Wed, 07 May 2025
11:00
L5

On statistical stationary solutions to the Schrödinger Map Equation in 1D

Dr Emanuela Gussetti
(Bielefeld University)
Abstract

In this talk, we discuss the existence of statistically stationary solutions to the Schrödinger map equation on a one-dimensional domain, with null Neumann boundary conditions, or on the one-dimensional torus. To approximate the Schrödinger map equation, we employ the stochastic  Landau-Lifschitz-Gilbert equation. By a limiting procedure à la Kuksin, we establish existence of a random initial datum, whose distribution is preserved under the dynamic of the deterministic equation. We explore the relationship between the Schrödinger map equation, the binormal curvature flow and the cubic non-linear Schrödinger equation. Additionally, we prove existence of statistically stationary solutions to the binormal curvature flow.[https://arxiv.org/abs/2501.16499]

This is a joint work with Professor M. Hofmanová.

Wed, 30 Apr 2025
11:00
L5

Hydrodynamic limit of an active-passive lattice gas

Maria Bruna
(Mathematical Institute)
Abstract

In this talk, I will discuss a model mixture of active (self-propelled) and passive (diffusive) particles with non-reciprocal effective interactions (or forces that violate Newton’s third law). We derive the hydrodynamic PDE limit for the particle densities, which is not a Wasserstein gradient flow of any free energy, consistent with the microscopic model having non-equilibrium steady states. We study the emergence of collective behaviour, which includes phase separation and dynamical (travelling) steady states.

A modelling assessment for the impact of control measures on highly pathogenic avian influenza transmission in poultry in Great Britain
Davis, C Hill, E Jewell, C Rysava, K Thompson, R Tildesley, M
Tue, 27 May 2025
13:00
L5

Monopoles, Dirac Strings and Generalised Symmetries

Chris Hull
(Imperial)
Abstract

Dirac’s quantum theory of magnetic monopoles requires a Dirac string attached to each monopole, and it is important that the field equations do not depend on the positions of the Dirac strings, provided that they comply with the Dirac veto: they must not intersect the worldliness of electrically charged particles. This theory is revisited, and it is shown that it has generalised symmetries related to the freedom of moving the Dirac strings. The Dirac veto is interpreted as an anomaly and the possibility of cancelling the anomaly by embedding in a higher-dimensional theory will be discussed. 

This talk is based on arXiv:2411.18741.

Tue, 06 May 2025
13:00
L2

A Background-Independent Target Space Action for String Theory

Alex Frenkel
(Stanford)
Abstract
I will address the question of how background independent target space physics emerges in string theory. The point of view I will take is to identify the configuration space of target space with the space of 2d worldsheet QFTs. On-shell configurations are identified with c=0 worldsheet theories (i.e. a c=26 matter sector), and non-conformal QFTs correspond to generic off-shell configurations. I will demonstrate that a quantity built from the sphere partition function and the Zamolodchikov c-function has the correct properties to be a valid background-independent action on this configuration space, and is valid for all possible relevant and irrelevant deformations on the worldsheet (including non-minimally coupled and descendant operators). For the massless and tachyonic sectors in target space, this action is equivalent by field-redefinition to known actions developed by Tseytlin and collaborators in the 80s and 90s, constructed by taking derivatives with respect to the sphere partition function. This talk is based on recent work by Amr Ahmadain and Aron Wall (https://arxiv.org/abs/2410.11938).


 

The Oxford AI Gala sees 350 AI professionals, founders, and researchers gather on 31 May 2025 at the Oxford University Museum of Natural History. This event is a unique opportunity to connect with Oxford's world-class AI ecosystem, global industry leaders, and University of Oxford researchers and students.

The Oxford and Warwick SIAM Student Chapters are excited to announce the second annual Applied Mathematics Postgraduate (AMP) Conference, to be held on 30th June - 2nd July 2025 in the Mathematical Institute.

The event will consist of:

QSHS: An Axion Dark Matter Resonant Search Apparatus
Alsulami, A Bailey, I Carosi, G Chapman, G Chakraborty, B Daw, E Du, N Durham, S Esmenda, J Gallop, J Gamble, T Godfrey, T Gregori, G Halliday, J Hao, L Hardy, E Laird, E Leek, P March-Russell, J Meeson, P Mostyn, C Pashkin, Y Peatain, S Perry, M Piscitelli, M Reig, M Romans, E Sarkar, S Smith, P Sokolov, A Song, N Sundararajan, A Tan, B West, S Withington, S (16 Apr 2025)
Tue, 03 Jun 2025
15:30
L4

Bordism categories and orientations of moduli spaces

Dominic Joyce
(Oxford)
Abstract
In many situations in Differential or Algebraic Geometry, one forms moduli spaces $\cal M$ of geometric objects, such that $\cal M$ is a manifold, or something close to a manifold (a derived manifold, Kuranishi space, …). Then we can ask whether $\cal M$ is orientable, and if so, whether there is a natural choice of orientation.
  This is important in the definition of enumerative invariants: we arrange that the moduli space $\cal M$ is a compact oriented manifold (or derived manifold), so it has a fundamental class in homology, and the invariants are the integrals of natural cohomology classes over this fundamental class.
  For example, if $X$ is a compact oriented Riemannian 4-manifold, we can form moduli spaces $\cal M$ of instanton connections on some principal $G$-bundle $P$ over $X$, and the Donaldson invariants of $X$ are integrals over $\cal M$.
  In the paper arXiv:2503.20456, Markus Upmeier and I develop a theory of "bordism categories”, which are a new tool for studying orientability and canonical orientations of moduli spaces. It uses a lot of Algebraic Topology, and computation of bordism groups of classifying spaces. We apply it to study orientability and canonical orientations of moduli spaces of $G_2$ instantons and associative 3-folds on $G_2$ manifolds, and of Spin(7) instantons and Cayley 4-folds on Spin(7) manifolds, and of coherent sheaves on Calabi-Yau 4-folds. These have applications to enumerative invariants, in particular, to Donaldson-Thomas type invariants of Calabi-Yau 4-folds.
   All this is joint work with Markus Upmeier.
Nonequilibrium physics of brain dynamics
Nartallo-Kaluarachchi, R Kringelbach, M Deco, G Lambiotte, R Goriely, A (16 Apr 2025)
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