About the Colloquium

The PG Colloquium is a bi-weekly seminar for PhD students from the School of Mathematics and jointly run by Heriot-Watt University, which currently takes place on Fridays in room 5.45 of the Bayes Centre and online via zoom. 

Each session, a speaker gives a talk (30-45 minutes), either about their research or some other aspect of mathematics they are interested in. These talks are intended to be accessible to all PhD students, so we encourage everyone to attend the colloquium, hear from their peers about what interests them, and volunteer to give a talk themselves.  If you are interested in giving a talk, please fill out this form. It can be on your research, or just on a piece of maths that you enjoy and would like to share!

After the colloquium talk there is a Q&A session followed by tea & biscuits in the common area. We encourage attendees to stick around for a chat!

Details of upcoming talks will be posted here in advance and links to the online sessions will be sent out through the mailling list. We are also open to guest speakers and audience members from other Schools who are interested in mathematics, as well as masters students. If you are not a MIGS student but are interested in attending the colloquium, please contact the PG Colloquium organisers, Joseph Malbon (J.Malbon@sms.ed.ac.uk) or Johnny Lee (johnny.myungwon.lee@ed.ac.uk).

Upcoming Colloquia

  • 26th Apr 2024 | TBC


Past Colloquia (Academic Year 2023/2024)

Semester 2

  • 5pm, 5th Apr 2024 | Clara Panchaud (School of Mathematics, University of Edinburgh)

    Counting snow leopards in Mongolia.

    Estimating wildlife species abundance and distribution is important for the conservation of animals and natural reserves. Data on uniquely identifiable individuals is increasingly collected from remote sensors such as camera traps, from which population estimates can be obtained using the popular spatially explicit capture-recapture (SCR) models.

    In this talk, I will explain how data can be collected in ecological surveys before introducing SCR models. I will then discuss some of the general challenges addressed in statistical ecology, and present as an example my recent collaboration and fieldwork experience with the Snow Leopard Trust in Mongolia.

  • 5pm, 1st Mar 2024 | Johnny MyungWon Lee (School of Mathematics, University of Edinburgh)

    Calming the Furious Inferno: Bayesian regularisation with smoothing for tail index regression.

    Extreme events can be better comprehended through the lens of regression models tailored for extreme values. This framework revolves around a conditional Pareto-type specification, enriched by the inclusion of Bayesian Lasso-type shrinkage priors and further refined through low-rank thin plate splines basis expansion.

    In this talk, I will validate via several simulations and illustrate our model to investigate extreme wildfire events in Portugal, delving into the key drivers behind these occurrences. Fingers crossed, we can turn this inferno into a controlled burn of knowledge!

  • 3pm, 16th Feb 2024 | Billy Sumners (School of Mathematics, University of Edinburgh)

    How do shape memory alloys work?

    A shape memory alloy (as demonstrated in the gem below) is a material which can be easily deformed when cool, but upon heating, reverts back to the shape that it had originally. This ability to seemingly remember its past (hence “memory”) could probably be explained by magic. But like all magic, this property is just a sleight of hand where the hidden inner structure of the material allows it to take on the appearance of having memory.
    In this talk, I’ll explain with some heuristics how a material with two solid phases (“austenite” and “martensite”), and the transformation from martensite to austenite gives rise to the shape memory effect. I’ll also talk a little about how the reverse transformation from the austenite to martensite determines what we observe microscopically, and how the property of self-accommodation contributes to the illusion of the shape memory effect.


  • 5pm, 2nd Feb 2024 | Zhaoxi Zhang (School of Mathematics, University of Edinburgh)

    The underlap coefficient with Bayesian estimators: A measure of evaluating diagnostic tests and classification models in multi-class settings?

    In clinical practice, after the discovery of a potential diagnostic test, it is crucial to rigorously assess its diagnostic capabilities. The most popular measures are predominantly ROC-based, including the volume under the receiver operating characteristic surface (VUS) and the three-class Youden index (YI) in the three-class setting, as well as the hypervolume under the ROC manifold (HUM) in the multi-class setting. However, these measures are only appropriate under a stochastic ordering assumption for the distributions of test outcomes across all the groups. This assumption is stringent and not always plausible, particularly when covariates are involved. Violating this assumption can lead to incorrect conclusions about a test’s performance to make classifications.

    To address this, we propose the underlap coefficient, study its properties, as well as its relationship with the VUS and YI, particularly when a stochastic order is enforced in the three-class setting. We further propose Bayesian nonparametric estimators for both the unconditional underlap coefficient and for its covariate-specific version. A simulation study reveals a good performance of the proposed estimators across a range of conceivable scenarios. We also illustrate the proposed approach with an application to an Alzheimer’s disease (AD) dataset to assess how different potential AD biomarkers distinguish between individuals with normal cognition, mild impairment, and dementia, and how age and gender impact this discriminatory ability.

Semester 1

  • 5pm, 8th Dec 2023 | Lambert de Monte (School of Mathematics, University of Edinburgh)

    Multivariate extremes: Inference for radially-stable distributions.

    Multivariate extreme value theory (MEVT) is a branch of probability and statistics concerned with characterising the extremes of finite-dimensional random vectors and estimating the probability of joint, rare events. Particular interest lies in extrapolating beyond the range of observed data; common environmental applications include modelling extreme hydrological events linked with flooding, damaging wind gusts, heatwaves, and their impacts on livelihood. A classical approach to MEVT consists of studying the distribution of exceedances of high thresholds, but current methods mostly rely on the constraining notion of multivariate regular variation.

    A new framework is introduced for multivariate threshold exceedances involving radially stable distributions based on the geometric approach to MEVT, a recent branch of extreme value theory arising through the study of suitably scaled independent observations from random vectors and their convergence in probability onto compact limit sets. Using a radial-angular decomposition of the random vector of interest, a Bayesian inference approach is adopted based on a limiting Poisson point process likelihood using information from the distribution of the radial exceedances and the distribution of the angles along which the exceedances occur. The method is showcased on case studies of river flow and sea level extremes.

  • 5pm, 24th Nov 2023 | Yannis Galanos (School of Mathematics, University of Edinburgh)

    Restriction Theory – The surprising behaviour of the Fourier transform when restricted on surfaces.

    You might have heard that the Fourier transform is a powerful tool for solving differential equations. But how does it do it?

    I will discuss linear and bilinear restriction estimates on model hypersurfaces (what they are and techniques for proving them) and explain how they can be interpreted as decay estimates for solutions to various PDE.

  • 3pm, 3rd Nov 2023 | Juan Carlos Morales Parra (School of Mathematical and Computer Sciences, Heriot-Watt University)

    Affinization of gauge theories: How to derive 1+1 integrable systems from Chern-Simons theory?

    The concept of conserved charge plays a fundamental role in modern physics because it formalizes the notion of a time-invariant quantity. Integrable dynamical systems have been extensively studied since they possess a notorious and handy property: their dynamics is fully described in terms of conserved charges.

    In this talk we will see how reductions of Loop group Chern-Simons theory lead to 1+1 dimensional integrable systems.  We specialize to the case G=SL(2), showing explicitly how different reductions provide derivations of well-known integrable systems like the Korteweg-De Vries, the Non-Linear Schrödinger and the Sine-Gordon models. Finally, we will explain why this is not completely unexpected, showing how the Affine Chern-Simons and Self-Dual Yang-Mills theories are intimately related.

  • 5pm, 20th Oct 2023 | James Chok (School of Mathematics, University of Edinburgh)

    Wigglyness is Linear: A Novel Approach to Polynomial and Rational Approximation.

    Linear regression is a classical framework for modeling linear relationships between variables. To model nonlinear relationships, though, a typical statistics course quickly introduces polynomial regressions for the job. However, they are dismissed just as quickly due to producing unwanted wigglyness in the model.

    One way to measure a model’s wigglyness is by the l2-norm on its second derivative, ||f”(x)||. In this talk, I will show how orthogonal polynomials linearize a generalized version of this norm, making this wigglyness measure linear with respect to the polynomial coefficient. I will also apply this idea to rational polynomials, an alternate way to model nonlinearity, providing better approximations than polynomial and spline-based methods.

  • 3pm, 6th Oct 2023 | Sidney Holden (School of Mathematics, University of Edinburgh)

    Disentangling the web of lies—in defense of Australia’s flora and fauna.

    What do you call it when a shark, a crocodile, and a giant spider walk into a bar? Another typical day in Australia…Such has been the type of opening remarks in many interactions I’ve had since moving to Edinburgh.

    Does Australia seem too dangerous to visit? Have you been told that you’d be taking your life into your own hands?

    Lies! This is an (Australian) aspiring mathematician’s apology. I’m here to show you that things aren’t so bad after all—no matter how mangled and dense the spiderwebs (a.k.a. quantum graphs) get.


For more details of the past talks, please click here for the full list.