OLGA 2022 is the third edition of a student-run seminar, targeted at everyone in the UK interested in gauge theory, mostly early career researchers. The event is planned as a two one-day in-person seminars in London and Oxford.
OLGA seeks to increase both the visibility and participation of underrepresented groups in the gauge theory community. We particularly encourage female, queer or non-white early career researchers in gauge theory or a related area to join the workshop. Also, we ask them to consider presenting a research poster, along with any others who might not have considered doing so otherwise. In order to guarantee the safety of everyone and encourage a good working environment, we require all participants to behave accordingly to our code of conduct.
The second day was cancelled due to extraordinary circumstances.
Schedule 11th November 2022 (times in Greenwich Mean Time):
Jakob Stein (University College London)
New families of \(G_2\)-instantons
Abstract: In this talk, we will review the theory of instantons on asymptotically conical (AC) metrics with exceptional holonomy \(G_2\), and discuss the construction of a new family of \(G_2\)-instantons using co-homogeneity one symmetries in a joint work with Matthew Turner (Bath).
Time permitting, we will discuss an ongoing project to use Hermitian Yang-Mills connections with these symmetries to construct \(G_2\)-instantons on asymptotically locally conical (ALC) \(G_2\) metrics.
Guillem Cazassus (University of Oxford)
Hamiltonian action on Floer homology and Fukaya categories
Abstract: I will talk about some algebraic structures arising on Lagrangian Floer homology and Fukaya categories in the presence of a Hamiltonian action of a compact Lie group.
On the one hand, this should be related to a conjecture of Teleman, motivated by Homological Mirror Symmetry. On the other hand, our motivation comes from gauge theory in low dimensions, and is part of a program aimed at recasting Donaldson-Floer theory into an extended field theory.
More speculatively, we also expect these structures to arise in higher dimensional gauge theory, following the Donaldson-Segal program, and in relation with the Moore-Tachikawa field theories.
This is based on two joint work in progress, one with Paul Kirk, Mike Miller-Eismeier and Wai-Kit Yeung, and another with Alex Hock and Thibaut Mazuir.
Derek Harland (University of Leeds)
Gauge theory and the Skyrme model
Abstract: The Skyrme model is a geometric model of nuclear physics based on generalisation of harmonic maps. Many of the tools that people use to study the Skyrme model come from gauge theory.
In this talk I will introduce the model, and explain how techniques such as the ADHM construction of instantons can be used to address long-standing problems in the model.
Ragini Singhal (King's College London)
Deformations of \(G_2\)-instantons on nearly \(G_2\) manifolds
Abstract: In this talk we will study the deformation theory of \(G_2\)-instantons on nearly \(G_2\) manifolds. There is a one-to-one correspondence between nearly parallel \(G_2\) structures and real Killing spinors, thus the deformation theory can be formulated in terms of spinors and Dirac operators.
We prove that the space of infinitesimal deformations of an instanton is isomorphic to the kernel of an elliptic operator. Using this formulation we prove that abelian instantons are rigid. Then we apply our results to describe the deformation space of the canonical connection on the four normal homogeneous nearly \(G_2\) manifolds. We also see that the deformation spaces obtained are integrable in one of the cases.
|Tea & Coffee|
Sir Simon Donaldson (Imperial College London)
Singularities in Yang-Mills fields in higher dimensions
Abstract: This will be an expository talk, with no new results. In the first part of the talk I will review some of the main facts, open questions and speculations about singular solutions and singularity formation for Yang-Mills fields, particularly for “instanton” solutions over manifolds with special holonomy.
The last part of the talk will be an expository outline of a (comparatively) recent proof by Smith and Uhlenbeck of the removability of codimension 4 singularities, under suitable hypotheses.
Provisional schedule 24th March 2023 (times in Greenwich Mean Time): [CANCELLED]
Please get in touch with the event organisers if you have further questions or comments.
Previous editions:OLGA I OLGA II
Alfred Holmes (University of Oxford, firstname.lastname@example.org)
Jaime Mendizabal (University College London, email@example.com)
Enric Solé-Farré (University College London/Imperial College firstname.lastname@example.org)