Seminars

Title: Random matrices, statistical physics and applications to complex ecosystems

Abstract: The theory of random matrices has fascinated physicists and mathematicians
for nearly 100 years. Wigner in particular used ensembles of random matrices to characterise the statistics of energy levels in atomic nuclei. Other applications include the theory of disordered systems in condensed matter physics, as well as finance and the study of neural networks. Robert May used the eigenvalue spectra of random matrices to study questions such as “When will a large complex system be stable?”,  
in particular in relation to complex ecosystems. He concluded that larger and
more complex communities ought to be unstable. Given that large and complex ecosystems are observed, May then asked what the “devious strategies” might be that nature uses to ensure stability. This then leads to the idea of structured random matrices. 
 
In this talk I will summarise some of our own work in random matrix
theory and on the stability of models of complex ecological communities. I first focus on random Lotka-Volterra systems and show how intricate non-Gaussian random matrices arise from the dynamics, how the spectra of these matrices can be computed using path-integral methods, and how this can then be used to characterise the stability
of feasible ecological communities. This will also lead us to a non-contrived example in which the commonly assumed “universally” of random matrix theory does not hold. 
 
I will then present further recent work on variations of the Lotka-Volterra dynamics, in particular including higher-order interactions, random interaction matrices with
generalised correlations, networked interactions, and systems with “fine structure” in the random matrix.

References:
- Generalised correlations in disordered dynamical systems: Insights from the many-species Lotka-Volterra model, SH Castedo, J Holmes, JW Baron, T Galla, arXiv:2409.12751 

- Higher-order interactions in random Lotka-Volterra communities, L Sidhom, T Galla, arXiv preprint arXiv:2409.10990- Interaction networks in persistent Lotka-Volterra communities, L Poley, T Galla, JW Baron, arXiv preprint arXiv:2404.08600 

- Eigenvalue spectra of finely structured random matrices, L Poley, T Galla, JW Baron, Physical Review E 109 (2024), 064301- Generalized Lotka-Volterra model with hierarchical interactions, L Poley, JW Baron, T Galla, Physical Review E 107 (2023) 024313

- Breakdown of random-matrix universality in persistent Lotka-Volterra communities. JW Baron, TJ Jewell, C Ryder, T Galla, Physical Review Letters 130 (2023), 137401
 
- Eigenvalues of random matrices with generalized correlations: A path integral approach, JW Baron, TJ Jewell, C Ryder, T Galla, Physical Review Letters 128 (2022), 120601

Title: The process of doing a PhD - lessons learned as a student and as a supervisor
 
Abstract:  This is an experiment. At the beginning of the session, I will summarise some of the lessons I learned during my own time as a PhD student, and then later as a supervisor. This is mainly about the process of doing a PhD, the different stages of a PhD, the role of the supervisor and of the student in these stages. I will also talk about the inevitable frustration along the way, and why it is normal (and in fact to an extent necessary) to struggle. This is based on these notes https://cloud.ifisc.uib-csic.es/nextcloud/index.php/s/tdsFEykS5c6R5Nr

Hopefully, members of the audience (students and supervisors) will also contribute. Everything I will say is biased by my own experience, and the conclusions will not apply to everyone. I don’t have the answers to all your questions. Overall, I hope that this will be a discussion more than me giving a talk.