Thu, 25 Feb 2016
12:00
L6

Concentration Compactness for the Critical Maxwell-Klein-Gordon Equation

Jonas Lührmann
(ETH Zurich)
Abstract
The Maxwell-Klein-Gordon equation models the interaction of an electromagnetic field with a charged particle field. We discuss a proof of global regularity, scattering and a priori bounds for solutions to the energy critical Maxwell-Klein-Gordon equation relative to the Coulomb gauge for essentially arbitrary smooth data of finite energy. The proof is based upon a novel "twisted" Bahouri-Gérard type profile decomposition and a concentration compactness/rigidity argument by Kenig-Merle, following the method developed by Krieger-Schlag in the context of critical wave maps. This is joint work with Joachim Krieger.
Thu, 04 Feb 2016
12:00
L6

Regularity of level sets and flow lines

Herbert Koch
(Universitat Bonn)
Abstract
Level sets of solutions to elliptic and parabolic problems are often much more regular than the equation suggests. I will discuss partial analyticity and consequences for level sets, the regularity of solutions to elliptic PDEs in some limit cases, and the regularity of flow lines for bounded stationary solutions to the Euler equation. This is joint work with Nikolai Nadirashvili.
Thu, 04 Feb 2016

16:00 - 17:00
L5

Strongly semistable sheaves and the Mordell-Lang conjecture over function fields

Damian Rössler
(University of Oxford)
Abstract

We shall describe a new proof of the Mordell-Lang conjecture in positive characteristic, in the situation where the variety under scrutiny is a smooth subvariety of an abelian variety. 
Our proof is based on the theory of semistable sheaves in positive characteristic, in particular on  Langer's theorem that the Harder-Narasimhan filtration of sheaves becomes strongly semistable after a finite number of iterations of Frobenius pull-backs. Our proof produces a numerical upper-bound for the degree of the finite morphism from an isotrivial variety appearing in the statement of the Mordell-Lang conjecture. This upper-bound is given in terms of the Frobenius-stabilised slopes of the cotangent bundle of the variety.

Querying with access patterns and integrity constraints
 Benedikt, M Leblay, J Tsamoura, E Proceedings of the VLDB Endowment volume 8 issue 6 690-701 (Feb 2015) doi:10.14778/2735703.2735708
Convection of a fluid with strongly temperature and pressure dependent viscosity
 Fowler, A Howell, P Khaleque, T Geophysical & Astrophysical Fluid Dynamics volume 110 issue 2 130-165 (03 Mar 2016) doi:10.1080/03091929.2016.1146264
Thu, 18 Feb 2016

16:00 - 17:00
L5

(Joint Number Theory and Logic) On a modular Fermat equation

Jonathan Pila
(University of Oxford)
Abstract

I will describe some diophantine problems and results motivated by the analogy between powers of the modular curve and powers of the multiplicative group in the context of the Zilber-Pink conjecture.

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