Jan 21 (Tue)
13:00 MCS2068 ASGYue Ren (Durham): Introduction to Tropical Geometry
14:00 MCS2068 APDESam Farrington (Durham University): Shape optimisation for Neumann eigenvalues
Asking which domain in a given class optimises a certain Neumann eigenvalue is a classical problem in shape optimisation. One can trace such questions back to the work of Szego and Weinberger in the 1950s. In recent years, a renewed interest in the optimisation of Neumann eigenvalues under a perimeter or a diameter constraint has emerged. We will discuss these new results and compare them to previously known results for Dirichlet eigenvalues. Time permitting, we will discuss some optimisation problems for Robin and Zaremba eigenvalues and open problems in this direction.
This talk is primarily based on the two complementary papers below:
[1] On the isoperimetric and isodiametric inequalities and the minimisation of eigenvalues of the Laplacian, S. Farrington, J. Geom. Anal. (2025)
[2] Optimization of Neumann eigenvalues under convexity and geometric constraints, B. Bogosel, A. Henrot, M. Michetti, SIAM J. Math. Anal. (2024)
Venue: MCS2068
Jan 22 (Wed)
11:00 zoom A&CDonal O'Connell (Edinburgh): Hawking Scattering Amplitudes
Hawking is famous for his computation of the temperature of black holes. What is less well known is that his computation depends crucially on a scattering computation very similar to the classical black hole scattering processes common in today's amplitudes literature. I will discuss this scattering process using the methods of amplitudes, and explain how resummation and crossing lead to a pair-production spectrum and the associated black hole temperature.
Venue: zoom
Zoom: https://durhamuniversity.zoom.us/j/92211250974?pwd=kzuSorCBj9TUa1bRNNnu4eM36D1FAA.1
Jan 23 (Thu)
14:00 MCS2068 G&TMohammad Al Attar (Durham): Regularity of Resolutions and Limits of Manifolds
In this talk we will show that, roughly speaking, the
problem of studying non-collapsed limits of manifolds under a weaker
condition than having uniform curvature bounds, is equivalent to
studying the regularity of resolutions of homology manifolds. We will
discuss applications to the areas of convergence theory, and controlled
topology. Furthermore, we will show that a conjecture due to Moore holds
true in a very general setting.
Venue: MCS2068
Jan 24 (Fri)
13:00 MCS0001 HEPMLivia Ferro (Hertfordshire University): Scattering amplitudes from null-cone geometry
In recent years it has become clear that particular geometric structures, called positive geometries, underlie various observables in quantum field theories. In this talk I will focus on scattering amplitudes. After a broad introduction, I will consider maximally supersymmetric Yang-Mills theory and discuss a positive geometry encoding scattering processes in this theory -- the momentum amplituhedron. In particular, I will show that using the null structure of the kinematic space, one finds a geometry whose canonical differential form produces loop-amplitude integrands. Finally, I will present some of the main goals and research directions for the future.
Venue: MCS0001
Jan 27 (Mon)
13:00 MCS0001 PureGabriel Fuhrmann (Durham University): TBA
14:00 MCS2068 ProbRui Bai (Durham, UK): Large deviations principle for invariant measures of stochastic Burgers equations
We study the small noise asymptotic for stochastic Burgers equations on $(0,1)$ with the Dirichlet boundary condition. We consider the case in which the noise is more singular than space-time white noise. We let the noise magnitude $\sqrt{\epsilon} \rightarrow 0$ and the covariance operator $Q_\epsilon$ converge to $(-\Delta)^{\frac 1 2}$ and prove the large deviations principle for solutions, uniformly with respect to the bounded initial value of the equation. Furthermore, we set $Q_\epsilon$ to be a trace class operator and converge to $(-\Delta)^{\frac{\alpha}{2}}$ with $\alpha<1$ in a suitable way such that the invariant measures exist. Then, we prove the large deviations principle for the invariant measures of stochastic Burgers equations.
Venue: MCS2068
Jan 28 (Tue)
13:00 MCS2068 ASGMads Christensen (University College London):
14:00 MCS2068 APDEOana Pocovnicu (Heriot-Watt University): Invariant Gibbs dynamics for fractional wave equations in negative Sobolev spaces
In this talk, we consider a fractional nonlinear wave equation with a general power-type nonlinearity (FNLW) on the two-dimensional torus. Our main goal is to construct invariant global-in-time Gibbs dynamics for FNLW. We first construct the Gibbs measure associated with this equation. By introducing a suitable renormalisation, we then prove almost sure local well-posedness with respect to Gibbsian initial data. Finally, we extend solutions globally in time by applying Bourgain's invariant measure argument. This talk is based on a joint work with Luigi Forcella (University of Pisa, Italy).
Venue: MCS2068
Click on title to see abstract.
Back to Homepage
Click on series to expand.
Usual Venue: zoom
Contact: arthur.lipstein@durham.ac.uk
Jan 22 11:00 Donal O'Connell (Edinburgh): Hawking Scattering Amplitudes
Hawking is famous for his computation of the temperature of black holes. What is less well known is that his computation depends crucially on a scattering computation very similar to the classical black hole scattering processes common in today's amplitudes literature. I will discuss this scattering process using the methods of amplitudes, and explain how resummation and crossing lead to a pair-production spectrum and the associated black hole temperature.
Venue: zoom
Usual Venue: MCS3070
Contact: sabine.boegli@durham.ac.uk
Jan 21 14:00 Sam Farrington (Durham University): Shape optimisation for Neumann eigenvalues
Asking which domain in a given class optimises a certain Neumann eigenvalue is a classical problem in shape optimisation. One can trace such questions back to the work of Szego and Weinberger in the 1950s. In recent years, a renewed interest in the optimisation of Neumann eigenvalues under a perimeter or a diameter constraint has emerged. We will discuss these new results and compare them to previously known results for Dirichlet eigenvalues. Time permitting, we will discuss some optimisation problems for Robin and Zaremba eigenvalues and open problems in this direction.
This talk is primarily based on the two complementary papers below:
[1] On the isoperimetric and isodiametric inequalities and the minimisation of eigenvalues of the Laplacian, S. Farrington, J. Geom. Anal. (2025)
[2] Optimization of Neumann eigenvalues under convexity and geometric constraints, B. Bogosel, A. Henrot, M. Michetti, SIAM J. Math. Anal. (2024)
Venue: MCS2068
Jan 28 14:00 Oana Pocovnicu (Heriot-Watt University): Invariant Gibbs dynamics for fractional wave equations in negative Sobolev spaces
In this talk, we consider a fractional nonlinear wave equation with a general power-type nonlinearity (FNLW) on the two-dimensional torus. Our main goal is to construct invariant global-in-time Gibbs dynamics for FNLW. We first construct the Gibbs measure associated with this equation. By introducing a suitable renormalisation, we then prove almost sure local well-posedness with respect to Gibbsian initial data. Finally, we extend solutions globally in time by applying Bourgain's invariant measure argument. This talk is based on a joint work with Luigi Forcella (University of Pisa, Italy).
Venue: MCS2068
Usual Venue: MCS2068
Contact: andrew.krause@durham.ac.uk
No upcoming seminars have been scheduled (not unusual outside term time).
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: martin.p.kerin@durham.ac.uk
Jan 23 14:00 Mohammad Al Attar (Durham): Regularity of Resolutions and Limits of Manifolds
In this talk we will show that, roughly speaking, the
problem of studying non-collapsed limits of manifolds under a weaker
condition than having uniform curvature bounds, is equivalent to
studying the regularity of resolutions of homology manifolds. We will
discuss applications to the areas of convergence theory, and controlled
topology. Furthermore, we will show that a conjecture due to Moore holds
true in a very general setting.
Venue: MCS2068
Jan 30 14:00 Ana García Lecuona (Glasgow): TBA
Feb 06 14:00 Anna Felikson (Durham): Hyperbolic geometry of friezes
Frieze patterns were introduced by Coxeter in the 1970s who,
with Conway, established a correspondence between frieze patterns and
triangulated polygons. It turned out later that this object is very rich
in connections with different fields in mathematics. We use hyperbolic
geometry to provide a classification of positive integral friezes on
marked bordered surfaces. This is a joint work with Pavel Tumarkin.
Venue: MCS2068
Feb 13 14:00 JeongHyeong Park (Sungkyunkwan University): Characterizations and classification of harmonic manifolds
A Riemannian manifold is called harmonic if there exists a
non-constant radial harmonic function in a punctured neighborhood for
any point, or equivalently every sufficiently small geodesic sphere has
constant mean curvature, or equivalently if a volume density function
centered at a point depends only on the distance from the center. There
are many other characterizations of harmonic spaces. In this talk, we
characterize harmonic manifolds in terms of the radial eigenspaces of
the Laplacian. The space forms, the complex hyperbolic spaces and the
quaternionic hyperbolic spaces are characterized as harmonic manifolds
with specific radial eigenfunctions of the Laplacian. We discuss the
lower volume bounds on even-dimensional negatively curved rank one
symmetric spaces, and we additionally present our recent progress on the
study of harmonic manifolds. (This is joint work with P. Gilkey.)
Venue: MCS2068
Feb 20 14:00 Anna Pratoussevitch (Liverpool): TBD
Feb 27 14:00 Sebastian Chenery (Bristol): Gyration Stability for Projective Planes
Gyrations are operations on manifolds that first arose in
geometric topology. A given manifold M may exhibit different gyrations
depending on the chosen twisting, prompting the following natural
question: do all gyrations of M share the same homotopy type regardless
of which twisting we choose? Inspired by recent work of Duan, which
demonstrated that the quaternionic projective plane is not gyration
stable (but with respect to diffeomorphism) in this talk we will explore
our question for projective planes in general, resulting in a complete
description of gyration stability for the complex, quaternionic, and
octonionic projective planes up to homotopy. Moreover, we will also see
that these results connect to several seemingly distinct contexts. This
is joint work with Stephen Theriault.
Venue: MCS2068
Mar 13 14:00 Macarena Arenas (Cambridge): TBD
Jun 12 14:00 Ilka Agricola (Marburg): TBD
Usual Venue: MCS0001
Contact: silvia.nagy@durham.ac.uk,enrico.andriolo@durham.ac.uk,tobias.p.hansen@durham.ac.uk
Jan 24 13:00 Livia Ferro (Hertfordshire University): Scattering amplitudes from null-cone geometry
In recent years it has become clear that particular geometric structures, called positive geometries, underlie various observables in quantum field theories. In this talk I will focus on scattering amplitudes. After a broad introduction, I will consider maximally supersymmetric Yang-Mills theory and discuss a positive geometry encoding scattering processes in this theory -- the momentum amplituhedron. In particular, I will show that using the null structure of the kinematic space, one finds a geometry whose canonical differential form produces loop-amplitude integrands. Finally, I will present some of the main goals and research directions for the future.
Venue: MCS0001
Jan 31 13:00 Yolanda Lozano (Oviedo University): AdS3/CFT2 and defect CFTs
I will discuss recently constructed AdS3 solutions with (0,6) and (0,4) supersymmetries and their field theory interpretations, in particular in relation with defects.
Venue: MCS0001
Feb 07 13:00 Cynthia Keeler (Arizona State University): TBA
Feb 14 13:00 Simon Ekhammar (King's College London): TBA
Feb 21 13:00 Georges Obied (Oxford University): TBA
Feb 28 13:00 Ana Maria Raclariu (King's College London): TBA
Mar 14 13:00 Po-Shen Hsin (King's College London): TBA
Mar 21 13:00 Gabriele Travaglini (Queen Mary University of London): TBA
Usual Venue: MCS2068
Contact: kohei.suzuki@durham.ac.uk
Jan 27 14:00 Rui Bai (Durham, UK): Large deviations principle for invariant measures of stochastic Burgers equations
We study the small noise asymptotic for stochastic Burgers equations on $(0,1)$ with the Dirichlet boundary condition. We consider the case in which the noise is more singular than space-time white noise. We let the noise magnitude $\sqrt{\epsilon} \rightarrow 0$ and the covariance operator $Q_\epsilon$ converge to $(-\Delta)^{\frac 1 2}$ and prove the large deviations principle for solutions, uniformly with respect to the bounded initial value of the equation. Furthermore, we set $Q_\epsilon$ to be a trace class operator and converge to $(-\Delta)^{\frac{\alpha}{2}}$ with $\alpha<1$ in a suitable way such that the invariant measures exist. Then, we prove the large deviations principle for the invariant measures of stochastic Burgers equations.
Venue: MCS2068
Feb 03 14:00 Robin Stephenson (Sheffield, UK): Where do trees grow leaves?
We study a model of random binary trees grown ``by the leaves" in the style of Luczak and Winkler (2004). If $\tau_n$ is a uniform plane binary tree of size $n$, Luczak and Winkler, and later explicitly Caraceni and Stauffer, constructed a measure $\nu_{\tau_n}$ such that the tree obtained by adding a cherry on a leaf sampled according to $\nu_{\tau_n}$ is still uniformly distributed on the set of all plane binary trees with size $n+1$. It turns out that the measure $\nu_{\tau_n}$, which we call the leaf-growth measure, is noticeably different from the uniform measure on the leaves of the tree $\tau_n$. In fact we prove that as $n \to \infty$, with high probability it is almost entirely supported by a subset of only $n^{3 ( 2 - \sqrt{3})+o(1)} \approx n^{0.8038...}$ leaves.
In the continuous setting, we construct the scaling limit of this measure, which is a probability measure on the Brownian Continuum Random Tree supported by a fractal set of dimension $ 6 (2 - \sqrt{3})$. We also compute the full (discrete) multifractal spectrum. This work is a first step towards understanding the diffusion limit of the discrete leaf-growth procedure.
Venue: MCS2068
Feb 10 14:00 Andreas Koller (Warwick, UK): TBA
Mar 03 14:00 Sarah Penington (Bath, UK): TBA
Mar 10 14:00 Isao Suezedde (Warwick, UK): TBA
Usual Venue: MCS0001
Contact: raphael.zentner@durham.ac.uk
Jan 27 13:00 Gabriel Fuhrmann (Durham University): TBA
Feb 10 13:00 Rachael Boyd (Glasgow University): TBA
Mar 10 13:00 Karen Vogtmann (University of Warwick): TBA
Mar 17 13:00 Andras Juhasz (University of Oxford): TBA
