Place: Room 723, 7th floor, Nils Henrik Abels hus, Blindern Campus, University of Oslo

Talks: Each talk is for ~40-45 Minutes, so we have good time for discussions and coffee between talks.

Note: The "introduction to rough paths" lecture on Wednesday 24. Nov. will not be streamed.

• Khoa Lê - TU Berlin, Germany - Applications of stochastic sewing techniques

Abstract: The stochastic sewing lemma exploits stochastic cancellation in the sewing argument originated from Lyons' theory rough paths. This approach provides unexpected answers to some problems in stochastic analysis. I will briefly describe the stochastic sewing techniques and present three recent applications: on strong convergence rate for numerical schemes for SDEs, well-posedness for SPDEs with distributional drifts.

• Lucio Galeati - University of Bonn, Germany - Some recent advances on SDEs with fractional noise

Abstract: In recent years, there has been a lot of interest in regularization by noise for SDEs driven by fractional Brownian motion of parameter H\in (0,1), with first results going back to Nualart, Ouknine (2002) and Catellier, Gubinelli (2016). In particular, strong well-posedness is known for drifts of regularity \alpha>1-1/(2H). In this talk I will present some novel results on the topic, including generalizations of the above in the regime H\in (1,\infty), stability estimates for SDEs driven by different drifts and solvability of McKean-Vlasov equations.

Based on joint work with F.A. Harang and A. Mayorcas (arXiv:2105.14063) and ongoing joint work with M. Gerencser.

• Torstein Kastberg Nilssen - University of Agder -Random dynamical systems generated by 3D stochastic Navier-Stokes equation.

Abstract: In this talk I will present an approach to generate a random dynamical system from the 3D Navier-Stokes equation which is perturbed by Brownian noise of transport type. The technique is based on a rough path formulation of the equation as well as a so-called selection procedure. The latter is tailored for choosing one solution which satisfy the flow-property which then generates the random dynamical system.

• Alexander Schmeding - Nord University - The continuous field of controlled paths and rough path approximations.

Abstract: It is well known that rough integration is stable, i.e., if we approximate the integrating rough path and the controlled rough path integrands in a suitable way, the rough integrals converge. As the spaces of controlled rough paths depend on the control, convergence is defined here with the help of an extrinsic metric. In this talk we shall investigate this dependence and explain how it arises from the intrinsic geometry of the “bundle of controlled rough paths”. To this end, we present an approximation result for rough paths. With its help the controlled rough paths turn into a continuous field of Banach spaces. This structure is weaker than a vector bundle but allows one to treat dynamical systems via bundle like techniques. Moreover, the continuity of the Ito-Lyons map can be naturally interpreted in our geometric setting.

• Fred E. Benth - University of Oslo - Infinite dimensional models in forward markets with rough volatility.

Abstract: We review some recent models on forward pricing in energy and commodity markets with a focus on spatial dependecies and stochastic volatility. In particular, we propose a rough volatility model in infinite dimensions and provide some analysis of this. Joint wirk with Fabian Andsem Harang (BI Oslo).

• Antoine Mouzard - University of Rennes - Rough paths, paracontrolled calculus and S(P)DEs

Abstract: In this talk, I will present how paracontrolled calculus emerged from the ideas of Lyon's rough paths and Gubinelli's controlled paths. As application, I will explain how this can be used to solve singular SPDEs appearing in the study of SDEs with distributionnal drift

• Espen Robstad Jacobsen - NTNU Trondheim - Well-posedness of some new mean field games models.

Abstract: Mean field games is an exiting and rapidly expanding topic bridging economics, game/control theory, stochastics, and PDEs. Such games are mean field limits of N-player games as N tends to infinity, where each player controls an SDE driven by Gaussian or Levy noise. We first give a heuristic derivation of the mean field game system - a system of two PDEs characterising the optimal Nash equilibrium strategies for the game. Here we consider there most standard case with Gaussian uncontrolled noise. Then we discuss two recent generalisations of this model: (i) games driven by Levy noise, and (ii) games with controlled noise. We motivate the new models, give well-posedness results for them, and some hints on the proofs.

• Erlend Grong - University of Bergen - Geometric rough paths in Hilbert spaces.

Abstract: We will give an introduction to rough paths in infinite dimensional spaces. The final goal of the talk will be to show that for paths that are between 1/3 and 1/2 Hölder, weakly geometric rough paths can be approximated by signatures of curves of bounded variation, given some tuning of the Hölder parameters. To achieve this result, we will need to consider infinite Carnot-Carathéodory geometry in detail

• Rémi Catellier - Universitè Côte d'Azur - TBA