Authors:

Anne Balter and Antoon Pelsser

Models can be wrong and recognising their limitations is important in financial and economic decision making under uncertainty. Robust strategies, which are least sensitive to perturbations of the underlying model, take uncertainty into account. Interpreting

the explicit set of alternative models surrounding the baseline model has been difficult so far. We specify alternative models by a stochastic change of probability measure and derive a quantitative bound on the uncertainty set. We find an explicit ex ante relation

between the choice parameter k, which is the radius of the uncertainty set, and the Type I and II error probabilities on the statistical test that is hypothetically performed to investigate whether the model specification could be rejected at the future test horizon.

The hypothetical test is constructed to obtain all alternative models that cannot be distinguished from the baseline model with sufficient power. Moreover, we also link the ambiguity bound, which is now a function of interpretable variables, to numerical

values on several divergence measures. Finally, we illustrate the methodology on a robust investment problem and identify how the robustness multiplier can be numerically interpreted by ascribing meaning to the amount of ambiguity.

In this talk, we will present results regarding the regularity and

rigidity of solutions to the Monge-Ampere equation, inspired by the role

played by this equation in the context of prestrained elasticity. We will

show how the Nash-Kuiper convex integration can be applied here to achieve

flexibility of Holder solutions, and how other techniques from fluid

dynamics (the commutator estimate, yielding the degree formula in the

present context) find their parallels in proving the rigidity. We will indicate

possible avenues for the future related research.

Gathering for women and non-binary mathematicians

Prof. Helen Byrne shares her academic path and experience as Director of Equality and Diversity.

More information will appear later.

Our meeting will be a relaxed opportunity to have informal discussions about issues facing minorities in academia and mathematics over lunch. In particular, if anyone would like to suggest a topic to start a discussion about (either in advance or on the day) then please feel free to do this, and it could be a spring board for organised sessions on the same topics in future terms!

I will discuss results relating different partially wrapped Fukaya categories.  These include a K\"unneth formula, a `stop removal' result relating partially wrapped Fukaya categories relative to different stops, and a gluing formula for wrapped Fukaya categories.  The techniques also lead to generation results for Weinstein manifolds and for Lefschetz fibrations.  The methods are mainly geometric, and the key underlying Floer theoretic fact is an exact triangle in the Fukaya category associated to Lagrangian surgery along a short Reeb chord at infinity.  This is joint work with Sheel Ganatra and Vivek Shende.

The Euler equation describing motion of ideal fluids goes back to 1755. 
The analysis of the equation is challenging since it is nonlinear and nonlocal. Its solutions are often unstable and spontaneously generate small scales. The fundamental question of global regularity vs finite time singularity formation 
remains open for the Euler equation in three spatial dimensions. In this lecture, I will review the history of this question and its connection with the arguably greatest unsolved problem of classical physics, turbulence. Recent results on small scale and singularity formation in two dimensions and for a number of related models will also be presented.

Robert Timms

Title: Multiscale modelling of lithium-ion batteries

Lithium-ion batteries are one of the most widely used technologies for energy storage, with applications ranging from portable electronics to electric vehicles. Due to their popularity, there is a continued interest in the development of mathematical models of lithium-ion batteries. These models encompass various levels of complexity, which may be suitable to aid with design, or for real-time monitoring of performance. After a brief introduction to lithium-ion batteries, I will discuss some of the modelling efforts undertaken here at Oxford and within the wider battery modelling community.
 

Jan Vonk

Title: Singular moduli for real quadratic fields

At the 1900 ICM, David Hilbert posed a series of problems, of which the 12th remains completely open today. I will discuss how to solve this problem in the simplest open case, by considering certain exotic (so called p-adic) metrics on the set of numbers, and using its concomitant theories of analysis and geometry.
 

Are you teaching intercollegiate classes or tutorials this term? Would you like to explore inclusive teaching strategies that could help all students make the most of your sessions? In this interactive workshop, we'll explore strategies that have been found effective. This will be a self-contained session, but will also be a good introduction to the "Developing Learning and Teaching" course offered by MPLS for graduate students and early career researchers. The session will be led by Vicky Neale (Mathematics) and Delia O'Rourke (Oxford Learning Institute).