Stephen C. Preston

Hello, my name is: Stephen C. Preston.
I am a Professor of Mathematics at Brooklyn College, with a joint appointment to the CUNY Graduate Center.

I was the Chairperson of the Brooklyn College Math Department from January 2018 to June 2020.

Before 2016 I was at the University of Colorado.
I obtained my Ph.D. in 2002 at Stony Brook under David G. Ebin.

Contact information:
Email:

Office: 2313 Ingersoll Hall
Department of Mathematics
1156 Ingersoll Hall
2900 Bedford Avenue
Brooklyn, NY 11210-2889
718-951-5246 (ph), 718-951-4674 (fax)

Teaching: Fall 2023: CUNY Graduate Center, Introduction to Differential Geometry (Math 70900).

Research:

2002: `Eulerian and Lagrangian stability of fluid motions,' doctoral dissertation.
2004: `For ideal fluids, Eulerian and Lagrangian instabilities are equivalent,' in GAFA, volume 14, no. 5.
2005: `Nonpositive curvature on the area-preserving diffeomorphism group,' in J. Geom. Phys., volume 53, no. 2.
2006: `Singularities of the exponential map on the volume-preserving diffeomorphism group,' with David G. Ebin and Gerard Misiołek, in GAFA, volume 16, no. 4.
2006: `On the volumorphism group, the first conjugate point is always the hardest,' in Comm. Math. Phys., volume 267, no. 2.
2008: `The WKB method for conjugate points in the volumorphism group,' in Indiana U. Math. J., volume 57, no. 7.
2009: `Fredholm properties of Riemannian exponential maps on diffeomorphism groups,' with Gerard Misiołek, in Invent. Math., volume 179, no. 1.
2010: `A geometric rigidity theorem for hydrodynamic blowup,' in Comm. PDE, volume 35, no. 10.
2011: `The motion of whips and chains,' in J. Diff. Eq., volume 251, no. 3.
2012: `The geometry of whips,' in Ann. Global Anal. Geometry, volume 41, no. 3.
2013: `An H¹ model for inextensible strings,' with Ralph Saxton, in DCDS-A, volume 33, no. 5.
2013: `Geometry of diffeomorphism groups, complete integrability and geometric statistics,' with Boris Khesin, Jonatan Lenells, and Gerard Misiołek, in GAFA, volume 23, no. 1.
2013: `Curvatures of Sobolev metrics on diffeomorphism groups,' with Boris Khesin, Jonatan Lenells, and Gerard Misiołek, in PAMQ, volume 9, no. 2.
2013: `The geometry of barotropic flow,' in J. Math. Fluid Mech, volume 15, no. 4.
2015: `Riemannian geometry of the contactomorphism group,' with David G. Ebin, in Arnold Math. J., volume 1, no. 1.
2015: `One-parameter solutions of the Euler-Arnold equation on the contactomorphism group,' with Alejandro Sarria, in DCDS-A, volume 35, no. 5.
2015: `Geometry of the contactomorphism group,' with Boramey Chhay, in Diff. Geo. Appl., volume 40.
2016: `Geometric investigations of a vorticity model equation,' with Martin Bauer and Boris Kolev, in J. Diff. Eq., volume 260, no. 1.
2016: `Lagrangian aspects of the axisymmetric Euler equation,' with Alejandro Sarria, in Nonlinearity, volume 29, no. 3.
2017: `The geometry of axisymmetric ideal fluid flows with swirl,' with Pearce Washabaugh, in Arnold Math. J., volume 3, no. 2.
2017: `Quotient elastic metrics on the manifold of arc-length parameterized plane loops,' with Barbara Tumpach, in J. Geometric Mech., volume 9, no. 2.
2017: `Local well-posedness of the Camassa-Holm equation on the real line,' with Jae Min Lee, in DCDS-A, volume 37, no. 6.
2018: `Euler-Arnold equations and Teichmüller theory,' with Pearce Washabaugh, in Diff. Geo. Appl., volume 59.
2018: `The exponential map of the group of area-preserving diffeomorphisms of a surface with boundary,' with James Benn and Gerard Misiołek, in ARMA, volume 229, no. 3.
2020: `Vanishing distance phenomena and the geometric approach to SQG,' with Martin Bauer and Philipp Harms, in ARMA, volume 235, no. 3.
2020: `Geodesic completeness of the H^3/2 metric on Diff(S¹),' with Martin Bauer and Boris Kolev, in Monatsh. Math., volume 193, no. 2.
2020: `Shape analysis of surfaces using general elastic metrics,' with Zhe Su, Martin Bauer, Hamid Laga, and Eric Klassen, in J. Math. Imaging Vis., volume 62, no. 8.
2020: `Axisymmetric diffeomorphisms and ideal fluids on Riemannian 3-manifolds,' with Leandro Lichtenfelz and Gerard Misiołek, in IMRN.
2021: `A diffeomorphism-invariant metric on the space of vector-valued one-forms,' with Martin Bauer, Eric Klassen, and Zhe Su, in PAMQ, volume 17, no. 1.
2021: `Nonpositive curvature of the quantomorphism group and quasigeostrophic motion,' with Jae Min Lee, in Diff. Geo. Appl., volume 74.
2021: `Fisher-Rao geometry of Dirichlet distributions,' with Alice Le Brigant and Stéphane Puechmorel, in Diff Geo. Appl., volume 74.
2022: `Solar models and McKean's breakdown theorem for the μCH and μDP equations,' in Math. Ann., volume 385.
2022: `Conjugate point criteria on the area-preserving diffeomorphism group,' in J. Geom. Phys, volume 183.
2023: `3 methods to put a Riemannian metric on shape space,' with Barbara Tumpach, in GSI conference proceedings.
2024: `Conjugate points along Kolmogorov flows on the torus,' with Alice Le Brigant, in J. Math. Fluid Mech., volume 26.
2024: `Isometric immersions and the waving of flags,' with Martin Bauer and Jakob Møller-Andersen, in ARMA, volume 248.
2024: `Geometric analysis of the generalized surface quasi-geostrophic equations,' with Martin Bauer, Patrick Heslin, and Gerard Misiołek, in Math. Ann.
2024: `Liouville comparison theory for breakdown of Euler-Arnold equations,' with Martin Bauer and Justin Valletta, in J. Diff. Eq., volume 407.
2024: `Geodesics, curvature, and conjugate points on Lie groups,' with Alice Le Brigant and Leandro Lichtenfelz, submitted.
2024: `Zeitlin's model for axisymmetric 3-D Euler equations,' with Klas Modin, submitted.

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