Solitons at Work

Past Events

This is a repository of past events of various kinds.

Previous Seminars

7th April 2021, 10am BST.

Andrzej Wereszczynski - (Collapse of) the vibrational moduli space and soliton dynamics

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I will show that thin spectral walls (a long range intersoliton interaction due to a transition of the normal mode to the continuum spectrum) are common phenomena in the dynamics of kinks in (1+1) dimensions. They occur in models based on two or more scalar fields with a nonempty Bogomol'nyi-Prasad-Sommerfield (BPS) sector, hosting two zero modes, where they are one of the main factors governing the soliton dynamics. I will also show that they can be found as points where the dynamical vibrational moduli space has singularities.

31st March 2021, 10am BST.

Gabriel Luchini - Towards hidden symmetries in gauge theories

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In this talk, we address and solve two long standing problems in non-abelian gauge theories. The first one is the construction of truly gauge invariant electric and magnetic charges that are dynamically conserved. The second one is the proof that the Wu-Yang monopole configuration can only be a consistent solution of pure SU(2) Yang-Mills theory if a point source, of a very definite form, is added to it. Those two results were made possible by an educated use of the integral Yang-Mills equations. We end by showing how such integral equations can be used to uncover hidden symmetries of the Yang-Mills theory on loop space.

24th March 2021, 10am GMT.

Jarah Evslin - Quantum Kink States

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We introduce two (compatible) new methods for the treatment of quantum kinks. First, we present a simpler and faster alternative to collective coordinates in which the momentum operator is treated perturbatively. It is less powerful than collective coordinates, but well-suited to certain problems such as finding quantum kink states and mass corrections. Second, we note that if the kink sector Hamiltonian is defined by a unitary transformation on the defining regularized Hamiltonian, then it automatically has the same spectrum and no regulator matching condition need be imposed. This new definition solves a problem from the last century, when it was shown that the usual definition of the kink sector Hamiltonian leads to the wrong quantum kink mass if the theory is regulated with an energy cutoff. We then apply these two advances to calculate two-loop mass corrections to quantum kinks and to compute the corresponding quantum states at two loops. The ground state is treated, as well as states excited by normal modes.

17th March 2021, 10am GMT.

Avner Karasik - Skyrmions, one flavored baryons, and one current to rule them all

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It has been proposed by Komargodski in that baryons in Nf=1 QCD can be described as singular solitons in the effective theory of the eta' meson. This construction raises the question of continuity between these solitons and the standard skyrmions. I will introduce corrections to the skyrmion current in the effective theory of pions and vector mesons based on the idea of hidden local symmetry. The contribution to the charge from these corrections is non-trivial only for singular configurations as the Nf=1 baryons. This modified current gives a unified picture for the two types of baryons and allows them to continuously transform one to the other in a natural way. The desired corrections can be derived from the effective Lagrangian assuming specific interactions between pions and vector mesons.

Remarkably, these interactions coincide in the large N limit with the phenomenological principle of vector mesons dominance. This coincidence provides an experimental evidence for the construction of Nf=1 baryons, as well as a theoretical explanation to vector dominance.

10th March 2021, 10am GMT.

Yuki Amari - Isolated skyrmions in the CP2 nonlinear sigma model with a Dzyaloshinskii-Moriya type interaction

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We will discuss an SU(3) generalization of magnetic skyrmions. Magnetic skyrmions are two-dimensional topological solitons, in most cases, stabilized by the Dzyaloshinskii-Moriya (DM) interaction. For the SU(3) generalization, we first derive an SU(3) counterpart of the DM interaction from a spin system, as well as the CP^2 nonlinear sigma model simultaneously. Then, we construct soliton solutions in the CP^2 model with the SU(3) symmetric DM-type interaction. This talk is based on our recent paper arXiv:2101.10566.

3rd March 2021, 10am GMT.

Jose Queiruga - Some BPS deformations of the Skyrme model

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I will present several deformations of the Skyrme model in three dimensions with self-dual sectors of arbitrary baryonic charge. I will show that, for a family of background metrics as well as for a family of field dependent couplings, the model has one BPS sector, which may have any topological charge. In the gravitating case I will discuss the possible existence of BPS sectors provided that a cosmological constant is added to the model.

17th February 2021, 10am GMT.

Chris Halcrow - Baby skyrmions from lumps

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Consider two baby skyrmions. We understand their interaction when they are widely separated. We also understand what happens when they get close -- they form a ring solution and their individual identities are lost. But how are the separated skyrmions and ring solution connected? How do the degrees of freedom match up as you bring the skyrmions together?

I'll answer this question using lumps, a new approximation which uses a simple map on target space and a new numerical technique. Using these new tools we find new baby skyrmion dynamics and solve the two-baby quantum problem. This is the first time a non-BPS soliton quantum problem has been solved on a manifold with enough degrees of freedom to describe two free solitons.

3rd February 2021, 10am GMT.

Boris Malomed - Multidimensional solitons

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It is commonly known that the interplay of linear and nonlinear effects gives rise to solitons, i.e., self-trapped localized structures, in a wide range of physical settings, including optics, Bose-Einstein condensates (BECs), hydrodynamics, plasmas, condensed-matter physics, etc. Nowadays, solitons are considered as an interdisciplinary class of modes, which feature diverse internal structures.

While most experimental realizations and theoretical models of solitons have been elaborated in one-dimensional (1D) settings, a challenging issue is prediction of stable solitons in 2D and 3D media. In particular, multidimensional solitons may carry an intrinsic topological structure in the form of vorticity. In addition to the "simple" vortex solitons, fascinating objects featuring complex structures, such as hopfions, i.e., vortex rings with internal twist, have been predicted too.

A fundamental problem is propensity of multidimensional solitons to being unstable (naturally, solitons with a more sophisticated structure, such as vortex solitons, are more vulnerable to instabilities). Recently, novel perspectives for the creation of stable 2D and 3D solitons were brought to the attention of researchers in optics and BEC. The present talk aims to provide an overview of the main results and ongoing developments in this vast field. An essential conclusion is the benefit offered by the exchange of concepts between different areas, such as optics, BEC, and hydrodynamics.

16th December 2020, 10am GMT.

Andy Royston - Accelerating Solitons

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We review soliton quantization in two-dimensional linear sigma models via the phase space path integral formalism. Working semiclassically, but relaxing the adiabatic assumption, leads to a new saddlepoint equation -- the forced soliton equation -- representing a kink undergoing arbitrary acceleration. We evaluate matrix elements of local operators between soliton states, at leading order in the semiclassical expansion but at arbitrary momentum transfer, in terms of (hypothetical) solutions to the forced soliton equation. Such matrix elements are related, by crossing symmetry, to the creation amplitude for virtual soliton-antisoliton pairs. This talk is based on work done in collaboration with Ilarion Melnikov and Costis Papageorgakis.

9th December 2020, 10am GMT.

Lorenzo Bartolini - Holographic QCD and Skyrmions

We did not record this seminar. Lorenzo gave a similar seminar at the Henan University Math Phys seminar series, which can be found here.

The holographic duality (also known as Gauge/Strings duality) has proven to be a powerful tool to obtain qualitative and often quantitative insights on the physics of strongly coupled systems. In this talk we review the top-down holographic model of QCD developed by Sakai and Sugimoto (after introducing some basic facts about string theory and QCD) with particular attention to the description of baryons and its ties to the concept of the baryon as a topological soliton. Then we show some recent results we obtained within the model: as a first step we show how a generalized Skyrme model is contained as a low energy limit of the Sakai-Sugimoto model, then we proceed to use the full model with an additional theta-term perturbation to compute the deformation of the baryons and the electric dipole moment it induces for the proton and the neutron (and as a result, for the deuteron). Finally, we provide a short overview of the current research areas on which we are employing the holographic approach and discuss their future directions.

2nd December 2020, 10am GMT.

Àrpàd Lukàcs - Q-balls in Abelian gauge theories coupled to U(1)×U(1) symmetric scalar fields

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In a series of recent works, Ishihara and Ogawa have investigated nontopological solitons (Q-balls) in a spontaneously broken Abelian gauge theory coupled to two complex scalar fields. The present paper extends their investigations to the most general U(1)×U(1) symmetric quartic potential. Also, a new class of charged Q-ball solutions with vanishing self-interaction terms is investigated and some of their remarkable properties are exhibited.

25th November 2020, 10am GMT.

Stavros Komineas - Dynamics of skyrmions in ferromagnets

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Both an axially-symmetric topological skyrmion with skyrmion number Q=1 and a non-topological skyrmionium with Q=0 are stable magnetization structures in Dzyaloshinskii-Moriya ferromagnets with easy-axis anisotropy. A topologically trivial (Q=0) configuration in the form of a skyrmion-antiskyrmion pair, called a chiral droplet, is stabilised in the same material.

We study the dynamics of a skyrmion and a skyrmionium under an external field gradient as well as under spin-transfer torque. Our analysis is based on an important link between topology and dynamics which is established through the construction of unambiguous conservation laws. The non-topological Q=0 skyrmionium is accelerated in the direction of the force (the field gradient) thus exhibiting ordinary Newtonian motion. In contrast, the topological Q=1 skyrmion undergoes Hall motion perpendicular to the direction of the force with a drift velocity proportional to it. When the force is switched-off the Q=1 skyrmion is spontaneously pinned whereas the Q=0 skyrmionium continues propagation.

Further, we study the motion of the skyrmionium in the case of spin-transfer torque and observe that this converges to a traveling skyrmionium with a constant velocity. Its velocity is analyzed in two parts: one due to the current flow and a second one acquired by Newtonian acceleration. Similar results are obtained for the chiral droplet.

18th November 2020, 10am GMT.

Maciej Dunajski - Kinks on a wormhole

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The sine-Gordon equation in 1+1 dimensions admits a static kink solution with with topological charge 1. The kinks do not exist in flat d+1 dimensions, where d>1. I shall prove the existence of static kinks on 3+1 dimensional curved wormhole space-time with two asymptotically flat regions, and discuss linear and non-linear stability of the kinks in the sine-Gordon and \phi^4 theory. This is joint work with Piotr Bizon, Michal Kahl, Michal Kowalczyk and Alice Waterhouse.

11th November 2020, 10am GMT.

Yasha Shnir - Solitons, Boson stars and Hairy Black Holes

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We study a new families of stationary rotating axially symmetric hairy black holes which represent solutions of the Einstein-Skyrme model in the Kerr spacetime. We found that the spinning axially symmetric cloudy solutions of the model also exist in the regular asymptotically flat space-time without the event horizon. The latter congurations are similar to the usual rotating boson stars, which, in the at flat space limit are linked to the axially symmetric Q-balls, in both cases the solutions exist for some restricted range of values of the angular frequency and possess a quantized angular momentum. Considering similar solution in the O(3) sigma model, we show that, depending on the values of the parameters of the model and the Hawking temperature, the branch structure of the corresponding cloudy solutions varies from the usual inspirraling pattern, which is typical for the boson stars, to the two branch structure, similar to that of the black holes with Skyrme hairs. As another examples of spinning black holes with synchronized hairs we consider families of parity-odd solutions of the Einstein-Klein-Gordon model. Finally, we discuss Dirac stars and compare their properties with the usual boson stars.

4th November 2020, 10am GMT.

David Ho - The Electroweak Sphaleron in a strong magnetic field

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The Electroweak sphaleron is an unstable solution to the field equations of Electroweak theory and is a source of baryon and lepton number violation in the Standard Model. In this talk, I will present the results of a numerical study into the effect of an external magnetic field on the sphaleron solution. I will show that the sphaleron energy vanishes precisely at the critical field strength where the Higgs symmetry is restored, where there is the potential for unsuppressed baryogenesis. I will also discuss the implications of these results on the possibility of observing sphaleron processes in heavy-ion collisions.

28th October 2020, 10am GMT.

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Tomasz Romanczukiewicz - Kinky collisions - are we there yet?

I would like to give an overview of what was done in the past with an emphasis on the most recent discoveries. There are a few new angles that can give us some new insight into these perversely complicated collisions of the simplest topological defects.

Henan Seminar: 28th October 2020, 2am GMT(UTC).

Yong-Liang Ma - Dichotomy of Baryons as Quantum Hall Droplets and Skyrmions in Compact-Star Matter

We discuss the ``sheet structure" of compressed baryonic matter possibly present in massive compact stars in terms of quantum Hall droplets and skyrmions for baryons in medium. The theoretical framework is anchored on a generalized scale symmetric hidden local symmetry that encompasses standard nuclear effective field theory (sEFT) and can access the density regimes relevant to massive compact stars. It hints at a basically different, hitherto unexplored structure of the densest baryonic matter stable against collapse to black hole. Hidden scale symmetry and hidden local symmetry together in nuclear effective field theory are seen to play a potentially crucial role in providing the hadron-quark duality in compressed baryonic matter.

30th September 2020, 10am BST.

Rene Garcia-Lara - Asymetric vortex-antivortex pairs of a gauged O(3) Sigma model

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Vortices of the gauged O(3) Sigma model are topological solitons appearing after breaking scale invariance in the model with the addition of a convenient potential term. At critical coupling, the model admits BPS static solutions forming a moduli space which carries a complex structure and a Kahler metric. In general, the moduli space of k+ vortices and k- antivortices is incomplete due to the impossibility of a vortex and an antivortex to coalesce. Shifting the vacuum manifold by a constant displacement tau, we obtain an asymmetric model in which vortices and antivortices have different effective mass and size. I will review the model and the L2 metric, and then explain how the governing elliptic problem relates to the properties of the metric for vortices and antivortices on the plane, concluding with some numerical results comparing the properties of the metric for different values of tau.

30th September 2020, 10am BST.

Marco Barsanti - Near-BPS baby skyrmions and nuclear matter

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The Skyrme model is a good candidate for describing the low-energy phase of QCD. It consists of a meson field theory whose static classical solutions are stable due to their geometrical properties. These "collective excitations" of the meson field, known as topological solitons, are called Skyrmions and they are supposed to describe the baryons and nuclei. Beyond the various successful results in the description of the nuclear matter, one of the main problems remains the too large binding energy predicted by the model for the nuclei. To this end, we proposed a field theory, known as "near-BPS model", that is supposed to resolve this problem.

23rd September 2020, 10am BST.

Miguel Huidobro Garcia and Alberto Garcia Martin-Caro - Neutron star properties from a generalized Skyrme model

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In this talk we will review the generalized Skyrme model ---the standard Skyrme model plus the sextic term--- as a suitable description of nuclear matter inside Neutron Stars (NS).

In the first part, we will follow previous approaches to obtain the Equation Of State (EOS) of nuclear matter at supranuclear densities based on Skyrmion crystals as well as fluid-like BPS solutions, and propose a new EOS based on the generalized Skyrme model that takes into account both crystalline and BPS properties at different pressure regimes.

In the second part, we will show how we can constrain the values of the free parameters of this new EOS by fitting some observable properties of stars, such as maximum masses and deformability, to the most recent observations of NS properties from the gravitational wave data of binary NS mergers.

16th September 2020, 10am BST.

Bruno Barton-Singer - Forces between well-separated magnetic skyrmions

Magnetic skyrmions are topologically non-trivial solutions to the 2D chiral magnet energy functional, similar to baby skyrmions but supported by the first-order Dzyaloshinskii-Moriya interaction (DMI) rather than a fourth-order term. This DMI can be interpreted as an SU(2) gauging of the O(3) sigma model.

Like baby skyrmions, their interaction forces can be calculated asymptotically based on certain approximations, and the DMI leads to an interaction energy that looks like a U(1) gauging of the baby skyrmion interaction energy. In this talk I will derive and apply this formula to a particular case, of skyrmions interacting in a background tilted magnetic field, and compare it to numerical results from the paper 'Turning a chiral skyrmion inside out' . The interaction has an unusual oscillating form.

16th September 2020, 10am BST.

Calum Ross - Magnetic skyrmions in solvable chiral magnets

In a previous talk in this series we met a two dimensional model of chiral magnets which is of Bogomol'nyi type. I will review this model before discussing a more general model, the solvable line, where we can construct exact single skyrmion solutions. Armed with these exact skyrmion configurations I want to present a first attempt at studying the interactions of these skyrmion configurations. Finally we can use the results about the interaction energy to try to construct a skyrmion lattice state, which is a candidate ground state for the model in particular parameter regions. This is based on joint work with Norisuke Sakai and Muneto Nitta contained in arXiv: 2003.07147.

9th September 2020, 10am BST.

Nick Manton and Katarzyna Oles - Collective Coordinate Geometry for Kinks and Antikinks

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We consider different possibilities for moduli spaces (collective coordinate manifolds) modelling kink-antikink(-kink) dynamics in sine-Gordon and phi^4 theory. The simplest construction based on a superposition of exact kink and antikink solutions can sometimes be improved by including a weight factor and/or by redefining the moduli. This allows us to solve the long-standing null vector problem for the superposed shape modes in phi^4 theory. In certain cases, a kink-antikink collision can be interpreted as a 90-degree scattering of the complexified kink position (separation).

2nd September 2020, 10am BST.

Jack McKenna - Fermions with background baby Skyrmion on S^2

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Fermions coupled to topological solitons can feature zero-energy modes, physically interpreted as bound states where the fermion is localised by the soliton. In some examples of Skyrmions and baby Skyrmions, it is known that these modes have zero energy for a critical value of the coupling constant. On S^3, the fermion coupled to a symmetric Skyrmion features a "chiral shift" where this localised mode, as well as some energy spectra for other modes, are asymmetric in their dependence on the coupling constant. I will briefly discuss my progress and some preliminary results in exploring the analogous system one dimension lower, of a fermion coupled to a baby Skyrmion on S^2.

2nd September 2020, 10am BST.

Josh Cork - A model for gauged skyrmions with low binding energies

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One of the major drawbacks of the Skyrme model is how it severely overestimates nuclear binding energies when compared to experimental results. One of the many proposed modifications for remedying this is a model introduced by Sutcliffe, derived from dimensional reduction of Yang-Mills theory on \mathbb{R}^4. The same approach can be applied to Yang-Mills theory on S^1\times\mathbb{R}^3, from which one obtains an SU(2) gauged Skyrme model. SU(2) instantons on S^1\times\mathbb{R}^3, also known as calorons, are natural examples from which to approximate gauged skyrmions, whose boundary conditions break the gauge group to U(1), and thus provide a natural way to incorporate an electromagnetic field into the Skyrme model. In this talk, I will present some joint work with Derek Harland, and Thomas Winyard, where we consider skyrmions generated from calorons with non-trivial holonomy, which we have used as a 'toy model' for calibrating the gauged model to optimise the ratio Energy/(Lower bound), with a view to developing a U(1) gauged Skyrme model with low binding energies.

26th August 2020, 10am BST.

Derek Harland and Chris Halcrow - The nucleon-nucleon interaction from Skyrmions

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In nuclear physics, one tries to describe the properties of atomic nuclei starting from the nucleon-nucleon (NN) interaction. Hence the NN problem is often called the fundamental problem in nuclear physics and its successful derivation from the Skyrme model would be a major success. Unfortunately, previous attempts have struggled to describe important and well-established features, such as the (isoscalar) spin-orbit interaction. Our new approach overcomes many of these problems. It shows that previous difficulties were a result of over-reliance on the product approximation, rather than problems with the Skyrme model itself.

19th August 2020, 10am BST.

Andrzej Wereszczynski - The Skyrme model with running coupling constants

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I will discuss the Skyrme model where both the kinetic term and the Skyrme term are multiplied by field-dependent coupling functions. For suitable choices, this "dielectric Skyrme model" has static solutions saturating the pertinent topological bound in the sector of baryon number B = ±1. Higher charge field configurations are unbound, and loosely bound higher skyrmions can be achieved by small deformations of this dielectric Skyrme model.

I will also consider inclusion of the sextic and the potential term and a possible relation with in-medium properties of chiral solitons.

12th August 2020, 10am BST.

Bernd Schroers - Magnetic Skyrmions andd Chiral Kinks

Chiral magnetic skyrmions are topological solitons in two-dimensional magnetic systems which are stabilised by the Dzyaloshinskii-Moriya interaction (DMI). For each DMI term, there is a model for magnetic skyrmions which is of Bogomol'nyi type and where solitons can be written down explicitly in terms of holomorphic functions. In this talk I will explain how these exact solutions can be used as initial configurations in a numerical scheme to obtain magnetic skyrmions away from the Bogomol'nyi point. This approach reveals a remarkable diversity of magnetic skyrmions and suggests a new way of interpreting their structure. In particular, configurations with positive topological charge are best understood in terms of one-dimensional domain walls carrying chiral kinks. I will explain this point of view, and speculate about possible generalisations. The talk is based on joint work with Vlad Kuchkin, Bruno Barton-Singer, Filipp Rybakov, Stefan Bluegel and Nikolai Kiselev, and on arxiv preprint 2007.06260.

Previous Coffee Clubs

2nd April 2021, 10am BST

26th March 2021, 10am GMT

19th March 2021, 10am GMT

12th March 2021, 10am GMT

5th March 2021, 10am GMT

26th February 2021, 10am GMT

19th February 2021, 10am GMT

12th February 2021, 10am GMT

Topic: Malomed's talk

5th February 2021, 10am GMT

18th December 2020, 10am GMT(UTC) - Christmas Party

Initial presenter: Father Christmas

4th December 2020, 10am BST.

Nick Manton - Large Skyrmions - Slides

27th November 2020, 10am GMT(UTC) - Hitchin's equations

Initial presenter: Calum Ross

20th November 2020, 10am GMT(UTC) - Asymptotic interactions of solitons

Initial presenter: Derek Harland

6th November 2020, 10am GMT(UTC) - Thermodynamic properties of solitons

Initial presenters: Andrzej Wereszczynski

30th October 2020, 10am GMT(UTC) - Magnetic Skyrmions

Initial presenters: Bruno Barton-Singer and Calum Ross

23th October 2020, 10am BST - Quantization of Skyrmions

Initial presenter: Christoph Adam

16th October 2020, 10am BST - Spectral walls

Initial presenter: Chris Halcrow

Previous Training

Starting November 19th, 2020

Carlos Naya - Numerical methods for solitons

A project based mini-course aimed at PhD students, and anyone else, who want to learn the basics of soliton numerics. Depending on progress, topics may include.

  • Review of the gradient flow method and its application to 1-dimensional problems.
  • Application of the previous concepts to other 1-dimensional structures such as kinks. Mainly practical sessions to acquire the corresponding capabilities.
  • Generalisation to 2-dimensional solitons by focusing on baby Skyrmions. Presentation of new required concepts and acquisition of the new skills by practical problems.
  • Further generalisation to 3-dimensional solitons to set the grounds for the study of Skyrmions in 3 dimensions and related objects.

The sessions will take place at 10am on Thursdays, starting November 19th 2020. If you'd like to join, please get in touch with Carlos at carlos.naya (at) le (dot) infn (dot) it or Chris at c.j.halcrow (at) leeds (dot) ac (dot) uk.

Old News

Jobs at Kent

There are two lectureships being advertised at the University of Kent, home to soliton Steffen Krusch. A 3-year lectureship in Applied Mathematics ( with deadline is 7th March 2021 and a 3-year lectureship in Pure Mathematics ( with deadline is 19th March 2021.

For more details, contact Steffen Krusch.

Henan University Short Course on Moduli Spaces

Henan University is organizing a short course on "Moduli Spaces in Gauge Theory" taught by Nuno Romão (U. Augsburg) in two parts, starting on 24th November 2020.
Part I will be an introduction to gauge theory in fiber bundles, and Part II will cover moduli of symplectic vortices. For more details, see Training.

LMS lectures on solitons

The LMS and the YDGD have announced a 5 week lecture course on solitons, aimed at starting PhD students. More details can be found here:

Postdoc Positions at Henan University

The mathematical physics group at Henan University has currently an opening for one or more postdoc positions, see the announcement on inspire.

Solitons at Work is launched

Solitons at Work aims to be a network for people working on solitons. We hope to strengthen the soliton community by organising events, holding training for PhD students and creating a central hub where people can advertise their events, jobs, papers and anything else!

Please take a look around the website. There are already ways you can contribute: send in a picture for the gallery, write a news item, or ask for an external link to be added to our list. This project is in its infacy, and this website will hopefully grow as time goes on. We also want more people to help steer and organise the project. More details to follow!