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Links to our Analysis and PDEs seminar and our departmental MASS seminar
My research interests lie in the analysis of nonlinear partial differential equations.
My most recent focus has been on the Navier-Stokes equations which describe the motion of a large class of viscous, incompressible fluids.
Click here and follow the links on that page for a summary of this long-standing and interesting problem.
as well for a summary of my research as it relates to that problem.
Click here for news of my recent EPSRC grant success through their 'First Grant' scheme.
The grant will run from August 2015 through July 2017, and will include a workshop (date TBD) on the Navier-Stokes regularity problem.
The link also provides quite a bit of background about my
research in general.
Here is the official link on EPSRC's "grants on the web": GOW_Koch (does not include Sussex's contribution in the grant amount)
Isabelle Gallagher, Gabriel S. Koch and Fabrice Planchon. Blow-up of critical Besov norms at a potential Navier-Stokes singularity, Comm. Math. Phys. (published online 05 March 2016).
Isabelle Gallagher, Gabriel S. Koch and Fabrice Planchon. A profile decomposition approach to the L∞t (L3x) Navier-Stokes regularity criterion. Math. Ann. (published online July 2012), 355(4):1527-1559, 2013.
Hajer Bahouri, Albert Cohen and Gabriel Koch. A general wavelet-based profile decomposition in the critical embedding of function spaces. Confluentes Mathematici (CM) 3(3):387-411, 2011.
Gabriel S. Koch. Profile decompositions and applications to Navier-Stokes. In Journees "Equations aux Derivees Partielles" (Port d'Albret, 2010), Exp. No. 12, 13. 2010.
Gabriel S. Koch. Profile decompositions for critical Lebesgue and Besov space embeddings. Indiana Univ. Math. J., 59:1801--1830, 2010.
Carlos E. Kenig and Gabriel S. Koch. An alternative approach to the Navier-Stokes equations in critical spaces. Ann. I. H. Poincare -- AN, 28(2):159 -- 187, 2011.
Gabriel Koch, Nikolai Nadirashvili, Gregory A. Seregin, and Vladimír verák. Liouville theorems for the Navier-Stokes equations and applications. Acta Math., 203(1):83--105, 2009.
1996-1999: B.A., Mathematics with honors, Magna Cum Laude, Brandeis University
2000-2006: Ph.D., Mathematics, University of Minnesota (advisor: Vladimír verák)
2006-2009: L. E. Dickson Instructor, Department of Mathematics, University of Chicago (mentor: Carlos E. Kenig)
2009-2011: Postdoctoral Research Fellow, Oxford Centre for Nonlinear PDE (OxPDE), Mathematical Institute, Oxford University (mentor: Gregory Seregin)
2012 (April - December): Lecturer, Institute of Mathematics, University of Zürich
2011-present: Lecturer in Mathematics, Mathematics Department,