Hello, my name is: Stephen C. Preston. I am an Associate Professor at the University of Colorado at Boulder. I obtained my Ph.D. in 2002 at Stony Brook under David G. Ebin. Contact information: Email: Office: Mathematics 302 Department of Mathematics, UCB 395 Boulder, CO 80309-0395 303-492-5026 (ph), 303-492-7707 (fax) Teaching: Spring 2013: Math 6230 (Differential Geometry 1)

• Kempner Colloquium
• Workshop on Infinite-Dimensional Geometry (UC Berkeley, December 7-8 2013)

• 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 Misiolek, 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 Misiolek, 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 H<sup>1</sup> 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 Misiolek, in GAFA, volume 23, no. 1.
• 2013: `Curvatures of Sobolev metrics on diffeomorphism groups,' with Boris Khesin, Jonatan Lenells, and Gerard Misiolek, to appear in PAMQ.
• 2013: `The geometry of barotropic flow,' to appear in J. Math. Fluid Mech.
• 2013: `Riemannian geometry of the quantomorphism group,' with David Ebin, submitted.

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