

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 NavierStokes 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 longstanding and interesting problem.
Click here
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 NavierStokes 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. Blowup of critical Besov norms at a potential NavierStokes singularity. arXiv:1407.4156 (July 2014) and Comm. Math. Phys. (to appear).
Isabelle Gallagher, Gabriel S. Koch and Fabrice Planchon. A profile decomposition approach to the L^{∞}_{t} (L^{3}_{x}) NavierStokes regularity criterion. Math. Ann. (published online July 2012), 355(4):15271559, 2013.
Hajer Bahouri, Albert Cohen and Gabriel Koch. A general waveletbased profile decomposition in the critical embedding of function spaces. Confluentes Mathematici (CM) 3(3):387411, 2011.
Gabriel S. Koch. Profile decompositions and applications to NavierStokes. 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., 59:18011830, 2010.
Carlos E. Kenig and Gabriel S. Koch. An alternative approach to the NavierStokes equations in critical spaces. Ann. I. H. Poincare  AN, 28(2):159  187, 2011.
Gabriel Koch, Nikolai Nadirashvili, Gregory A. Seregin, and Vladimír Šverák. Liouville theorems for the NavierStokes equations and applications. Acta Math., 203(1):83105, 2009.
19961999: B.A., Mathematics with honors, Magna Cum Laude, Brandeis University
20002006: Ph.D., Mathematics, University of Minnesota (advisor: Vladimír Šverák)
20062009: L. E. Dickson Instructor, Department of Mathematics, University of Chicago (mentor: Carlos E. Kenig)
20092011: 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
2011present: Lecturer in Mathematics, Mathematics Department,
University
of Sussex