Seminars from until

We study the family of Cartan-Schouten connections on Lie groups, parameterized by $\lambda\in[0,1]$, whose geodesics through the identity are one-parameter subgroups. We compute their curvature, torsion, parallel transport, and geodesics, and develop Euler-Poincaré and Lie-Poisson reduction for mechanical systems via these connections, unifying the “minus” and “plus” cases. These inspire us to introduce a connection-dependent variational principle where the Lagrangian is expressed in terms of the parallel-transported velocity, leading to an integro-differential Euler-Lagrange equation that explicitly involves torsion and curvature memory terms. The general framework is illustrated on two concrete examples: the Heisenberg group, where the equations simplify to an ODE system, and the rotation group SO(3), where the integro-differential system is solved numerically via a Magnus expansion.

An important aspect of socially interacting rational agents are the strategic abilities of individual agents and groups (coalitions) of agents to guarantee the achievement of their desired goals, while acting and interacting within an entire society of agents. Several logical systems have been proposed for formalising and capturing such reasoning were introduced in the early 2000s, starting with the Coalition Logic (CL), the Alternating Time Temporal Logic (ATL), and some extensions of these. Coalition Logic provides a natural, but rather restricted perspective: the agents in the proponent coalition are viewed as acting in full cooperation with each other but in complete opposition to all agents outside of the coalition, which are thus treated as adversaries. The Alternating Time Temporal Logic extends Coalition Logic with temporal operators allowing for expressing long-term temporised goals. The strategic interaction in real societies is much more complex, usually involving various patterns combining cooperation and competition. To capture these, more expressive and versatile logical frameworks are needed. In this talk I will give a brief overview of some of these, and will then focus on the Logic of Coalitional Goal Assignments (LCGA), capturing reasoning about strategic abilities of the entire society to cooperate in order to ensure achievement of the societal goals, while simultaneously protecting the abilities of individuals and groups within the society to achieve their individual and group goals.

We prove that a parabolically rescaled and suitably renormalised height function of a weakly asymmetric simple exclusion process on a circle converges to the Cole-Hopf solution of the KPZ equation. This is an analogue of the celebrated result by Bertini and Giacomin from 1997 for the exclusion process on a circle with any particles density. The main goal of this article is to analyse the interacting particle system using the framework of regularity structures without applying the Gärtner transformation, a discrete version of the Cole-Hopf transformation which linearises the KPZ equation. Our analysis relies on discretisation framework for regularity structures developed by Erhard and Hairer [AIHP 2019] as well as estimates for iterated integrals with respect to jump martingales derived by Grazieschi, Matetski and Weber [PTRF 2025]. The main technical challenge addressed in this work is the renormalisation procedure which requires a subtle analysis of regularity preserving discrete convolution operators. Joint work with R. Huang (Münster) and K. Matetski (Michigan State).

Tennenbaum's theorem states that PA does not admit any nonstandard computable model. In 2022, Fedor Pakhomov proved that this theorem is fragile in regards to how PA is expressed, by constructing a theory that is definitionally equivalent to PA (roughly: “it’s PA but with a different choice of signature”) for which there is a computable nonstandard model. I will introduce the audience to this result and, time allowing, present the way in which we have been able to improve on Pakhomov's original construction and some remaining open questions.