B.S., Pennsylvania State University (Physics and Mathematics), 1996
Ph.D., Stony Brook University (Mathematics), 2002
Our Faculty
Courses
1231 Applied Calculus:Econ Bus&Finc
Stephen Preston
Profile
Stephen Preston is Professor of Mathematics at Brooklyn College and at the CUNY Graduate Center. He was Mathematics Department Chairperson at Brooklyn College from January 2018 to July 2020. At the undergraduate level he has primarily taught courses in Advanced Calculus, Ordinary and Partial Differential Equations, Probability and Statistics, Financial Mathematics, and Multivariable Calculus. His research is focused on partial differential equations viewed as geodesics in infinite-dimensional Riemannian geometry, of which the most prominent example is the Euler equations of an ideal fluid. Prior to joining Brooklyn College, he was on the faculty of the University of Colorado (Boulder) for ten years.
Education
Selected Research, Scholarship, and Creative Activity
Books and Publications
"Solar models and McKean's breakdown theorem for the μCH and μDP equations" https://doi.org/10.1007/s00208-022-02376-x Math. Ann. (2022).
A. Le Brigant and S. Puechmorel, "Fisher-Rao geometry of Dirichlet distributions," Differential Geo. Appl. 74 https://doi.org/10.1016/j.difgeo.2020.101702 (2021)
J.M. Lee and S.C. Preston, "Nonpositive curvature of the quantomorphism group and quasigeostrophic motion," Differential Geom. Appl., 74 (2021) https://doi.org/10.1016/j.difgeo.2020.101698.
M. Bauer, E. Klassen, S.C. Preston, and Z. Su, "A diffeomorphism-invariant metric on the space of vector-valued one-forms," to appear in Pure Appl. Math. Q (2021).
L. Lichtenfelz, G. Misiolek, and S.C. Preston, "Axisymmetric diffeomorphisms and ideal fluids on Riemannian 3-manifolds," Int. Math. Res. Notices (2020), https://doi.org/10.1093/imrn/rnaa139
M. Bauer, B. Kolev, and S.C. Preston, "Geodesic completeness of the H^{3/2} metric on Diff(S^1)," Monatsh. Math. 193, 233-245.
M. Bauer, E. Klassen, H. Laga, S.C. Preston, and Z. Su, "Shape analysis of surfaces using general elastic metrics," J. Math. Imaging Vision, 62 1087-1106.
M. Bauer, P. Harms, and S.C. Preston, "Vanishing distance phenomena and the geometric approach to SQG," Arch. Ration. Mech. Anal. 235 1445-1466.
Benn, J., G. Misiolek, and S.C. Preston, "The exponential map of the group of area-preserving diffeomorphisms of a surface with boundary," Arch. Ration. Mech. Anal. 229.3, 1015-35.
Lee, J.M. and S.C. Preston, "Local well-posedness of the Camassa-Holm equation on the real line," Discrete Contin. Dyn. Syst. 37.6, 3285-99.
Tumpach, A.B. and S.C. Preston, "Quotient elastic metrics on the manifold of arc-length parameterized plane loops," J. Geom. Mech. 2.2, 227-56.
Bauer, M., B. Kolev, and S.C. Preston, "Geometric investigations of a vorticity model equation," J. Differential Equations 260.1, 478-516.
Preston, S.C. and A. Sarria, "Lagrangian aspects of the axisymmetric Euler equation," Nonlinearity 29.3 1080-95.
Awards, Honors and Fellowships
Simons Foundation Collaboration Grant for Mathematicians no. 318969, "Infinite-dimensional geodesic equations," $35,000, 2014-19.
NSF Geometric Analysis #1157293, "Thematic Program on Geometric Analysis and Spectral Theory," $50,000, 2012-16.
Conferences, Seminars and Symposiums
"Solar models and breakdown of the mu-Camassa-Holm equation", talk in the Special Session on Analysis of Nonlinear Evolution Equations, AMS Spring Central Sectional Meeting.
"Axisymmetric ideal fluids on Riemannian 3-manifolds," AMS Special Session on Geometry and Analysis of Fluid Equations, Northeastern University, April 22.
"Axisymmetric ideal fluids on Riemannian 3-manifolds," AMS Special Session on Nonlinear Evolution Equations, Ohio State University, March 17.
"Solar models for 1D Euler-Arnold equations," Math in the Black Forest: Workshop on New Directions in Shape Analysis, Freiburg, Germany, July 17.
"The furling of flags," AMS Special Session on Geometric Methods in Shape Analysis, Ohio State University, March 17.
"Solar models for Euler-Arnold equations," BIRS Workshop 18w5151 on Shape Analysis, Stochastic Geometric Mechanics and Applied Optimal Transport, Banff, Alberta, Canada, Dec. 12.
"Some open problems in Euler-Arnold equations," Math in the Countryside Shape Analysis Workshop, Skrunda, Latvia, July 25.
"The elastic metric on the space of unit-speed curves," Shape Group Seminar, Florida State University. Feb. 7.
"Geometric models of the 3D Euler equation," Analysis of PDEs of Fluid Mechanics Workshop, Rice University, May 10.
"The geometric approach to partial differential equations," Dean's Speaker Series, Binghamton University, April 15.
Professional Leadership
Mathematics Department Chairperson, January 2018-present
Primary organizer, Research in Pairs Workshop in Oberwolfach Research Institute for Mathematics in Germany, "The geometry of infinite-dimensional manifolds and applications to physics," with Marcelo Disconzi, David Ebin, Gerard Misiolek, and Stephen Preston.