Nov 27 (Thu)
13:00 MCS2068 G&TYan 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
14:00 MCS2068 ProbOmer Angel (University of British Columbia): The phase transitions in the frog model.
The frog model is an interacting particle system, where particles are of type A (asleep) until hit by a particle of type B. Despite the simplicity of the definition, many questions remain open. We prove existence and sharpness of the phase transition for the frog model on transitive graphs of either polynomial growth, or non-amenable.
Venue: MCS2068
Nov 28 (Fri)
13:00 MCS0001 HEPMTim Meier (Santiago de Compostela): Noncommutative deformations of gauge theories via Drinfel'd twists of the scale symetry
Integrability within the AdS/CFT correspondence provides a powerful framework for studying quantum field theories and their AdS duals at finite coupling, offering an ideal playground for testing the duality and exploring nonperturbative aspects of QFT. In recent years, considerable attention has been focused on integrable deformations of the AdS5 string, particularly the class of homogeneous Yang–Baxter deformations, whose CFT duals are conjectured to be twisted versions of N=4 SYM. When these deformations act on the AdS sector of the background, they generically give rise to noncommutative field theories. However, a key challenge has been the lack of a systematic construction of gauge-invariant noncommutative Yang–Mills theories for the relevant twists.
In this talk, I will present a new approach that resolves this issue by providing a gauge-invariant formulation of noncommutative Yang–Mills theory for twists generated by scale and Poincaré transformations. This framework opens the door to investigating the CFT duals of a broad class of Yang–Baxter–deformed AdS backgrounds and paves the way for deeper tests of integrability-based deformations within AdS/CFT.
Venue: MCS0001
Dec 01 (Mon)
13:00 MCS3070 ApplDoireann O'Kiely (Limerick): Wrinkle patterns: evolution in time and space
14:00 MCS2068 PureBrian Petri (Jussieu): TBA
Dec 02 (Tue)
13:00 MCS2068 APDEEstefania Loayza Romero (University of Strathclyde): A Riemannian Approach for PDE-Constrained Shape Optimization Using Outer Metrics
In PDE-constrained shape optimisation, shapes are traditionally viewed as elements of a Riemannian manifold, specifically as embeddings of the unit circle into the plane, modulo reparameterizations. The standard approach employs the Steklov-Poincaré metric to compute gradients for Riemannian optimisation methods. A significant limitation of current methods is the absence of explicit expressions for the geodesic equations associated with this metric. Consequently, algorithms have relied on retractions (often equivalent to the perturbation of identity method in shape optimisation) rather than true geodesic paths. Previous research suggests that incorporating geodesic equations, or better approximations thereof, can substantially enhance algorithmic performance. This talk presents numerical evidence demonstrating that using outer metrics, defined on the space of diffeomorphisms with known geodesic expressions, improves Riemannian gradient-based optimisation by significantly reducing the number of required iterations and preserving mesh quality throughout the optimisation process.
Venue: MCS2068
14:00 MCS2068 ASGJay Taylor (University of Manchester): Modular Reduction of Nilpotent Orbits
The general linear group 𝐺 = GLₙ(𝕜) over a field 𝕜 acts on the space 𝔤 = 𝔤𝔩ₙ(𝕜) of (𝑛 × 𝑛)-matrices by conjugation. The set 𝒩(𝔤) of nilpotent matrices is preserved by this action and 𝐺 acts with finitely many orbits. The Jordan normal form gives a representative of each orbit that is contained in 𝔤𝔩ₙ(ℤ). Importantly, the structure of the centralizer of this nilpotent matrix is independent of 𝕜.
It is natural to ask to what extent this statement extends to a connected reductive algebraic group 𝐺 acting on its Lie algebra 𝔤 or the dual space 𝔤* via the (co-)adjoint representation. In general, the structure of centralisers of nilpotent elements will depend on 𝕜 but one can hope that the centraliser dimension remains the same. In this talk I will propose two variants of this idea, generalising the classical situation above, and report on on-going joint work with Adam Thomas (Warwick) to establish the existence of elements satisfying the proposed properties.
Venue: MCS2068
Dec 03 (Wed)
13:00 MCS2068 G&TSamüel Borza (University of Vienna): Ollivier-Ricci curvature in non-smooth Lorentzian geometry and causal set theory
This talk will explore some aspects of non-smooth Lorentzian geometry, the mathematical theory underlying Einsteins general relativity, which is currently being developed. Just as metric length spaces provide a synthetic generalisation of smooth Riemannian manifolds, the time-separation function plays the role of a distance in Lorentzian geometry. The need for a non-smooth Lorentzian framework appeared early on, most famously with Penroses singularity theorems. After introducing the basic concepts and some initial results in this synthetic setting, we will turn to Causal Set Theory, a radical approach to quantum gravity in which spacetime is modelled as a discrete causal graph. I will formulate a new notion of curvature in the spirit of Ollivier-Ricci curvature, using optimal transport between causal diamonds (Alexandrov intervals).
Venue: MCS2068
Dec 04 (Thu)
14:00 MCS2068 ProbKohei Suzuki (Department of Mathematics, Durham University): Interacting Brownian Motions, Wasserstein Gradient Flow and Ricci Curvature
In this talk, we focus on an infinite-dimensional model of interacting Brownian motions: Dyson Brownian motion at soft-edge scaling. Its stationary process is the Airy line ensemble, a central object in KPZ universality. We show that its time-marginal law forms a Wasserstein gradient flow of the relative entropy in the space of probability measures over the infinite-dimensional configuration space an infinite-dimensional analogue of Jordan-Kinderlehrer-Otto theory. This yields an optimal transport-first construction of the model, bridging Airy line ensemble/KPZ and optimal transport. From a metric-geometric viewpoint, our result shows that the configuration space endowed with the Airy_2 point process is an RCD space, a space having a uniform lower Ricci curvature bound in the sense of Lott-Villani/Sturm. As an application, (a) we establish various new functional inequalities (e.g., HWI, Brunn-Minkowski, dimension-free Harnack) for the model; (b) we discover a new propagation-of-rigidity phenomenon: the time-marginal law exhibits number rigidity in the sense of Ghosh and Peres, revealing a formation of a random crystal by long-range repulsively interacting Brownian motions. This talk is based on arXiv:2509.06869<https://arxiv.org/abs/2509.06869>.
Venue: MCS2068
Click on title to see abstract.
Back to Homepage
Click on series to expand.
Usual Venue: MCS2068
Contact: yohance.a.osborne@durham.ac.uk
Dec 02 13:00 Estefania Loayza Romero (University of Strathclyde): A Riemannian Approach for PDE-Constrained Shape Optimization Using Outer Metrics
In PDE-constrained shape optimisation, shapes are traditionally viewed as elements of a Riemannian manifold, specifically as embeddings of the unit circle into the plane, modulo reparameterizations. The standard approach employs the Steklov-Poincaré metric to compute gradients for Riemannian optimisation methods. A significant limitation of current methods is the absence of explicit expressions for the geodesic equations associated with this metric. Consequently, algorithms have relied on retractions (often equivalent to the perturbation of identity method in shape optimisation) rather than true geodesic paths. Previous research suggests that incorporating geodesic equations, or better approximations thereof, can substantially enhance algorithmic performance. This talk presents numerical evidence demonstrating that using outer metrics, defined on the space of diffeomorphisms with known geodesic expressions, improves Riemannian gradient-based optimisation by significantly reducing the number of required iterations and preserving mesh quality throughout the optimisation process.
Venue: MCS2068
Dec 09 13:00 Giacomo Borghi (Heriot-Watt University): TBC
Usual Venue: MCS3070
Contact: andrew.krause@durham.ac.uk
Dec 01 13:00 Doireann O'Kiely (Limerick): Wrinkle patterns: evolution in time and space
Wrinkles occur in a plethora of everyday situations and technological applications, across skin, balloons, flexible electronics and metal forming processes. In many cases these wrinkles can be described in terms of quasistatic compression of a stiff elastic sheet on a soft substrate; wrinkle patterns are then selected by minimizing energy subject to a nonlinear constraint. However, wrinkles can also be dynamic: when they form through fluid flow, wrinkles can either coarsen or rarify. In this talk I will explore the role of fluid flow in the evolution of wrinkle patterns. If time permits, I will also discuss wrinkle patterns that evolve in space.
Venue: MCS3070
Dec 08 13:00 Margarita Staykova (Durham (Physics)): Membrane biophysics: from understanding living cells to creating artificial ones
I will present ongoing work from my group that explores how the physical properties of cell membranes shape biological process as diverse as surface area regulation in cells, cell adhesion, and even lumen formation in embryos. I will finish with showing how we use lipid membranes to create bio hybrid materials, made of living cells coupled to artificial scaffolds.
Venue: MCS3070
Usual Venue: MCS2068
Contact: herbert.gangl@durham.ac.uk
Dec 02 14:00 Jay Taylor (University of Manchester): Modular Reduction of Nilpotent Orbits
The general linear group 𝐺 = GLₙ(𝕜) over a field 𝕜 acts on the space 𝔤 = 𝔤𝔩ₙ(𝕜) of (𝑛 × 𝑛)-matrices by conjugation. The set 𝒩(𝔤) of nilpotent matrices is preserved by this action and 𝐺 acts with finitely many orbits. The Jordan normal form gives a representative of each orbit that is contained in 𝔤𝔩ₙ(ℤ). Importantly, the structure of the centralizer of this nilpotent matrix is independent of 𝕜.
It is natural to ask to what extent this statement extends to a connected reductive algebraic group 𝐺 acting on its Lie algebra 𝔤 or the dual space 𝔤* via the (co-)adjoint representation. In general, the structure of centralisers of nilpotent elements will depend on 𝕜 but one can hope that the centraliser dimension remains the same. In this talk I will propose two variants of this idea, generalising the classical situation above, and report on on-going joint work with Adam Thomas (Warwick) to establish the existence of elements satisfying the proposed properties.
Venue: MCS2068
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
No upcoming seminars have been scheduled (not unusual outside term time).
Usual Venue: MCS2068
Contact: fernando.galaz-garcia@durham.ac.uk
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
Dec 03 13:00 Samüel Borza (University of Vienna): Ollivier-Ricci curvature in non-smooth Lorentzian geometry and causal set theory
This talk will explore some aspects of non-smooth Lorentzian geometry, the mathematical theory underlying Einsteins general relativity, which is currently being developed. Just as metric length spaces provide a synthetic generalisation of smooth Riemannian manifolds, the time-separation function plays the role of a distance in Lorentzian geometry. The need for a non-smooth Lorentzian framework appeared early on, most famously with Penroses singularity theorems. After introducing the basic concepts and some initial results in this synthetic setting, we will turn to Causal Set Theory, a radical approach to quantum gravity in which spacetime is modelled as a discrete causal graph. I will formulate a new notion of curvature in the spirit of Ollivier-Ricci curvature, using optimal transport between causal diamonds (Alexandrov intervals).
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
Nov 28 13:00 Tim Meier (Santiago de Compostela): Noncommutative deformations of gauge theories via Drinfel'd twists of the scale symetry
Integrability within the AdS/CFT correspondence provides a powerful framework for studying quantum field theories and their AdS duals at finite coupling, offering an ideal playground for testing the duality and exploring nonperturbative aspects of QFT. In recent years, considerable attention has been focused on integrable deformations of the AdS5 string, particularly the class of homogeneous Yang–Baxter deformations, whose CFT duals are conjectured to be twisted versions of N=4 SYM. When these deformations act on the AdS sector of the background, they generically give rise to noncommutative field theories. However, a key challenge has been the lack of a systematic construction of gauge-invariant noncommutative Yang–Mills theories for the relevant twists.
In this talk, I will present a new approach that resolves this issue by providing a gauge-invariant formulation of noncommutative Yang–Mills theory for twists generated by scale and Poincaré transformations. This framework opens the door to investigating the CFT duals of a broad class of Yang–Baxter–deformed AdS backgrounds and paves the way for deeper tests of integrability-based deformations within AdS/CFT.
Venue: MCS0001
Dec 05 13:00 Marco Meineri (Torino University): The Numerical Bootstrap of Points and Lines
I will describe how to constrain the conformal field theory data attached to boundary conditions of two dimensional theories, using the numerical bootstrap. Even for rational theories, it is hard to construct examples of boundary conditions which break all symmetry except Virasoro, let alone classify them. Yet, as always, the OPE data associated with each conformal boundary condition obeys crossing and unitarity. The ensuing constraints can be organized in a semidefinite program, which allows exploration of a multi-dimensional parameter space involving bulk and boundary data.
Venue: MCS0001
Dec 12 13:00 Sungwoo Hong (KAIST, Taejon): Global Aspects of Particle and Defect Physics
In this talk, I will introduce the notion of global aspects in the physics of particles and topological defects. A well-known example is the global structure ambiguity of the Standard Model (SM) gauge group. I will discuss the correlation between the quantization conditions of axiongauge couplings and this global structure, and its implications on axion domain wall physics.
As another example, I will describe how various global structures play important roles in the domain wall problem of the DFSZ axion model. A precise identification of the axion stringdomain wall networkand hence the true nature of the domain wall problembecomes possible by recognizing a discrete overlap between the Peccei-Quinn symmetry and the SM gauge group.
An elegant solution to the domain wall problem can also be realized by introducing another global structure shared between the color and family gauge groups, which gives rise to discrete non-invertible Peccei-Quinn symmetries. This discrete non-invertible symmetry can then be slightly broken by small instanton effects in a UV completion in the form of an SU(9) colorflavor unification.
If time permits, I will also discuss group-theoretic methods for analyzing topological sectors and global structures in Grand Unified Theories, and homotopy group and their exact sequence analysis for non-topological as well as topological defects.
Venue: MCS0001
Usual Venue: MCS2068
Contact: tyler.helmuth@durham.ac.uk,oliver.kelsey-tough@durham.ac.uk
Nov 27 14:00 Omer Angel (University of British Columbia): The phase transitions in the frog model.
The frog model is an interacting particle system, where particles are of type A (asleep) until hit by a particle of type B. Despite the simplicity of the definition, many questions remain open. We prove existence and sharpness of the phase transition for the frog model on transitive graphs of either polynomial growth, or non-amenable.
Venue: MCS2068
Dec 04 14:00 Kohei Suzuki (Department of Mathematics, Durham University): Interacting Brownian Motions, Wasserstein Gradient Flow and Ricci Curvature
In this talk, we focus on an infinite-dimensional model of interacting Brownian motions: Dyson Brownian motion at soft-edge scaling. Its stationary process is the Airy line ensemble, a central object in KPZ universality. We show that its time-marginal law forms a Wasserstein gradient flow of the relative entropy in the space of probability measures over the infinite-dimensional configuration space an infinite-dimensional analogue of Jordan-Kinderlehrer-Otto theory. This yields an optimal transport-first construction of the model, bridging Airy line ensemble/KPZ and optimal transport. From a metric-geometric viewpoint, our result shows that the configuration space endowed with the Airy_2 point process is an RCD space, a space having a uniform lower Ricci curvature bound in the sense of Lott-Villani/Sturm. As an application, (a) we establish various new functional inequalities (e.g., HWI, Brunn-Minkowski, dimension-free Harnack) for the model; (b) we discover a new propagation-of-rigidity phenomenon: the time-marginal law exhibits number rigidity in the sense of Ghosh and Peres, revealing a formation of a random crystal by long-range repulsively interacting Brownian motions. This talk is based on arXiv:2509.06869<https://arxiv.org/abs/2509.06869>.
Venue: MCS2068
Usual Venue: MCS3070
Contact: joe.thomas@durham.ac.uk
No upcoming seminars have been scheduled (not unusual outside term time).
