Oct 27 (Mon)
13:00 MCS2068 StatBen Swallow (University of St. Andrews): Some recent developments in Bayesian Gaussian processes for non-linear systems in computational biology
Gaussian processes are a widely-used statistical tool for
conducting non-parametric inference in computational biology. In this
talk, I will outline a couple of recent projects where we have
developed Bayesian computational approaches to approximating complex,
non-linear dynamics in systems biology and infectious disease
epidemiology, taking advantage of the analytical tractability of
Gaussian processes. Firstly, I will discuss an extension to the linear
noise approximation in high-dimensional, non-linear systems of chemical
kinetics, embedded within a Bayesian MCMC framework for accurate
parameter inference and uncertainty quantification. The approach is
applied to cell-signalling and circadian clock systems of up to 20
variables. Secondly, I will describe an approach to modelling
spatio-temporally indexed data on notifiable diseases in England, using
software packages that can interact with tensorflow probability. The
approach enables a relatively straightforward implementation on GPUs
with significant speed increase over standard CPU calculations, whilst
still allowing asymptotically exact inference and uncertainty
quantification. Long-term temporal accuracy is maintained in both
approaches.
Venue: MCS2068
Oct 28 (Tue)
13:00 MCS2068 APDEMarius Tiba (King's College London): Stability of Geometric and Functional Inequalities
The Brunn-Minkowski inequality is a fundamental result in convex geometry and analysis, closely related to the isoperimetric inequality. It states that for (open) sets \(A\) and \(B\) in \(\mathbb{R}^d\), we have \[|A+B|^{1/d} \geq |A|^{1/d}+|B|^{1/d}.\] Here \(A+B={x+y : x \in A, y \in B}.\) Equality holds if and only if \(A\) and \(B\) are homothetic and convex sets in \(\mathbb{R}^d\). The Prekopa-Leindler inequality is a functional generalization of the Brunn-Minkowski inequality with important applications to high dimensional probability theory. If \(t \in (0,1) \) and \(f,g,h : \mathbb{R}^d \to \mathbb{R}_+\) are continuous functions with bounded support such that \[h(z) = \sup_{z = tx + (1-t)y} f^t(x) g^{1-t}(y),\] then \[\int h dx \geq \left(\int f dx\right)^t \left(\int g dx\right)^{1-t}.\] Equality holds if and only if \(f\) and \(g\) are homothetic (i.e. \(f=ag(x+b) \)) and log-concave (i.e. \(\log(f)\) is concave). The Borell-Brascamp-Lieb inequality is a strengthening of the Prekopa-Leindler inequality, replacing the geometric mean with other means.
The stability of these inequalities has been intensely studied lately. The stability of the Brunn-Minkowski inequality states that if we are close to equality, then \(A\) and \(B\) must be close to being homothetic and convex. Similarly, the stability of the Prekopa-Leindler and Borell-Brascamp-Lieb inequalities states that if we are close to equality, then \(f\) and \(g\) must be close to being homothetic and concave. In this talk, we present sharp stability results for the Brunn-Minkowski, Prekopa-Leindler and Borell-Brascamp-Lieb inequalities, establishing the exact dependency between the two notions of closeness, thus concluding a long line of research on these problems.
This talk is based on joint work with Alessio Figalli and Peter van Hintum.
Venue: MCS2068
13:10 MCS3052 E&PLitka Milian (Durham (Chemistry)): Listening to Student Voices: Disability and Inclusion in STEM
What does it really feel like to study chemistry at Durham as a disabled student? In this session, we will share insights from interviews with disabled students in the Chemistry Department, aiming to uncover the reasons behind the Awarding Gap in academic outcomes between disabled and non-disabled students.
Through open conversations, students described barriers they face, sometimes as obvious as struggling to get into a lecture room, sometimes as subtle as feeling left out of group activities or not knowing where to find help. One student captured the frustration many feel, saying, “Sometimes it feels like the system wasn’t designed for people like me.” Another highlighted the problem of low expectations: “People often assume I need help with everything, but what I really need is for the environment to be accessible from the start.” These stories show that both attitudes and practical support need to change.
Our project is a partnership between staff and student interns, who bring fresh perspectives and energy to the work. They have helped shape our questions, analyse the interviews, and will join us in presenting what we’ve learned. This collaborative approach reflects the principle of active pedagogy, where students are partners in shaping their own learning experience.
We are still working on this project and are using what we’ve learned to write recommendations for future improvements. Our aim is to create more opportunities for students to share feedback, help shape solutions, and feel truly represented. By listening to student voices and acting on their ideas, we are putting inclusive learning design into practice, building a Chemistry Department and a STEM community where diversity is celebrated and every student has the chance to thrive, creating meaningful change.
Venue: MCS3052
Online: https://teams.microsoft.com/l/meetup-join/19%3ameeting_ZGQ3NDg0YzgtNTJiNi00MzVjLWFhYTAtYjc5N2IxOTc2YTQx%40thread.v2/0?context=%7b%22Tid%22%3a%227250d88b-4b68-4529-be44-d59a2d8a6f94%22%2c%22Oid%22%3a%226cb8930b-1559-4659-8c60-d0b762855115%22%7d
14:00 MCS2068 ASGVictoria Schleis (Durham University): General linear monoids over hyperfields
After a gentle introduction to hyperfields and their utility in combinatorics and combinatorial algebraic geometry, I will introduce their general linear monoids. This talk is based on joint work in progress with Yifan Guo.
Venue: MCS2068
Oct 29 (Wed)
15:00 MCS2050 A&CTim Adamo (University of Edinburgh): Scattering on self-dual black holes
Tree-level graviton scattering amplitudes provide an on-shell model for wave-wave scattering in general relativity, but computing them with traditional perturbative methods is hard due to the non-polynomial nature of the Einstein-Hilbert action. This is particularly true for graviton scattering in curved spacetimes, like black holes, which remains an extremely difficult problem. I will discuss a toy model of this problem: graviton scattering on a self-dual black hole (in particular, a self-dual Taub-NUT metric). This lets us bring powerful integrability methods to bear while still exhibiting the non-linear and non-perturbative hallmarks of 'real world' graviton scattering on black holes. Remarkably, in this setting it is possible to obtain explicit formulae for graviton scattering amplitudes which are exact in the background.
Venue: MCS2050
Oct 30 (Thu)
13:00 MCS2068 G&TJohn Parker (Durham University): Real hyperbolic on the outside, complex hyperbolic on the inside (2)
The title of the talk is the title of a paper by Richard Schwartz (Inventiones 2003) where he constructs a complex hyperbolic orbifold whose boundary is homeomorphic to a closed real hyperbolic three-manifold. The fundamental group of the orbifold is an index two subgroup of a group generated by three reflections where certain products of the reflections have particular finite orders. The proof is by way of an explicit construction of a fundamental polyhedron. In these talks I will discuss a joint project with Yohei Komori and Makoto Sakuma where we take the first step to generalise Schwartz’s construction. Namely, we give a topological construction of a candidate fundamental domain, and thereby we are able to describe the topology of the boundary manifold explicitly in terms of the finite orders of the products of reflections. In particular, we are able to topologically identify Schwartz’s boundary manifold.
Venue: MCS2068
14:00 MCS2068 ProbJulie Tourniaire (Laboratoire de Mathématiques, Université de Franche-Comté): Stochastic neutral fractions and the effective population size
Population genetics aims to explain observed genetic diversity through past evolutionary forces. In the neutral setting, i.e., in the absence of natural selection and ecological constraints, diversity arises solely from demographic fluctuations. In this simplified framework, the allelic composition of a population converges, in the large-population limit, to the Wright–Fisher diffusion.
This Wright–Fisher model is a purely genetic model, and a key question is how ecological constraints (such as population structure) may influence genetic composition. In this context, the ‘effective population size’, defined as the size of a Wright–Fisher population experiencing the same level of genetic drift as the population under study, plays a central role.
In this talk, I will introduce a stochastic differential equation with an infinite decomposability property to model the dynamics of general structured populations. This property allows the population to be decomposed into an arbitrary number of neutral allelic components (or fractions). When demographic fluctuations are small, a fast–slow principle yields a general expression for the effective population size in structured settings.
This is joint work with R. Forien, E. Schertzer, and Z. Talyigas
Venue: MCS2068
Oct 31 (Fri)
13:00 MCS0001 HEPMMax Velásquez Cotini Hutt (Imperial College London): Non-invertible Symmetries of 2d Non-Linear Sigma Models
Global symmetries can be generalised to transformations generated by topological operators, including cases in which this operator does not have an inverse. A family of such topological operators are related to dualities via the procedure of half-space gauging. I will discuss the construction of non-invertible defects based on T-duality in two dimensions, generalising the well-known case of the free compact boson to any Non-Linear Sigma Model with Wess-Zumino term which is T-dualisable. I will discuss how these symmetries can be used to constrain renormalisation group flows, and their fate in String Theory.
Venue: MCS0001
Nov 03 (Mon)
13:00 MCS2068 StatSam Livingstone (UCL):
Click on title to see abstract.
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Contact: arthur.lipstein@durham.ac.uk
Oct 29 15:00 Tim Adamo (University of Edinburgh): Scattering on self-dual black holes
Tree-level graviton scattering amplitudes provide an on-shell model for wave-wave scattering in general relativity, but computing them with traditional perturbative methods is hard due to the non-polynomial nature of the Einstein-Hilbert action. This is particularly true for graviton scattering in curved spacetimes, like black holes, which remains an extremely difficult problem. I will discuss a toy model of this problem: graviton scattering on a self-dual black hole (in particular, a self-dual Taub-NUT metric). This lets us bring powerful integrability methods to bear while still exhibiting the non-linear and non-perturbative hallmarks of 'real world' graviton scattering on black holes. Remarkably, in this setting it is possible to obtain explicit formulae for graviton scattering amplitudes which are exact in the background.
Venue: MCS2050
Usual Venue: MCS2068
Contact: yohance.a.osborne@durham.ac.uk
Oct 28 13:00 Marius Tiba (King's College London): Stability of Geometric and Functional Inequalities
The Brunn-Minkowski inequality is a fundamental result in convex geometry and analysis, closely related to the isoperimetric inequality. It states that for (open) sets \(A\) and \(B\) in \(\mathbb{R}^d\), we have \[|A+B|^{1/d} \geq |A|^{1/d}+|B|^{1/d}.\] Here \(A+B={x+y : x \in A, y \in B}.\) Equality holds if and only if \(A\) and \(B\) are homothetic and convex sets in \(\mathbb{R}^d\). The Prekopa-Leindler inequality is a functional generalization of the Brunn-Minkowski inequality with important applications to high dimensional probability theory. If \(t \in (0,1) \) and \(f,g,h : \mathbb{R}^d \to \mathbb{R}_+\) are continuous functions with bounded support such that \[h(z) = \sup_{z = tx + (1-t)y} f^t(x) g^{1-t}(y),\] then \[\int h dx \geq \left(\int f dx\right)^t \left(\int g dx\right)^{1-t}.\] Equality holds if and only if \(f\) and \(g\) are homothetic (i.e. \(f=ag(x+b) \)) and log-concave (i.e. \(\log(f)\) is concave). The Borell-Brascamp-Lieb inequality is a strengthening of the Prekopa-Leindler inequality, replacing the geometric mean with other means.
The stability of these inequalities has been intensely studied lately. The stability of the Brunn-Minkowski inequality states that if we are close to equality, then \(A\) and \(B\) must be close to being homothetic and convex. Similarly, the stability of the Prekopa-Leindler and Borell-Brascamp-Lieb inequalities states that if we are close to equality, then \(f\) and \(g\) must be close to being homothetic and concave. In this talk, we present sharp stability results for the Brunn-Minkowski, Prekopa-Leindler and Borell-Brascamp-Lieb inequalities, establishing the exact dependency between the two notions of closeness, thus concluding a long line of research on these problems.
This talk is based on joint work with Alessio Figalli and Peter van Hintum.
Venue: MCS2068
Usual Venue: MCS3070
Contact: andrew.krause@durham.ac.uk
No upcoming seminars have been scheduled (not unusual outside term time).
Usual Venue: MCS2068
Contact: herbert.gangl@durham.ac.uk
Oct 28 14:00 Victoria Schleis (Durham University): General linear monoids over hyperfields
After a gentle introduction to hyperfields and their utility in combinatorics and combinatorial algebraic geometry, I will introduce their general linear monoids. This talk is based on joint work in progress with Yifan Guo.
Venue: MCS2068
Nov 04 14:00 Yu-Chen Sun (University of Bristol):
Nov 11 14:00 Robin Bartlett (Glasgow University): Moduli spaces of mod p Galois representations and explicit equations for the crystalline locus of a fixed Hodge type.
Nov 25 14:00 Dante Luber (Queen Mary University of London): Matroid theory, algebra, and computation
Matroids combinatorially abstract independence properties of
finite dimensional linear algebra. They have become ubiquitous in
modern mathematics, and yield connections between graph theory,
algebra, polyhedral geometry, optimization, and beyond. Special
matroids capture the properties of point line arrangementments in
complex 2-projective space. The moduli space of all line arrangements
corresponding to a matroid is known as its realization space. After an
introduction to matroid theory, we will discuss how we have used the
OSCAR software system to study large datasets of matroids, isolating
examples whose realization spaces have interesting algebro-geometric
Venue: MCS2068
Dec 02 14:00 Jay Taylor (University of Manchester):
Dec 09 14:00 Fredrik Stromberg (University of Nottingham):
Usual Venue: OC218
Contact: mohamed.anber@durham.ac.uk
For more information, see HERE.
No upcoming seminars have been scheduled (not unusual outside term time).
Usual Venue: MCS3052
Contact: andrew.krause@durham.ac.uk
Oct 28 13:10 Litka Milian (Durham (Chemistry)): Listening to Student Voices: Disability and Inclusion in STEM
What does it really feel like to study chemistry at Durham as a disabled student? In this session, we will share insights from interviews with disabled students in the Chemistry Department, aiming to uncover the reasons behind the Awarding Gap in academic outcomes between disabled and non-disabled students.
Through open conversations, students described barriers they face, sometimes as obvious as struggling to get into a lecture room, sometimes as subtle as feeling left out of group activities or not knowing where to find help. One student captured the frustration many feel, saying, “Sometimes it feels like the system wasn’t designed for people like me.” Another highlighted the problem of low expectations: “People often assume I need help with everything, but what I really need is for the environment to be accessible from the start.” These stories show that both attitudes and practical support need to change.
Our project is a partnership between staff and student interns, who bring fresh perspectives and energy to the work. They have helped shape our questions, analyse the interviews, and will join us in presenting what we’ve learned. This collaborative approach reflects the principle of active pedagogy, where students are partners in shaping their own learning experience.
We are still working on this project and are using what we’ve learned to write recommendations for future improvements. Our aim is to create more opportunities for students to share feedback, help shape solutions, and feel truly represented. By listening to student voices and acting on their ideas, we are putting inclusive learning design into practice, building a Chemistry Department and a STEM community where diversity is celebrated and every student has the chance to thrive, creating meaningful change.
Venue: MCS3052
Usual Venue: MCS2068
Contact: fernando.galaz-garcia@durham.ac.uk
Oct 30 13:00 John Parker (Durham University): Real hyperbolic on the outside, complex hyperbolic on the inside (2)
The title of the talk is the title of a paper by Richard Schwartz (Inventiones 2003) where he constructs a complex hyperbolic orbifold whose boundary is homeomorphic to a closed real hyperbolic three-manifold. The fundamental group of the orbifold is an index two subgroup of a group generated by three reflections where certain products of the reflections have particular finite orders. The proof is by way of an explicit construction of a fundamental polyhedron. In these talks I will discuss a joint project with Yohei Komori and Makoto Sakuma where we take the first step to generalise Schwartz’s construction. Namely, we give a topological construction of a candidate fundamental domain, and thereby we are able to describe the topology of the boundary manifold explicitly in terms of the finite orders of the products of reflections. In particular, we are able to topologically identify Schwartz’s boundary manifold.
Venue: MCS2068
Nov 13 13:00 Pierre Will (Université Grenoble Alpes): TBA
Nov 20 13:00 Amy Herron (University of Bristol): Triangle Presentations in ~A_2 Bruhat-Tits Buildings
The 1-skeleton of an ~A_2 Bruhat-Tits building is isomorphic to the Cayley graph of an abstract group with relations coming from triangle presentations. This abstract group either embeds into PGL(3, Fq((x))) or PGL(3, Qq), or else is exotic. Currently, the complete list of triangle presentations is only known for projective planes of orders q=2 or 3. However, one abstract group that embeds into PGL(3,Fq((x))) for any prime power q is known via the trace function corresponding to the finite field of order q^3. I found a new method to derive this group via perfect difference sets. This method demonstrates a previously unknown connection between difference sets and ~A_2 buildings. Moreover, this method makes the final computation of triangle presentations easier, which is computationally valuable for large q.
Venue: MCS2068
Nov 27 13:00 Yan Rybalko (University of Oslo): Generic regularity of the two-component Novikov system
In my talk I will discuss the generic regularity of the Cauchy problem for the two-component Novikov system. This system is integrable (i.e., it is bi-Hamiltonian, has a Lax pair, and an infinite number of conservation laws), and admits peakon solutions of the form p(t)exp(-|x-q(t)|). Another important feature of the Novikov system is the wave-breaking phenomenon: the solutions remain bounded for all times, but the slope can blow-up in finite time. In our work, we show that there exists an open dense subset of C^k regular initial data, such that the corresponding global solutions persist the regularity for all t,x except, possibly, a finite number of piecewise C^{k-1} characteristic curves. Our approach builds on the work by Bressan and Chen, which relies on transforming solutions from Eulerian variables to a new set of Bressan-Constantin variables, in which all possible singularities of the original solutions are resolved. Then, applying the Thoms transversality theorem to the map related to the wave-breaking, we can construct an appropriate open dense subset of C^k regular initial data.
The talk is based upon the following papers:
K.H. Karlsen, Ya. Rybalko, "Generic regularity and a Lipschitz metric for the two-component Novikov system," in preparation.
K.H. Karlsen, Ya. Rybalko, "Global semigroup of conservative weak solutions of the two-component Novikov equation," Nonlinear Analysis: Real World Applications 86, 104393 (2025). DOI: 10.1016/j.nonrwa.2025.104393.
Venue: MCS2068
Jan 22 13:00 Chunyang Hu (Durham University): TBA
Mar 06 13:00 Julian Scheuer (Goethe University Frankfurt): TBA
Usual Venue: MCS0001
Contact: p.e.dorey@durham.ac.uk,enrico.andriolo@durham.ac.uk,tobias.p.hansen@durham.ac.uk
Oct 31 13:00 Max Velásquez Cotini Hutt (Imperial College London): Non-invertible Symmetries of 2d Non-Linear Sigma Models
Global symmetries can be generalised to transformations generated by topological operators, including cases in which this operator does not have an inverse. A family of such topological operators are related to dualities via the procedure of half-space gauging. I will discuss the construction of non-invertible defects based on T-duality in two dimensions, generalising the well-known case of the free compact boson to any Non-Linear Sigma Model with Wess-Zumino term which is T-dualisable. I will discuss how these symmetries can be used to constrain renormalisation group flows, and their fate in String Theory.
Venue: MCS0001
Nov 07 13:00 Stathis Vitouladitis (Université Libre de Bruxelles): Entanglement asymmetry and the limits of symmetry breaking
Entanglement asymmetry is a novel diagnostic of symmetry breaking, rooted in quantum information theory, particularly effective at capturing such effects within subsystems. In this talk, I will first introduce this observable, outline recent developments, and then generalise it to higher-form symmetries, with applications to topological phases and systems with continuous symmetry breaking. As a main application, I will establish an entropic Mermin-Wagner-Coleman theorem, valid for both 0-form and higher-form symmetries, and extended to subregions. These entropic theorems not only detect but also quantify symmetry breaking. In Goldstone phases (when allowed), the Rényi and entanglement asymmetries, increase monotonically with subregion size. Along the way, I will clarify subtleties in defining and computing entanglement asymmetry by Euclidean path integral methods and present standalone results on the entanglement entropy of gauge fields.
Venue: MCS0001
Nov 14 13:00 Christian Copetti (Oxford): TBA
Nov 21 13:00 Ida Zadeh (Southampton): TBA
Nov 28 13:00 Tim Meier (Santiago de Compostela): TBA
Dec 05 13:00 Marco Meineri (Torino): TBA
Dec 12 13:00 Sungwoo Hong (KAIST, Taejon): TBA
Usual Venue: MCS2068
Contact: tyler.helmuth@durham.ac.uk,oliver.kelsey-tough@durham.ac.uk
Oct 30 14:00 Julie Tourniaire (Laboratoire de Mathématiques, Université de Franche-Comté): Stochastic neutral fractions and the effective population size
Population genetics aims to explain observed genetic diversity through past evolutionary forces. In the neutral setting, i.e., in the absence of natural selection and ecological constraints, diversity arises solely from demographic fluctuations. In this simplified framework, the allelic composition of a population converges, in the large-population limit, to the Wright–Fisher diffusion.
This Wright–Fisher model is a purely genetic model, and a key question is how ecological constraints (such as population structure) may influence genetic composition. In this context, the ‘effective population size’, defined as the size of a Wright–Fisher population experiencing the same level of genetic drift as the population under study, plays a central role.
In this talk, I will introduce a stochastic differential equation with an infinite decomposability property to model the dynamics of general structured populations. This property allows the population to be decomposed into an arbitrary number of neutral allelic components (or fractions). When demographic fluctuations are small, a fast–slow principle yields a general expression for the effective population size in structured settings.
This is joint work with R. Forien, E. Schertzer, and Z. Talyigas
Venue: MCS2068
Nov 06 14:00 William Da Silva (University of Vienna): The longest increasing subsequence of Brownian separable permutons
The Brownian separable permutons form a one-parameter family of permutons, which are the universal scaling limits of pattern-avoiding permutations. In this talk, we will be interested in the length of the longest increasing subsequence (LIS) in permutations of size n sampled from the Brownian permutons. We give an answer to the celebrated Ulam-Hammersley problem in this context: what is the behaviour of LIS as n goes to infinity? A significant portion of the talk will be dedicated to our motivation behind the problem, emphasising connections to various objects in probability and combinatorics, such as random decorated trees, random graphs, directed planar maps and SLE/LQG. The talk is based on joint work with Arka Adhikari, Jacopo Borga, Thomas Budzinski and Delphin Sénizergues.
Venue: MCS2068
Nov 20 14:00 PiNE (University of Edinburgh): No seminar PiNE in Edinburgh.
PiNE will take place in Edinburgh, see https://www.maths.dur.ac.uk/PiNE/25-11-20/index.html. Accordingly we will not have a seminar this week.
Venue: MCS2068
Usual Venue: MCS3070
Contact: joe.thomas@durham.ac.uk
No upcoming seminars have been scheduled (not unusual outside term time).
Usual Venue: MCS2068
Contact: hyeyoung.maeng@durham.ac.uk,andrew.iskauskas@durham.ac.uk
Oct 27 13:00 Ben Swallow (University of St. Andrews): Some recent developments in Bayesian Gaussian processes for non-linear systems in computational biology
Gaussian processes are a widely-used statistical tool for
conducting non-parametric inference in computational biology. In this
talk, I will outline a couple of recent projects where we have
developed Bayesian computational approaches to approximating complex,
non-linear dynamics in systems biology and infectious disease
epidemiology, taking advantage of the analytical tractability of
Gaussian processes. Firstly, I will discuss an extension to the linear
noise approximation in high-dimensional, non-linear systems of chemical
kinetics, embedded within a Bayesian MCMC framework for accurate
parameter inference and uncertainty quantification. The approach is
applied to cell-signalling and circadian clock systems of up to 20
variables. Secondly, I will describe an approach to modelling
spatio-temporally indexed data on notifiable diseases in England, using
software packages that can interact with tensorflow probability. The
approach enables a relatively straightforward implementation on GPUs
with significant speed increase over standard CPU calculations, whilst
still allowing asymptotically exact inference and uncertainty
quantification. Long-term temporal accuracy is maintained in both
approaches.
Venue: MCS2068
Nov 03 13:00 Sam Livingstone (UCL):
Dec 01 13:00 Markus Rau (Newcastle):
