In this talk I will analyse ERK time course data by developing mathematical models of enzyme kinetics. I will present how we can use differential algebra and geometry for model identifiability, and topological data analysis to study these the dynamics of ERK. This work is joint with Lewis Marsh, Emilie Dufresne, Helen Byrne and Stanislav Shvartsman.

Introducing cheap function proxies for quickly producing approximate random numbers, we show convergence of modified numerical schemes, and coupling between approximation and discretisation errors. We bound the cumulative roundoff error introduced by floating-point calculations, valid for 16-bit half-precision (FP16). We combine approximate distributions and reduced-precisions into a nested simulation framework (via multilevel Monte Carlo), demonstrating performance improvements achieved without losing accuracy. These simulations predominantly perform most of their calculations in very low precisions. We will highlight the motivations and design choices appropriate for SVE and FP16 capable hardware, and present numerical results on Arm, Intel, and NVIDIA based hardware.

The goal of the talk is to present a proof of the following statement:
Let (K,v) be an algebraic extension of (Q_p,v_p) whose completion is perfectoid. We show that K is relatively decidable to its tilt K^♭, i.e. if K^♭ is decidable in the language of valued fields, then so is K. 
In the first part [of the talk], I will try to cover the necessary background needed from model theory and the theory of perfectoid fields.

We study a class of non linear integro-differential equations on the Wasserstein space related to the optimal control of McKean-Vlasov jump-diffusions. We develop an intrinsic notion of viscosity solutions that does not rely on the lifting to an Hilbert space and prove a comparison theorem for these solutions. We also show that the value function is the unique viscosity solution. Based on a joint work with V. Ignazio, M. Reppen and H. M. Soner

In the seminar I will present a recent work joint with  S. Suhr (Bochum) giving an optimal transport formulation of the full Einstein equations of general relativity, linking the (Ricci) curvature of a space-time with the cosmological constant and the energy-momentum tensor. Such an optimal transport formulation is in terms of convexity/concavity properties of the Shannon-Bolzmann entropy along curves of probability measures extremizing suitable optimal transport costs. The result gives a new connection between general relativity and  optimal transport; moreover it gives a mathematical reinforcement of the strong link between general relativity and thermodynamics/information theory that emerged in the physics literature of the last years.