Week 22.02.2026 – 28.02.2026

The Theory of Dynamical Systems studies how systems evolve over time,
often through differential equations or iterated transformations. Even
deterministic systems governed by simple laws can display chaotic
behaviour, marked by extreme sensitivity to initial conditions — tiny
changes in the starting state may lead to dramatically different
outcomes. Using the Lorenz attractor as an example, we illustrate this
unpredictability, popularly known as the butterfly effect. We then
show how a probabilistic approach provides the appropriate framework
for analysing chaotic systems, offering the right tools to make
meaningful predictions precisely where a purely deterministic
description proves inadequate.

In the area of combinatorics known as ‘permutation patterns’, seemingly innocuous questions can conceal a surprising degree of difficulty, giving rise to combinatorial problems that range from trivial to unsolved (despite decades of work). In this talk, we will explore several ways in which permutation pattern questions interface with probability — sometimes giving rise to probabilistic processes, sometimes illuminated by probabilistic reasoning. Some of these will be generalizations of known processes, others new, and still others conjectural.



Based on forthcoming joint work with Slim Kammoun and Einar Steingrimsson.

In the area of combinatorics known as ‘permutation patterns’, seemingly innocuous questions can conceal a surprising degree of difficulty, giving rise to combinatorial problems that range from trivial to unsolved (despite decades of work). In this talk, we will explore several ways in which permutation pattern questions interface with probability — sometimes giving rise to probabilistic processes, sometimes illuminated by probabilistic reasoning. Some of these will be generalizations of known processes, others new, and others still conjectural.

Based on forthcoming joint work with Slim Kammoun and Einar Steingrimsson.

See: https://www.londonmathfinance.org.uk/seminar

See: https://www.londonmathfinance.org.uk/seminar

In this talk we shall discuss the status of local-global principles for semi-integral points on orbifold pairs of Markoff type. If time permits, we will discuss a way to count Markoff orbifold pairs which satisfy the semi-integral Hasse principle while the corresponding Markoff surface lacks integral points. This talk is based on a joint work with Justin Uhlemann.

We provide a new perspective on Takens' Theorem from the theory of dynamical systems to investigate the importance of path dependent modelling in Finance and Machine Learning. We also provide some insight on the construction of architectures from the point
of view of invariant theory.