Seminars in Mathematical Sciences

Seminars in the next week
Jan 20 (Mon)

13:00 MCS0001 PureMikolaj Fraczyk (Krakow): Waist inequalities, higher expansion and branched covers

Let M be a reasonably nice n-dimensional topological space, like a closed Riemannian manifold or a finite simpilcial complex. The d-waist of a continuous map f:M-> R^d is defined as the maximum of n-d volumes of fibers of f and the d-waist of M is then the infimum of waist of all such maps f. Estimating waists is a classical problem, drawing from minimal surface theory, higher expanders and quantitative algebraic topology. I will talk about these connections and illustrate them with some new results for locally symmetric spaces (mainly octonionic hyperbolic manifolds). Based on a joint work with Ben Lowe.

Venue: MCS0001

14:00 MCS2068 ProbIrene Ayuso Ventura (Durham, UK): Ising model on random trees with a random external field

I will present my work with Q. Berger on the Ising model on Galton-Watson trees, where we add “interfering” vertices to the model, treating them as a random external field. I’ll start with a short motivation for considering this kind of model. Then, I’ll introduce random tree recursions, which are not only useful for this specific problem but also for other statistical mechanics models on trees, like the random cluster model. Finally, I’ll state our main result and discuss the proof strategy, which includes, among other things, a beautiful tree-pruning method.

Venue: MCS2068

Jan 21 (Tue)

13:00 MCS2068 ASGYue Ren (Durham): Introduction to Tropical Geometry

Venue: MCS2068

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):

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


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Current and Upcoming Events

These events are hosted in and/or organised by members of the Department (follow links for details):

Mar 25--28 [MCS0001, L50] Durham Symposium 116: Mean Field Games

Apr 14--15 [MCS2068] Spectral Theory Workshop

Invited speakers: van den Berg, Fischer, Marletta, Siffert

Venue: MCS2068 at/from 10:00

Link: here

Upcoming Seminars by Series

Click on series to expand.

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• Amplitudes and Correlators

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

• Analysis and PDE

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

• Applied Mathematics

Usual Venue: MCS2068

Contact: andrew.krause@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time).

• Arithmetic Study Group

Usual Venue: MCS2068

Contact: herbert.gangl@durham.ac.uk

Jan 21 13:00 Yue Ren (Durham): Introduction to Tropical Geometry

Venue: MCS2068

Feb 04 13:00 Sergey Oblezin (BIMSA, Beijing):

Venue: MCS2068

Feb 11 13:00 Victor Wang (Institute of Science and Technology Austria (ISTA), Vienna):

Venue: MCS2068

Feb 25 13:00 Haluk Sengun (University of Sheffield):

Venue: MCS2068

Feb 28 13:00 Mads Christensen (University College London):

Venue: MCS2068

Mar 04 13:00 Thomas Bloom (University of Manchester):

Venue: MCS2068

Mar 11 13:00 Markus Szymik (Sheffield University): Artin–Schreier quandles of involutions in absolute Galois groups

Venue: MCS2068

Mar 18 13:00 Kalyani Kansal (Imperial College):

Venue: MCS2068

• CPT Colloquium

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).

• Department Research Colloquium

Usual Venue: MCS0001

Contact: inaki.garcia-etxebarria@durham.ac.uk,sunil.chhita@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time).

• Distinguished and Public Lectures

Usual Venue: MCS0001

Contact: sabine.boegli@durham.ac.uk,alpar.r.meszaros@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time).

• Education and Pedagogy

Usual Venue: MCS3052

Contact: andrew.krause@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time).

• Ergodic Theory and Dynamics

Usual Venue: MCS3070

Contact: gabriel.fuhrmann@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time).

• Gandalf

Usual Venue: MCS3070

Contact: daniel.n.disney@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time).

• Geometry and Topology

Usual Venue: MCS2068

Contact: martin.p.kerin@durham.ac.uk

Jan 23 14:00 Mohammad Al Attar (Durham):

Venue: MCS2068

Jan 30 14:00 Ana García Lecuona (Glasgow): TBA

Venue: MCS2068

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

Venue: MCS2068

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

Venue: MCS2068

Jun 12 14:00 Ilka Agricola (Marburg): TBD

Venue: MCS2068

• HEP Journal Club

Usual Venue: MCS3070

Contact: andrea.grigoletto@durham.ac.uk,nakarin.lohitsiri@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time).

• HEP Lunchtime

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

TBA

Venue: MCS0001

Feb 14 13:00 Simon Ekhammar (King's College London): TBA

TBA

Venue: MCS0001

Feb 21 13:00 Georges Obied (Oxford University): TBA

TBA

Venue: MCS0001

Feb 28 13:00 Ana Maria Raclariu (King's College London): TBA

TBA

Venue: MCS0001

Mar 14 13:00 Po-Shen Hsin (King's College London): TBA

TBA

Venue: MCS0001

Mar 21 13:00 Gabriele Travaglini (Queen Mary University of London): TBA

TBA

Venue: MCS0001

• Probability

Usual Venue: MCS2068

Contact: kohei.suzuki@durham.ac.uk

Jan 20 14:00 Irene Ayuso Ventura (Durham, UK): Ising model on random trees with a random external field

I will present my work with Q. Berger on the Ising model on Galton-Watson trees, where we add “interfering” vertices to the model, treating them as a random external field. I’ll start with a short motivation for considering this kind of model. Then, I’ll introduce random tree recursions, which are not only useful for this specific problem but also for other statistical mechanics models on trees, like the random cluster model. Finally, I’ll state our main result and discuss the proof strategy, which includes, among other things, a beautiful tree-pruning method.

Venue: MCS2068

Jan 27 14:00 Rui Bai (Durham, UK): TBA

TBA

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

TBA

Venue: MCS2068

Mar 03 14:00 Sarah Penington (Bath, UK): TBA

TBA

Venue: MCS2068

Mar 10 14:00 Isao Suezedde (Warwick, UK): TBA

TBA

Venue: MCS2068

• Pure Maths Colloquium

Usual Venue: MCS0001

Contact: raphael.zentner@durham.ac.uk

Jan 20 13:00 Mikolaj Fraczyk (Krakow): Waist inequalities, higher expansion and branched covers

Let M be a reasonably nice n-dimensional topological space, like a closed Riemannian manifold or a finite simpilcial complex. The d-waist of a continuous map f:M-> R^d is defined as the maximum of n-d volumes of fibers of f and the d-waist of M is then the infimum of waist of all such maps f. Estimating waists is a classical problem, drawing from minimal surface theory, higher expanders and quantitative algebraic topology. I will talk about these connections and illustrate them with some new results for locally symmetric spaces (mainly octonionic hyperbolic manifolds). Based on a joint work with Ben Lowe.

Venue: MCS0001

Jan 27 13:00 Gabriel Fuhrmann (Durham University): TBA

TBA

Venue: MCS0001

Feb 10 13:00 Rachael Boyd (Glasgow University): TBA

TBA

Venue: MCS0001

Mar 10 13:00 Karen Vogtmann (University of Warwick): TBA

TBA

Venue: MCS0001

Mar 17 13:00 Andras Juhasz (University of Oxford): TBA

TBA

Venue: MCS0001

• Spectra and Moduli

Usual Venue: MCS3070

Contact: irving.d.calderon-camacho@durham.ac.uk,joe.thomas@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time).

• Statistics

Usual Venue: MCS2068

Contact: hyeyoung.maeng@durham.ac.uk,andrew.iskauskas@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time).

• Stats4Grads

Contact: adam.stone2@durham.ac.uk

No upcoming seminars have been scheduled (not unusual outside term time).