Education:
Ph.D., Stony Brook University - 2002 (Mathematics)
B.S., Pennsylvania State University - 1996 (Physics and Mathematics)
Areas of Expertise:
Partial differential equations of fluid mechanical type; Infinite-dimensional Riemannian geometry; shape space.
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). (Books and Publications: Article (Peer-reviewed)) 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) (Books and Publications: Article (Peer-reviewed)) 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. (Books and Publications: Article (Peer-reviewed)) 2021
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). (Books and Publications: Forthcoming Publications) 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 (Books and Publications: Article (Peer-reviewed)) 2020
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. (Books and Publications: Article (Peer-reviewed)) 2020
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. (Books and Publications: Article (Peer-reviewed)) 2020
M. Bauer, P. Harms, and S.C. Preston, "Vanishing distance phenomena and the geometric approach to SQG," Arch. Ration. Mech. Anal. 235 1445-1466. (Books and Publications: Article (Peer-reviewed)) 2020
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. (Books and Publications: Article (Peer-reviewed)) 2018
Preston, S.C. and P. Washabaugh, "Euler-Arnold equations and Teichmüller theory," Differential Geom. Appl. 59, 1-11. (Books and Publications: Article (Peer-reviewed)) 2018
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. (Books and Publications: Article (Peer-reviewed)) 2017
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. (Books and Publications: Article (Peer-reviewed)) 2017
Bauer, M., B. Kolev, and S.C. Preston, "Geometric investigations of a vorticity model equation," J. Differential Equations 260.1, 478-516. (Books and Publications: Article (Peer-reviewed)) 2016
Preston, S.C. and A. Sarria, "Lagrangian aspects of the axisymmetric Euler equation," Nonlinearity 29.3 1080-95. (Books and Publications: Article (Peer-reviewed)) 2016
Awards, Honors and Fellowships
Simons Foundation Collaboration Grant for Mathematicians no. 318969, "Infinite-dimensional geodesic equations," $35,000, 2014-19. (Grants and Fellowships) 2014
NSF Geometric Analysis #1157293, "Thematic Program on Geometric Analysis and Spectral Theory," $50,000, 2012-16. (Grants and Fellowships) 2012
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. (Conferences, Seminars and Symposiums: Invited Talk) 2022
"Axisymmetric ideal fluids on Riemannian 3-manifolds," AMS Special Session on Geometry and Analysis of Fluid Equations, Northeastern University, April 22. (Conferences, Seminars and Symposiums: Conference Presentation) 2018
"Axisymmetric ideal fluids on Riemannian 3-manifolds," AMS Special Session on Nonlinear Evolution Equations, Ohio State University, March 17. (Conferences, Seminars and Symposiums: Conference Presentation) 2018
"Solar models for 1D Euler-Arnold equations," Math in the Black Forest: Workshop on New Directions in Shape Analysis, Freiburg, Germany, July 17. (Conferences, Seminars and Symposiums: Conference Presentation) 2018
"Solar models for Euler-Arnold equations," BIRS Workshop 18w5151 on Shape Analysis, Stochastic Geometric Mechanics and Applied Optimal Transport, Banff, Alberta, Canada, Dec. 12. (Conferences, Seminars and Symposiums: Invited Talk) 2018
"The furling of flags," AMS Special Session on Geometric Methods in Shape Analysis, Ohio State University, March 17. (Conferences, Seminars and Symposiums: Conference Presentation) 2018
"Some open problems in Euler-Arnold equations," Math in the Countryside Shape Analysis Workshop, Skrunda, Latvia, July 25. (Conferences, Seminars and Symposiums: Conference Presentation) 2017
"The elastic metric on the space of unit-speed curves," Shape Group Seminar, Florida State University. Feb. 7. (Conferences, Seminars and Symposiums: Invited Talk) 2017
"The Riemannian approach to universal Teichmüller space," Workshop on Applications-Driven Geometric Functional Data Analysis, Florida State University, October 10. (Conferences, Seminars and Symposiums: Conference Presentation) 2017
"Euler equations and Teichmüller theory," International Conference on Evolution Equations, Vanderbilt University, May 16. (Conferences, Seminars and Symposiums: Conference Presentation) 2016
"Geometric models of the 3D Euler equation," Analysis of PDEs of Fluid Mechanics Workshop, Rice University, May 10. (Conferences, Seminars and Symposiums: Conference Presentation) 2016
"The geometric approach to partial differential equations," Dean's Speaker Series, Binghamton University, April 15. (Conferences, Seminars and Symposiums: Invited Talk) 2016
Professional Leadership
Mathematics Department Chairperson, January 2018-present (Professional Leadership: Organizational Leadership Position) 2018
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. (Professional Leadership: Organizational Leadership Position) 2016
