Seminars in Mathematical Sciences

Seminars in the next week
Jan 13 (Tue)

13:00 MCS2068 APDEDan Hill (University of Oxford): Think Global, Act Local: Inducing Fully Localised 2D Patterns via Spatial Heterogeneity

The existence of localised two-dimensional patterns has been observed and studied in numerous experiments and simulations: ranging from optical solitons, to patches of desert vegetation, to fluid convection. And yet, our mathematical understanding of these emerging structures remains extremely limited beyond one-dimensional examples.

In this talk I will discuss how adding a compact region of spatial heterogeneity to a PDE model can not only induce the emergence of fully localised 2D patterns, but also allows us to rigorously prove and characterise their bifurcation. The idea is inspired by experimental and numerical studies of magnetic fluids and tornados, where our compact heterogeneity corresponds to a local spike in the magnetic field and temperature gradient, respectively. In particular, we obtain local bifurcation results for fully localised patterns both with and without radial or dihedral symmetry, and rigorously continue these solutions to large amplitude. Notably, the initial bifurcating solution (which can be stable at bifurcation) varies between a radially-symmetric spot and a 'dipole' solution as the width of the spatial heterogeneity increases.

This work is in collaboration with David J.B. Lloyd and Matthew R. Turner (both University of Surrey).

Venue: MCS2068

Jan 14 (Wed)

16:00 MCS3052 A&CBurkhard Eden (Humboldt University): The off-shell one and two-loop box recovered from intersection theory

We advertise intersection theory for generalised hypergeometric functions as a means of evaluating Mellin-Barnes representations. As an example, we study two-parameter representations of the off-shell one-and two-loop box graphs in exactly four-dimensional configuration space. Closing the integration contours for the MB parameters we transform these into double sums. Polygamma functions in the MB representation of the double box and the occurrence of higher poles are taken into account by parametric differentiation. Summing over any one of the counters results into a p+1Fp that we replace by its Euler integral representation. The process can be repeated a second time and results in a two- or four-parameter Euler integral, respectively. We use intersection theory to derive Pfaffian systems of equations on related sets of master integrals and solve for the box and double box integrals reproducing the known expressions. Finally, we use a trick to re-derive the double box from a two-parameter Euler integral. This second computation requires only very little computing resources.

Venue: MCS3052

Jan 15 (Thu)

13:00 MCS2068 G&TLéo Schelstraete (MPI Bonn): Super TFQTs and odd Khovanov homology

Odd Khovanov homology is a homological invariant of links that categorifies the Jones polynomial. It is the "evil twin" of Khovanov homology: while the two theories categorify the Jones polynomial and coincide over Z/2Z, they differ over Z and seem to detect different topological properties.

In some vague sense, the construction of odd Khovanov homology is an anti-commutative analogue of its even counterpart. In this talk, I will explain how the "oddness" can be given a precise sense, using super TQFTs and a super tensor product of complexes. In the process, we give an extension of odd Khovanov homology to tangles and use it to show that all torsion appear in odd Khovanov homology.

Venue: MCS2068

14:00 MCS2068 ProbBrett Kolesnik (University of Warwick): K_r-percolation

Start with an Erdõs–Rényi random graph G(n,p) and then iteratively add a missing edge if it creates a new copy of the complete graph K_r. We find the critical threshold probability p_c at which all other edges in K_n are eventually added to G(n,p). This solves a problem of Balogh, Bollobás, and Morris. Joint work with Zsolt Bartha, Gal Kronenberg, and Yuval Peled (arXiv:2510.26724).

Venue: MCS2068

Jan 19 (Mon)

14:00 MCS2068 PureJan Vonk (Leiden University, The Netherlands): An equation of Diophantus

This is the story of an old equation of Diophantus, which will take us on an excursion along a branch of number theory that stretches over an important part of the subject's history. It will be our motivation for a friendly introduction to some modern developments on torsion and ranks of elliptic curves.

Venue: MCS2068

Jan 20 (Tue)

14:00 MCS2068 ASGJan Vonk (Leiden University, The Netherlands): p-adic modular forms and differences of singular moduli

Following a suggestion of Blasius and Calegari, we explore analogies between Maass forms and p-adic modular forms. I will discuss an application to singular moduli for real quadratic fields (joint with Henri Darmon) and the zero locus of overconvergent eigenforms (joint with Paolo Bordignon).

Venue: MCS2068


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Upcoming Seminars by Series

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• Amplitudes and Correlators

Contact: arthur.lipstein@durham.ac.uk

Jan 14 16:00 Burkhard Eden (Humboldt University): The off-shell one and two-loop box recovered from intersection theory

We advertise intersection theory for generalised hypergeometric functions as a means of evaluating Mellin-Barnes representations. As an example, we study two-parameter representations of the off-shell one-and two-loop box graphs in exactly four-dimensional configuration space. Closing the integration contours for the MB parameters we transform these into double sums. Polygamma functions in the MB representation of the double box and the occurrence of higher poles are taken into account by parametric differentiation. Summing over any one of the counters results into a p+1Fp that we replace by its Euler integral representation. The process can be repeated a second time and results in a two- or four-parameter Euler integral, respectively. We use intersection theory to derive Pfaffian systems of equations on related sets of master integrals and solve for the box and double box integrals reproducing the known expressions. Finally, we use a trick to re-derive the double box from a two-parameter Euler integral. This second computation requires only very little computing resources.

Venue: MCS3052

• Analysis and PDE

Usual Venue: MCS2068

Contact: yohance.a.osborne@durham.ac.uk

Jan 13 13:00 Dan Hill (University of Oxford): Think Global, Act Local: Inducing Fully Localised 2D Patterns via Spatial Heterogeneity

The existence of localised two-dimensional patterns has been observed and studied in numerous experiments and simulations: ranging from optical solitons, to patches of desert vegetation, to fluid convection. And yet, our mathematical understanding of these emerging structures remains extremely limited beyond one-dimensional examples.

In this talk I will discuss how adding a compact region of spatial heterogeneity to a PDE model can not only induce the emergence of fully localised 2D patterns, but also allows us to rigorously prove and characterise their bifurcation. The idea is inspired by experimental and numerical studies of magnetic fluids and tornados, where our compact heterogeneity corresponds to a local spike in the magnetic field and temperature gradient, respectively. In particular, we obtain local bifurcation results for fully localised patterns both with and without radial or dihedral symmetry, and rigorously continue these solutions to large amplitude. Notably, the initial bifurcating solution (which can be stable at bifurcation) varies between a radially-symmetric spot and a 'dipole' solution as the width of the spatial heterogeneity increases.

This work is in collaboration with David J.B. Lloyd and Matthew R. Turner (both University of Surrey).

Venue: MCS2068

• Applied Mathematics

Usual Venue: MCS3070

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 20 14:00 Jan Vonk (Leiden University, The Netherlands): p-adic modular forms and differences of singular moduli

Following a suggestion of Blasius and Calegari, we explore analogies between Maass forms and p-adic modular forms. I will discuss an application to singular moduli for real quadratic fields (joint with Henri Darmon) and the zero locus of overconvergent eigenforms (joint with Paolo Bordignon).

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).

• 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: fernando.galaz-garcia@durham.ac.uk

Jan 15 13:00 Léo Schelstraete (MPI Bonn): Super TFQTs and odd Khovanov homology

Odd Khovanov homology is a homological invariant of links that categorifies the Jones polynomial. It is the "evil twin" of Khovanov homology: while the two theories categorify the Jones polynomial and coincide over Z/2Z, they differ over Z and seem to detect different topological properties.

In some vague sense, the construction of odd Khovanov homology is an anti-commutative analogue of its even counterpart. In this talk, I will explain how the "oddness" can be given a precise sense, using super TQFTs and a super tensor product of complexes. In the process, we give an extension of odd Khovanov homology to tangles and use it to show that all torsion appear in odd Khovanov homology.

Venue: MCS2068

Jan 22 13:00 Chunyang Hu (Durham / University of Science and Technology of China): On a magneto-spectral invariant for finite graphs

In this talk, I will introduce a new spectral invariant on finite graphs, called "magneto-spectral height". This invariant vanishes on forests and is maximized by complete graphs. We compute this invariant for cycles, complete graphs, wheel graphs, hypercubes, complete bipartite graphs and suspensions of trees and derive vatious lower and upper bounds. If time permits, I will introduce a sharp upper bound for regular bipartite graphs and derive a direct relation between the class of graphs assuming this upper bound and the class of unit weighing matrices, which are generalizations of complex Hadamard matrices. Moreover, this class of regular bipartite graphs has non-negative magnetic Bakry-Émery curvature. I will also discuss the behavior of this invariant under various graphs operations and investigate relations to the spectral gap. This is joint work with Bobo Hua, Supanat Kamtue, Shiping Liu, Florentin Muench and Norbert Peyerimhoff.

Venue: MCS2068

Jan 29 13:00 Daniel Disney (Durham): TBA

Venue: MCS2068

Feb 05 13:00 Sarah Whitehouse (Sheffield): Homotopy theory and geometry related to multicomplexes

A multicomplex is a variant of a bicomplex and these structures arise naturally in many geometric, topological and algebraic contexts; for example, from filtered simplicial sets. I will explain some recent joint work with Joana Cirici and Muriel Livernet which explores homotopy theories related to the two spectral sequences of a truncated multicomplex. There are potential applications to the study of homotopy types of almost and generalized complex manifolds.

Venue: MCS2068

Feb 12 13:00 Tom Nye (Newcastle): Metric geometry for statistics in spaces of trees, forests and graphs

Venue: MCS2068

Feb 19 13:00 Raphael Zentner (Durham): TBA

Venue: MCS2068

Feb 26 13:00 Brendan Guilfoyle (Munster Technological University): TBA

Venue: MCS2068

Mar 06 13:00 Julian Scheuer (Goethe University Frankfurt): TBA

Venue: MCS2068

Mar 12 13:00 Andy Wand (Glasgow): TBA

Venue: MCS2068

Apr 30 13:00 Anthea Monod (Imperial): TBA

Venue: MCS2068

• HEP Journal Club

Usual Venue: MCS3070

Contact: mendel.t.nguyen@durham.ac.uk

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

• HEP Lunchtime

Usual Venue: MCS0001

Contact: p.e.dorey@durham.ac.uk,enrico.andriolo@durham.ac.uk,tobias.p.hansen@durham.ac.uk

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

• Probability

Usual Venue: MCS2068

Contact: tyler.helmuth@durham.ac.uk,oliver.kelsey-tough@durham.ac.uk

Jan 15 14:00 Brett Kolesnik (University of Warwick): K_r-percolation

Start with an Erdõs–Rényi random graph G(n,p) and then iteratively add a missing edge if it creates a new copy of the complete graph K_r. We find the critical threshold probability p_c at which all other edges in K_n are eventually added to G(n,p). This solves a problem of Balogh, Bollobás, and Morris. Joint work with Zsolt Bartha, Gal Kronenberg, and Yuval Peled (arXiv:2510.26724).

Venue: MCS2068

• Pure Maths Colloquium

Usual Venue: MCS2068

Contact: michael.r.magee@durham.ac.uk

Jan 19 14:00 Jan Vonk (Leiden University, The Netherlands): An equation of Diophantus

This is the story of an old equation of Diophantus, which will take us on an excursion along a branch of number theory that stretches over an important part of the subject's history. It will be our motivation for a friendly introduction to some modern developments on torsion and ranks of elliptic curves.

Venue: MCS2068

• Spectra and Moduli

Usual Venue: MCS3070

Contact: 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

Jan 26 13:00 Adam Iqbal, Rakan Al Rekayan (Durham): TBA

TBA

Venue: MCS2068

Feb 02 13:00 Jon Cockayne (Southampton): TBA

TBA

Venue: MCS2068

Feb 09 13:00 Juraj Medzihorsky (Durham): TBA

TBA

Venue: MCS2068

Feb 16 13:00 Vanda Inacio (Edinburgh): TBA

TBA

Venue: MCS2068

Feb 23 13:00 Long Tran-Thanh (Warwick): TBA

TBA

Venue: MCS2068

Mar 02 13:00 Helen Ogden (Southampton): TBA

TBA

Venue: MCS2068

Mar 09 13:00 Irini Moustaki (LSE): TBA

TBA

Venue: MCS2068

Mar 16 13:00 Mengchu Li (Birmingham): TBA

TBA

Venue: MCS2068

• Stats4Grads

Contact: adam.stone2@durham.ac.uk

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

Special Series

These link to some of the special events hosted by the Department:


• [LMS|EPSRC] Durham Symposia (from 1974)
• Collingwood Lectures (from 1984)