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


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Upcoming Seminars by Series

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• Amplitudes and Correlators

Contact: arthur.lipstein@durham.ac.uk

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

• 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

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

• 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): TBA

Venue: MCS2068

Jan 22 13:00 Chunyang Hu (Durham University): TBA

TBA

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 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

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

• 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)