardees, The Simons Foundation