Michal Branicki: Reduced-order predictions of nonlinear, partially observed dynamical systems.
I will focus on improving probabilistic predictions of complex dynamical systems which are based on imperfect, reduced-order models and sparse empirical information. I will briefly outline one promising approach which involves combining ideas from stochastic modelling, filtering/data assimilation and information theory.
James Maddison: Modelling and theory of ocean eddies.
The ocean is populated by an active field of "eddies". Compared to the global ocean these eddies are small, but they have a significant effect on the overall large-scale dynamics. Techniques for studying the ocean eddies will be discussed, and some open questions will be introduced.
Johan Martens: Higgs bundles: where do they come from and what are they good for?As an illustration of the role moduli spaces play in modern geometry and related areas, I will give a brief overview of Higgs bundles, highlighting their historic origins in physics and some of their recent uses in number theory.
Jon Pridham: Derived algebraic geometry
I will give an overview of the motivation behind derived algebraic geometry, possibly including intersection theory and moduli.