Speaker: Clive Elphick
Date: 1st October 2025
Title: Recent progress on my conjectures in spectral graph theory
Abstract:
Spectral graph theory uses the eigenvalues of matrices that represent graphs to reveal information about the structure of the underlying graph. This is my third seminar at JHI about my conjectures, so this time I will focus only on progress during the last year. In particular, I will talk about:
- a conjecture which has been proved during the last year;
- a conjecture where substantial progress has been achieved;
- a new conjecture.
I did my PhD in spectral graph theory in 1980, so I will conclude by comparing maths research then and now.
Speaker: Russell Smith
Date: 12th November 2025
Title: A new window on old galaxies: stochastic spectroscopy of unresolved stellar populations
Abstract:
The central regions of giant elliptical galaxies will not be resolved into individual stars in our lifetimes. Most of our understanding of their stellar populations is thus drawn from interpreting their integrated light spectra: we measure the “total” light from all the stars, mixing together contributions from all the dwarfs, giants, etc. And we compare the observations to model spectra which likewise combine our understanding of stars in all the relevant phases we think might contribute significantly. Our conclusions rest delicately on whether this understanding is correct, but this is hard to test, since we have no local equivalents for the types of stars involved (e.g. old, but high-metallicity, alpha-enhanced, possibly helium-enhanced cool giants). A new approach is needed. In this talk I will describe a method to exploit the “semi-resolved” regime, where even the brightest individual stars cannot be isolated, but where Poisson sampling fluctuations are significant. The fluctuations cause measurable pixel-to-pixel differences in the integrated spectrum, analogous to the “surface brightness fluctuations” in imaging observations. Applied to integral field unit observations, our method can reconstruct the detailed spectra of the brightest type (or types) of giants present in the population. I will show the results from recent extension of our model predictions to explore a broad range in wavelength and population parameters. I will demonstrate the method in practice using data on NGC 5128 from high-resolution VLT/MUSE-AO observations in the optical, and new data from VLT/ERIS in the infra-red. I will close with some discussion of prospects for extending this method to the centres of “true” elliptical galaxies with the ELT.
Speaker: Calum Ross
Date: 19th November 2025
Title: Topological Solitons in Chiral Magnets
Abstract:
Topological solitons are stable particle like lumps of energy that appear in many physical systems with their stability coming from the topology of the fields. I will review some details about topological solitons in general before focussing on examples of them in magnetic systems. In particular I will discuss an idealised, solvable, model of chiral magnets where we can construct explicit magnetic skyrmion configurations, as well as a zoo of further configurations sharing the key properties of the skyrmions found in real systems. Time permitting, I will also mention some further configurations known as domain wall skyrmions, where it is easier to control the motion of the skyrmions. The first part will be based on work published in Magnetic Skyrmions at Critical Coupling. Commun. Math. Phys. 375, 2259–2280 (2020), while the second part is work carried out in collaboration with Muneto Nitta and Yuki Amari at Keio University.