Oct 13 (Tue)
14:00 MCS2068 APDEPhoebe Valentine (University of Warwick): Characterising 1-rectifiable metric spaces via connected tangent spaces
Characterising rectifiability using the existence of tangents is a very classical technique in GMT and positive results can be found even when using very weak notions of a tangent. This work goes further to only require that tangents are supported on a connected set. Despite this weak requirement, we can still prove that 1-rectifiability in complete metric spaces is implied by the existence of connected tangents almost everywhere. This, combined with prior results of Bate, establishes a characterisation of 1-rectifiability in complete metric spaces, which is in particular also new for Euclidean space. Inspired by geometric ideas from Besicovitch in the plane, we achieve our result by exploiting the inherent gappiness of purely 1-unrectifiable sets. To this end, we will give rigorous meaning to this 'gappiness' and show how it may be quantified.
Venue: MCS2068
Oct 14 (Wed)
11:00 MJC2006 ApplColin Bain (Durham): Drying Droplets in Wells
Inkjet printing is an attractive technology for the manufacture of OLED (organic light-emitting diode) displays. A key question is how to achieve uniform deposition of four or more active layers of organic molecules (small molecules or polymers) within the pixels of the display. One of the underlying scientific questions is how does a small drop of liquid dry in a small-aspect-ratio well. This might seem to be a very simple question, but even for a pure liquid the shape of the liquid in the well can evolve through a C, U or W shape, with consequences for the distribution of a solid deposited from solution. As soon as one adds a solute or a co-solvent to a liquid it becomes a binary (or ternary or higher-order) system. We have studied binary solvent mixtures in which the more volatile liquid can have either the higher or the lower surface tension. We have observed at least five drying behaviours, in addition to the three patterns seen for pure solvents.
This talk will briefly describe the experimental approach and a selection of results. Mathematical models, within the lubrication approximation, for the evaporation of pure and binary solvents will be presented. Qualitative and, where achieved, quantitative explanations for the eight categories of behaviour will be proposed.
Venue: MJC2006
16:00 zoom A&CKyrill Michaelson (University of Hamburg): Observing Massive Scattering from Null Infinity
Flat space holographic proposals such as celestial and Carrollian holography struggle to describe scattering processes with massive external states, since massive particles asymptote to timelike rather than null infinity. In this talk, based on joint work with W. Melton and R. Ruzziconi, I will take a step toward addressing this limitation by showing how information about massive scattering amplitudes is carried to the late-time limit of null infinity by soft graviton radiation. I will demonstrate that the continuity between the boundaries of timelike and null infinity implies that the late-time limit of the Bondi mass aspect naturally acts as a detector operator for massive outgoing radiation. Moreover, I will show that in-in correlation functions of the late-time Bondi mass aspect at null infinity are related to weighted sums of scattering cross sections. This implies that an observer at null infinity can extract information about massive scattering processes at late times. Finally, I will interpret the Bondi mass aspect as a Carrollian stress-tensor component, and derive Ward identities to constrain its two-point functions.
Venue: zoom
Online: https://teams.microsoft.com/meet/3509397888656179?p=n796hNuMENltpAMHUx
Oct 15 (Thu)
13:00 MCS3070 E&PSam Cuthbertson and Ho Yan Charlotte Wong (Durham (students)): Mind The Gap: Improving Transitional Support for Incoming Mathematics Undergraduates
There has been growing concern within higher education institutions that incoming mathematics students are not adequately prepared for the nature and demands of university learning, and as such there has been a greater effort to provide tailored support to incoming mathematics students. At Durham University, first-year mathematics research interns Sam and Charlotte have been conducting research on how to improve current pre-university transitional support materials to improve the transitional process into undergraduate mathematics for incoming students.
Firstly, Charlotte will present her investigation to specifically improve this transition for international students, including findings and discussions from a comparative taxonomy analysis on 5 popular international curricula, Durham Mathematics diagnostic test, and early first-year module assessments. She will then propose design principles to improve pre-university transition materials for international students, informed by her investigation and current pedagogical literature.
Then, Sam will discuss the overarching factors which can define the effectiveness of pre-university transition material in both consolidating a baseline level of knowledge required for entering their course through careful mapping and analysis of course content as well as fostering a strong engagement with support materials using research-informed feedback mechanisms and question designs that promote valuable progress from students with the transitional material.
Venue: MCS3070 (MAGIC)
Online: https://teams.microsoft.com/l/meetup-join/19%3ameeting_MTVjYWIzMTMtNjYxNy00YTQzLWI0OGYtMGQxMTc0MTQ0Nzgw%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 ASGMaleeha Khawaja: New Algebraic Points on Curves
Faltings (1983) proved that a nice curve C/Q of genus at least 2 has only finitely many points defined over any given number field. A natural follow-up question is to study C(L) when L varies over all number fields of a given degree. For a number field L, let C(L)_new be the set of points on C defined over L, but not over any strictly smaller field. In this talk, we will discuss several examples of curves which have infinitely many algebraic points of degrees 2 or 3, but we will see that these points are in fact sparsely distributed amongst all number fields of that degree.
Venue: MCS2068
Oct 16 (Fri)
13:00 MCS2068 HEPMJoaquin Liniado (Edinburgh University): Holography for integrable field theories
Since its introduction, four-dimensional ChernSimons theory has offered a unifying origin for classically integrable field theories in two dimensions. However, the quantum aspects of this construction have remained largely mysterious. In this talk, I will present a first step in exploring this direction, based on a holographic construction in topological string theory.
Venue: MCS2068
Oct 19 (Mon)
13:00 MCS2068 ProbLoren Coquille (Université de Grenoble Alpes): Extremal Ising Gibbs States on non amenable graphs
On Z^2, the set of extremal states of the subcritical Ising model consists of the two pure « plus » and « minus » phases. On Z^3 is conjectured to be at most countable at low temperature. On a regular tree, it is known to be uncountable at low temperature. I will explain how to exhibit an uncountable family of extremal (non-automorphism invariant) Gibbs measures of the low temperature Ising model on non-amenable graphs. These states arise as low temperature perturbations of local ground states having a sparse enough set of frustrated edges, the sparseness being measured in terms of the isoperimetric constant of the graph. On regular tilings of the hyperbolic plane, our techniques allow to deduce extremality of uncountably many Series-Sinai states (having one interface along a continuous geodesic of H^2), and lead to the study of nice questions about hyperbolic billiards.
Based on joint works with Matteo DAchille, Christof Kuelske, Arnaud Le Ny and Jean Vereecke.
Venue: MCS2068
Oct 20 (Tue)
14:00 MCS2068 APDEOfelia Bonesini (London School of Economics): Continuous-time persuasion by filtering
We frame dynamic persuasion in a partial observation stochastic control Leader-Follower game with an ergodic criterion. The Receiver controls the dynamics of a multidimensional unobserved state process. Information is provided to the Receiver through a device designed by the Sender that generates the observation process. The commitment of the Sender is enforced. We develop this approach in the case where all dynamics are linear and the preferences of the Receiver are linear-quadratic. We prove a verification theorem for the existence and uniqueness of the solution of the HJB equation satisfied by the Receiver's value function. An extension to the case of persuasion of a mean field of interacting Receivers is also provided. We illustrate this approach in two applications: the provision of information to electricity consumers with a smart meter designed by an electricity producer; the information provided by carbon footprint accounting rules to companies engaged in a best-in-class emissions reduction effort. In the first application, we link the benefits of information provision to the mispricing of electricity production. In the latter, we show that even in the absence of information cost, it might be optimal for the regulator to blur information available to firms to prevent them from coordinating on a higher level of carbon footprint to reduce their cost of reaching a below average emission target. This is a joint work with René Aïd, Giorgia Callegaro and Luciano Campi.
Venue: MCS2068
Click on title to see abstract.
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These events are hosted in and/or organised by members of the Department (follow links for details):
Oct 16 [Kenworthy Hall, St Mary's] Willmore Day 2026
Speakers: A Barber, L Dahlmeier, D Disney, S Mohapatra, J Quijas, F Salerno, S Shepherd
Venue: Kenworthy Hall, St Mary's at/from 09:30
Oct 19 [CB0011] LMS Tropical Mathematics and its Applications
Click on series to expand.
Contact: arthur.lipstein@durham.ac.uk
Oct 14 16:00 Kyrill Michaelson (University of Hamburg): Observing Massive Scattering from Null Infinity
Flat space holographic proposals such as celestial and Carrollian holography struggle to describe scattering processes with massive external states, since massive particles asymptote to timelike rather than null infinity. In this talk, based on joint work with W. Melton and R. Ruzziconi, I will take a step toward addressing this limitation by showing how information about massive scattering amplitudes is carried to the late-time limit of null infinity by soft graviton radiation. I will demonstrate that the continuity between the boundaries of timelike and null infinity implies that the late-time limit of the Bondi mass aspect naturally acts as a detector operator for massive outgoing radiation. Moreover, I will show that in-in correlation functions of the late-time Bondi mass aspect at null infinity are related to weighted sums of scattering cross sections. This implies that an observer at null infinity can extract information about massive scattering processes at late times. Finally, I will interpret the Bondi mass aspect as a Carrollian stress-tensor component, and derive Ward identities to constrain its two-point functions.
Venue: zoom
Usual Venue: MCS2068
Contact: yohance.a.osborne@durham.ac.uk
Oct 13 14:00 Phoebe Valentine (University of Warwick): Characterising 1-rectifiable metric spaces via connected tangent spaces
Characterising rectifiability using the existence of tangents is a very classical technique in GMT and positive results can be found even when using very weak notions of a tangent. This work goes further to only require that tangents are supported on a connected set. Despite this weak requirement, we can still prove that 1-rectifiability in complete metric spaces is implied by the existence of connected tangents almost everywhere. This, combined with prior results of Bate, establishes a characterisation of 1-rectifiability in complete metric spaces, which is in particular also new for Euclidean space. Inspired by geometric ideas from Besicovitch in the plane, we achieve our result by exploiting the inherent gappiness of purely 1-unrectifiable sets. To this end, we will give rigorous meaning to this 'gappiness' and show how it may be quantified.
Venue: MCS2068
Oct 20 14:00 Ofelia Bonesini (London School of Economics): Continuous-time persuasion by filtering
We frame dynamic persuasion in a partial observation stochastic control Leader-Follower game with an ergodic criterion. The Receiver controls the dynamics of a multidimensional unobserved state process. Information is provided to the Receiver through a device designed by the Sender that generates the observation process. The commitment of the Sender is enforced. We develop this approach in the case where all dynamics are linear and the preferences of the Receiver are linear-quadratic. We prove a verification theorem for the existence and uniqueness of the solution of the HJB equation satisfied by the Receiver's value function. An extension to the case of persuasion of a mean field of interacting Receivers is also provided. We illustrate this approach in two applications: the provision of information to electricity consumers with a smart meter designed by an electricity producer; the information provided by carbon footprint accounting rules to companies engaged in a best-in-class emissions reduction effort. In the first application, we link the benefits of information provision to the mispricing of electricity production. In the latter, we show that even in the absence of information cost, it might be optimal for the regulator to blur information available to firms to prevent them from coordinating on a higher level of carbon footprint to reduce their cost of reaching a below average emission target. This is a joint work with René Aïd, Giorgia Callegaro and Luciano Campi.
Venue: MCS2068
Oct 27 14:00 Dante Kalise (Imperial College London): Stabilising Feedback Laws for Mean-Field Control and Global Optimisation
We look at feedback control of large systems of interacting particles. In the mean-field limit, this becomes the stabilisation of McKeanVlasov PDEs. When the free energy is non-convex, the target states may be unstable or reached only very slowly. We linearise the Wasserstein gradient flow around the target and act on its finitely many slow or unstable modes. This gives a Riccati feedback law that locally exponentially stabilises the full nonlinear dynamics, and it can be seen as a local convexification of the free energy.
The same idea applies to consensus-based optimisation (CBO), which is itself a McKeanVlasov particle system whose target is the global minimiser. We treat global optimisation as an optimal stabilisation problem and add a stabilising feedback, obtained from the associated HJB equation, to the CBO dynamics. Convergence becomes faster and more robust, including in high dimensions.
Based on joint works with M. Herty, Y. Huang, N. Kantas, H. Kouhkouh, L. Moschen and G. A. Pavliotis.
Venue: MCS2068
Usual Venue: MCS3070
Contact: andrew.krause@durham.ac.uk
Oct 14 11:00 Colin Bain (Durham): Drying Droplets in Wells
Inkjet printing is an attractive technology for the manufacture of OLED (organic light-emitting diode) displays. A key question is how to achieve uniform deposition of four or more active layers of organic molecules (small molecules or polymers) within the pixels of the display. One of the underlying scientific questions is how does a small drop of liquid dry in a small-aspect-ratio well. This might seem to be a very simple question, but even for a pure liquid the shape of the liquid in the well can evolve through a C, U or W shape, with consequences for the distribution of a solid deposited from solution. As soon as one adds a solute or a co-solvent to a liquid it becomes a binary (or ternary or higher-order) system. We have studied binary solvent mixtures in which the more volatile liquid can have either the higher or the lower surface tension. We have observed at least five drying behaviours, in addition to the three patterns seen for pure solvents.
This talk will briefly describe the experimental approach and a selection of results. Mathematical models, within the lubrication approximation, for the evaporation of pure and binary solvents will be presented. Qualitative and, where achieved, quantitative explanations for the eight categories of behaviour will be proposed.
Venue: MJC2006
Usual Venue: MCS2068
Contact: johannes.girsch@durham.ac.uk
Oct 15 14:00 Maleeha Khawaja: New Algebraic Points on Curves
Faltings (1983) proved that a nice curve C/Q of genus at least 2 has only finitely many points defined over any given number field. A natural follow-up question is to study C(L) when L varies over all number fields of a given degree. For a number field L, let C(L)_new be the set of points on C defined over L, but not over any strictly smaller field. In this talk, we will discuss several examples of curves which have infinitely many algebraic points of degrees 2 or 3, but we will see that these points are in fact sparsely distributed amongst all number fields of that degree.
Venue: MCS2068
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 15 13:00 Sam Cuthbertson and Ho Yan Charlotte Wong (Durham (students)): Mind The Gap: Improving Transitional Support for Incoming Mathematics Undergraduates
There has been growing concern within higher education institutions that incoming mathematics students are not adequately prepared for the nature and demands of university learning, and as such there has been a greater effort to provide tailored support to incoming mathematics students. At Durham University, first-year mathematics research interns Sam and Charlotte have been conducting research on how to improve current pre-university transitional support materials to improve the transitional process into undergraduate mathematics for incoming students.
Firstly, Charlotte will present her investigation to specifically improve this transition for international students, including findings and discussions from a comparative taxonomy analysis on 5 popular international curricula, Durham Mathematics diagnostic test, and early first-year module assessments. She will then propose design principles to improve pre-university transition materials for international students, informed by her investigation and current pedagogical literature.
Then, Sam will discuss the overarching factors which can define the effectiveness of pre-university transition material in both consolidating a baseline level of knowledge required for entering their course through careful mapping and analysis of course content as well as fostering a strong engagement with support materials using research-informed feedback mechanisms and question designs that promote valuable progress from students with the transitional material.
Venue: MCS3070 (MAGIC)
Usual Venue: MCS3070
Contact: yi-lok-enoch.leung@durham.ac.uk
Nov 23 10:00 Benjamin Muntz (University of Nottingham): TBA
Dec 09 13:00 Alonso Perez-Lona (Max Planck Institute for Mathematics in the Sciences): TBA
Usual Venue: MCS2068
Contact: martin.p.kerin@durham.ac.uk
Oct 23 14:00 Yuri Santos Rego (Lincoln): TBA
Oct 30 14:00 Dirk Schütz (Durham): TBA
Nov 06 14:00 David Lanners (Durham): TBA
Nov 13 14:00 Michael Kohn (Durham): \( \mathfrak{sl}_p \)-homology over \( \mathbb{F}_p \)
\( \mathfrak{sl}_N \) homology is a quantum invariant of
knots and links, generalising Khovanov homology. In this talk we will
provide a brief introduction to how this is defined via objects called
foams. We will also introduce s-invariants, which have applications in
4-manifold topology. We will then show that for the case of N a prime p,
and working over \( \mathbb{F}_p \), the chain complex that this theory
associates to a link diagram has a remarkably simple decomposition. From
this, we can deduce new results and reprove existing results regarding
s-invariants and the structure of \( \mathfrak{sl}_p \) homology.
Venue: MCS2068
Nov 20 14:00 Luke Jeffreys (Bristol): TBA
Nov 20 15:00 Philipp Bartmann (Potsdam): TBA
Nov 27 14:00 Emily Roff (Edinburgh): TBA
Dec 04 14:00 Simon Willerton (Sheffield): TBA
Jan 29 14:00 Marco Radeschi (Torino): TBA
Feb 12 14:00 Kasia Wyczesany (Leeds): TBA
Usual Venue: MCS2068
Contact: p.e.dorey@durham.ac.uk,parita.r.shah@durham.ac.uk,tobias.p.hansen@durham.ac.uk
Oct 16 13:00 Joaquin Liniado (Edinburgh University): Holography for integrable field theories
Since its introduction, four-dimensional ChernSimons theory has offered a unifying origin for classically integrable field theories in two dimensions. However, the quantum aspects of this construction have remained largely mysterious. In this talk, I will present a first step in exploring this direction, based on a holographic construction in topological string theory.
Venue: MCS2068
Oct 23 13:00 Enoch Leung (Durham University): Resolving Continuous Symmetries in Holography
We study topological operators that generate continuous symmetries in the context of holography. Such operators can be modeled as solitonic branes in the supergravity bulk, whose ends are anchored on the conformal boundary with a finite separation. This holographic realization mirrors the field-theoretic regularization of symmetry operators in terms of objects with finite thickness and tension. We further discuss how these objects measure the charge of Wilson lines ending on the boundary. Despite sharing similar low-energy physics, the top-down descriptions of such hanging branes generally differ, depending on the UV completion of the bulk theory, and on the geometric origins of the symmetries involved.
Venue: MCS2068
Oct 30 13:00 Ruth Gregory (Kings College London): TBA
Nov 06 13:00 Hugh Osborn (Cambridge University): TBA
Nov 13 13:00 Anton Kapustin (Caltech): Locality, higher symmetries, and anomalies: an operator-algebraic approach
In the usual Euclidean path-integral picture, higher symmetries are represented by invertible topological defects, and ’t Hooft anomalies are described by anomaly inflow from a topological action in one dimension higher. Is there a corresponding construction that starts directly from the algebra of local operators and its symmetries? To address this question, I will describe a mathematically precise framework based on localized symmetry transformations and their commutators. To each spatial region U, one associates a group of transformations localized in U. Locality implies that the commutator of transformations localized in regions U and V is localized in their intersection. From these data one can extract a system of higher groups, one per cover of space. Both anomalies and higher symmetries are encoded in this system of higher groups. The framework is designed to treat algebraic QFT and quantum lattice systems in a common language. The guiding idea is that topology emerges from the interplay of symmetry and locality.
Venue: MCS2068
Nov 20 13:00 Prahar Mitra (Southampton University): TBA
Nov 27 13:00 Mariana Carrillo Gonzalez (Southampton University): TBA
Dec 04 13:00 Daniel Brennan (University of Birmingham): TBA
Dec 11 13:00 Alessandro Georgoudis (Queen Mary University of London): TBA
Usual Venue: MCS2068
Contact: tyler.helmuth@durham.ac.uk,oliver.kelsey-tough@durham.ac.uk
Oct 19 13:00 Loren Coquille (Université de Grenoble Alpes): Extremal Ising Gibbs States on non amenable graphs
On Z^2, the set of extremal states of the subcritical Ising model consists of the two pure « plus » and « minus » phases. On Z^3 is conjectured to be at most countable at low temperature. On a regular tree, it is known to be uncountable at low temperature. I will explain how to exhibit an uncountable family of extremal (non-automorphism invariant) Gibbs measures of the low temperature Ising model on non-amenable graphs. These states arise as low temperature perturbations of local ground states having a sparse enough set of frustrated edges, the sparseness being measured in terms of the isoperimetric constant of the graph. On regular tilings of the hyperbolic plane, our techniques allow to deduce extremality of uncountably many Series-Sinai states (having one interface along a continuous geodesic of H^2), and lead to the study of nice questions about hyperbolic billiards.
Based on joint works with Matteo DAchille, Christof Kuelske, Arnaud Le Ny and Jean Vereecke.
Venue: MCS2068
Usual Venue: MCS2068
Contact: alexander.mangerel@durham.ac.uk
Nov 02 16:00 Francesco Lin (Columbia): TBA
Nov 24 13:00 Giannis Platis (Patras): TBA
Dec 01 13:00 Rob Kurinczuk (Sheffield): TBA
Jan 27 13:00 Marco Radeschi (Torino): TBA
Feb 09 13:00 Tim Browning (UCL): TBA
Feb 23 13:00 Tara Brendle (Glasgow): TBA
Mar 16 13:00 Rémi Coulon (Dijon): TBA
Usual Venue: MCS3070
Contact: joe.thomas@durham.ac.uk
No upcoming seminars have been scheduled (not unusual outside term time).
