Gerard Misiolek

Professor

Education

Ph.D., SUNY at Stony Brook, 1992
M.A., Uniwersytet Warszawski, 1988
M.S., Politechnika Warszawska, 1987
I.B., United World College of the Atlantic, 1981

Research Groups

Analysis and Partial Differential Equations, Differential Geometry, Partial Differential Equations

Research Area

Analysis and Geometry

Bio

Research Interests

Geometric Analysis, Partial Differential Equations, Fluids

Selected Publications

• B. Khesin, G. Misio{\l}ek and A. Shnirelman, Geometric Hydrodynamics in open problems, ARMA, Arch. Ration. Mech. Anal. 247 (2023), 43pp.

• B. Khesin, G. Misiołek and K. Modin, Geometric Hydrodynamics and infinite-dimensional Newton’s equations, Bull. Amer. Math. Soc. 58 (2021), 377-442.

• G. Misiolek and T. Yoneda, Continuity of the solution map of the Euler equations in Holder spaces and weak norm inflation in Besov spaces, Trans. Amer. Math. Soc. 370 (2018), 4709-4730. 

• B. Khesin, J. Lenells, G. Misiolek and S. Preston, Geometry of diffeomorphism groups, complete integrability and geometric statistics, GAFA, Geom. funct. anal. 23 (2013), 334-366.

• G. Misiolek and S. Preston, Fredholm properties of Riemannian exponential maps on diffeomorphism groups, Invent. math. 179 (2010), 191-227.

• A. Himonas and G. Misiolek, Non-uniform dependence on initial data of solutions to the Euler equations of hydrodynamics, Comm. Math. Phys. 296 (2010), 285-301.

• D. Ebin, G. Misio{\l}ek and S. Preston, Singularities of the exponential map on the volume-preserving diffeomorphism group, GAFA, Geom. funct. anal. 16 (2006), 850-868.

• B. Khesin and G. Misiolek, Euler equations on homogeneous spaces and Virasoro orbits, Adv. Math. 176 (2003), 116-144.

• G. Misiolek, The exponential map on the free loop space is Fredholm, GAFA, Geom. funct. anal. 7 (1997), 954-969.

• G. Misiolek, Conjugate points in D_µ(T^2), Proc. Amer. Math. Soc. 124 (1996), 977-982.