## Dynamics, Geometry, & Groups - Abdullah Zafar (U of T)

### Friday, February 28th, 2020

**Time:** 10:30 a.m** Place:** Jeffery Hall 319

**Speaker:** Abdullah Zafar (University of Toronto)

**Title:** Flows, Braids and Fractal Dynamics: Understanding Patterns of Play in Professional Football.

**Abstract:** Team movement analysis in football is critical in the preparation and evaluation of performance. Previous studies have analyzed team performance using reductionist approaches such as team centroid analysis with limited consideration of individual player movement and physical performance. In this talk we will look at how we can model the movement of a team as a flow field, derive metrics to quantify the team tempo, and then demonstrate the utility and importance of tempo to the physical training of players as well as team performance as a whole. We will then explore the tempo time series in more depth to better understand the dynamics of a football match: discovering the underlying Fractional Brownian Motion, the changing multi-fractal spectrum, and the difference between attractors around goal-scoring moments. We will then supplement the modelling of team movement with the use of algebraic braids by considering the space-time trajectories of the players. The prominence of different braid groups within the team and during different moments of the match demonstrate the varying movement strategies used by teams, and the computation of braid entropy is explored in order to determine the intra-team structure and coherence in team movement.