Solitons at Work

## Past Events

This is a repository of past events of various kinds.

## Previous Seminars

### 1st February 2023 - 10am GMT

#### Harry Braden - Curves and Monopoles: Old and New

The modern approach to integrable systems typically proceeds via a curve, the spectral curve, with the parameters of the curve encoding the actions of the system and the solutions of the integrable system being built from appropriate functions on the curve. I will describe some generic features of this approach, focussing particularly on the curve, and illustrate a number of new and old results. Throughout I will focus on BPS monopoles for the system of equations of interest though the results are more widely applicable.

### 14th December 2022, 10am GMT

#### Maxim Chernodub - Rotation with imaginary angular frequency in Yang-Mills theories: calorons, phase structure, and fractals

We find an instanton (caloron) solution in the finite-temperature SU(2) gluon gas subjected to (imaginary, in Euclidean spacetime) rotation. We demonstrate that the imaginary rotation leads to the delocalization of its topological charge over fractionally charged constituents. Furthermore, we show that in the high-temperature limit, the rapidly-rotating caloron becomes a circulon'': a self-dual monopole (dyon) possessing a spatial toroidal core. We also present the results of first-principle numerical simulations of Euclidean SU(3) Yang-Mills plasma rotating with a high imaginary angular frequency and discuss fractal thermodynamics associated with imaginary rotation.

### 7th December 2022 - 10am GMT

#### Kai Shao - Vortices and cosmic strings in the Born-Infeld model

The Born-Infeld theory has long been an important nonlinear model in electrodynamics. The model was introduced by Max Born and Leopold Infeld to overcome the issue of the infinite energy of electric point charge. This talk is focused on vortices and cosmic strings in the Born-Infeld theory. After a brief introduction to the classical Born-Infeld model, I will discuss a generalized Born-Infeld model and its BPS equations. I will present the existence of the solution with prescribed vortices to the system using the method from PDE. After that, I will discuss the cosmic string problem when the equations of motion of the Born-Infeld model are coupled with the Einstein equations. The cosmic strings are realized as static solutions with prescribed zeros to the coupled system. I will also discuss the proof of the existence of such solutions.

### 30th November 2022 - 10am GMT

#### Filip Blaschke - Mechanization of scalar fields in 1+1-dimensions - An agnostic approach to Collective Coordinate Models

We present a general-purpose Collective Coordinate Model for scalar field dynamics in 1+1 dimensions that we dubb mechanization'. The idea is to chop up' a continuous field into N straight segments. The positions of joints and slopes of the segments become the collective coordinates in a family of effective mechanical theories.

We show that even such a simplistic triangulation' of configuration space does capture all essential phenomena of field dynamics in the case of the ϕ4 model. We emphasize the benefits and drawbacks of our approach and point out future directions.

### 16th November 2022, 10am GMT

#### Pawel Klimas - Compact oscillons

Compact oscillons are peculiar exact solutions in the signum Gordon model. Unperturbed, they live indefinitely without losing energy. They also play an important role as a mechanism of emission of energy from excited kinks in models with non-analytic (V-shaped) potentials where the mass threshold is formally infinite. The radiation spectrum in such models is dominated by oscillon-type compact packages. I will discuss these solutions and their interaction which involves a scattering problem considering oscillon-oscillon and oscillon-kink configurations.

### 9th November 2022, 4pm GMT

#### Fabrizio Canfora - Analytic techniques in the analysis of solitons in the low energy limit of QCD

In this talk effective analytic techniques able to disclose relevant physical features of the non-perturbative configurations of the low energy limit of QCD will be introduced. In particular, it will be discussed how such framework allows to analyze explicitly transport properties of Baryonic tubes and layers. The electric and thermal conductivities as well as the shear viscosity of the known analytic hadronic non homogeneous condensates at finite Baryon density in the Skyrme model in (3+1) dimensions will be discussed. The qualitative agreement of the analytic formulas with the phenomenological data will be emphasized.

### 2nd November 2022, 10am GMT

#### Benjamin Bode - Stable knots and links in electromagnetic fields

An electromagnetic field consists of two time-dependent vector fields on ℝ3, namely the electric and the magnetic field, which together satisfy Maxwell's equations. Sets of closed flow lines of a vector field form a link. We show that for every link L there is an electromagnetic field, whose magnetic field has a set of closed flow lines ambient isotopic to L for all time, and whose time evolution is given by pushforwards by a family of diffeomorphisms.

The closed flow lines turn out to be projections of real analytic Legendrian links with respect to the standard contact structure on the 3-sphere.

If time permits, I will also discuss similar stability results for nodal links (or vortex links) that are formed by the zeros of the fields.

### 26th October 2022 - 10am BST

#### Albert Samoilenka - Ground state fractal crystals

Is it possible to have a fractal as a stable state of a classical field theory? Are uniform, wave-like states and solitons all there is to it? We propose a simple continuous-space-discrete-field model whose ground state is a crystal, where each unit cell is a fractal. Based on arXiv:2206.04343.

### 19th October 2022 - 10am BST

#### Claire Cisowski - Optical Skyrmions

We introduce a simple mathematical expression based on rational maps to construct ideal paraxial optical skyrmions fields including Neel-type and Bloch-type skyrmions, anti-skyrmions, bimerons and multi-skyrmions, including skyrmion lattices. We review the rules that fully polarized paraxial light fields must obey to be considered as optical skyrmions. This work provides guidelines for the experimental generation of general skyrmion fields, beyond conventional single skyrmion beams. This lays the foundation for the exploration of nucleation and annihilation mechanisms in multiskyrmions fields. Based on arXiv:2207.12741

### 12th October 2022 - 10am BST

#### Azadeh Mohammadi - Fermion mediated resonance in fermion-kink systems

This talk will focus on fermions bound by kink structures. This subject has been considered several times in the literature. However, in many of these studies, the back reaction of the fermions on the kinks has been neglected or considered only in the static case. We included the back reaction of the fermion on the colliding kink-antikink. The fermion field generates a force, either attractive or repulsive, depending on the distribution of the fermion field on kink and antikink. We have shown that the collision and the consequent resonance windows could be highly affected by the presence of the fermion. In this talk, I will also present one of the most fascinating conclusions of our study, which was that the fermion could also mediate the energy exchange mechanism, generating resonance windows even for integrable sine-Gordon model.

### 28th September 2022 - 10am BST

#### Tigran Tchrakian - Chern-Simons (CS), Higgs--Chern-Simons (HCS) and Skyrme--Chern-Simons (SCS)

After some standard definitions, certain examples of solitons in systems featuring Chern-Simons (CS) dynamics are quoted. Specifically, the unusual dependence of the mass on electric-charge and angular momentum are quoted in Abelian gauged 2+1 and 4+1 dimensional models including CS terms. (In the 2+1 dimensional case, also the "baryon number" can change.) Motivated by these results, it is proposed to find CS-like densities for systems in both odd and even dimensions, and all (allowed) gauge groups. The first of these are the Higgs-CS (HCS) densities which result from the dimensional descent of Chern-Pontryagin densities, and the second are the Skyrme-CS (SCS) densities that are extracted from the gauge deformed baryon number densities that are themselves defined in all dimensions and for all (allowed) gauge groups. It turns out that the SCS densities are useful for application in soliton construction, while the HCS find application in Chern-Simons gravities.

### Geometric Models of Nuclear Matter Conference

For more details, and a nicer table, go to the Conference Website.

To watch a recorded talk, just click on the talk title.

There are also posters!

#### DAY 1: Wednesday 20th July

Time (BST) Speaker Title
10:00-10:30 Martin Speight Geometry of vortices in the sphere in the dissolving limit
10:40-11:10 Josh Cork ADHM skyrmions
11:50-12:20 Jack McKenna A (1+1)d model of soliton-fermion coupling with analytic solutions
12:30-13:00 Carlos Naya Hunting 3D solitons in frustrated magnets
14:30-15:00 Calum Ross Calorons and constituent monopoles
15:10-15:40 Nicholas Manton Skyrmions, Isospin and Beta decay
16:30-17:00 Arpad Lukacs Stability analysis of electroweak-dark strings

#### DAY 2: Thursday 21st July

Time (BST) Speaker Title
10:00-10:30 Paul Sutcliffe A broken Skyrme model
10:40-11:10 Maciej Dunajski Elizabethan vortices
11:50-12:20 Matthew Wheeler Vortex connections across topological interfaces in spin-2 BECs
12:30-13:00 Patrick Dorey Resonant collisions of weakly-bound kinks
14:30-15:00 Shota Yanai Variety of Q-compactons and compact boson star
15:10-15:40 Jarah Evslin A Very Linear Perturbation Theory for Quantum Solitons
16:30-17:00 Thomas Galvin Monopoles of Large Magnetic Charge

#### DAY 3: Friday 22nd July

Time (BST) Speaker Title
10:00-10:30 Derek Harland Instantons and the nucleon-nucleon potential
10:40-11:10 Nuno Romao A tale of two metrics
11:50-12:20 Paul Leask Skyrmion Crystals
12:30-13:00 Alberto Alonso Izquierdo Wobbling kinks in the φ4 and MSTB models: interaction between shape modes
14:30-15:00 Marco Barsanti Near-BPS Skyrmions
15:10-15:40 Magnus Borgh Towards Non-Abelian Defects: Vortices with Discrete Point-Group Symmetries
16:30-17:00 Nicholas Manton Summary

### 29th June 2022 - 10am BST

#### SIG X: Peter Forgacs & Lucacs Arpad - Q-balls: Something old and something new, with components one and two

Watch Peter's talk and Arpad's talk on Youtube.

### 27th June 2022 - 2pm BST

#### SIG X: Zoltan Bajnok & Marton Lajer - Bootstrapping and measuring S-matrices and form factors

Watch Zoltan's talk and Marton's talk on Youtube.

### 24th June 2022 - 10am BST

#### SIG X: Bruno Barton-Singer - Magnetic skyrmion stability

Open problems:

How are the 'zero tension domain wall' and 'diverging decay lengthscale methods of calculating elliptical instability' related?

Can we model the collapse instability?

Can we find lower-energy periodic groundstates of the chiral magnet than those found so far by using higher charge solutions/varying the lattice properly as well?

### 22nd June 2022 - 10am BST

#### SIG X: Miguel Huidobro - Asymmetric nuclear EoS and kaon condensation in Skyrme neutron stars

Open problems:

Is it possible to construct a full EoS (from the crust to high densities) within the Skyrme model?

More nuclear physics observables are needed to constrain the values of the parameters, since NS observations are too not restrictive. A good try could be to fit the compression modulus.

Also the Coulomb energy seems important in the low density regime of the neutron star. Maybe we could be appear to describe the pasta phase structures with the Skyrme model.

### 27th April 2022 - 10am BST

#### Nick Manton - Quantum Statistical Mechanics of Vortices

The classical statistical mechanics of BPS (Abelian Higgs) vortices was calculated exactly some time ago, assuming purely kinetic dynamics on moduli space. This talk discusses the quantised analogue, where the Hamiltonian is proportional to the Laplace--Beltrami operator on moduli space. The asymptotic partition function at high temperature combines the classical result and the first quantum correction, which depends on a curvature integral. The quantum correction can reverse the sign of the second viral coefficient.

### 6th April 2022 - 10am BST

#### Alberto Garcia Martin-Caro and Muigel Huidobro - Quantization and low density regime of Skyrme crystals.

The Skyrme crystals are periodic, infinitely extended solutions which can be used to describe isospin-symmetric infinite nuclear matter. However, isospin asymmetry must be taken into account for a more accurate description of matter inside neutron stars. In the first part of the talk we will present the results of including the symmetry energy effects via the canonical quantization of collective coordinates of the Skyrme crystals, which also allows us to constrain the parameters of the model with measurements from nuclear experiments. In the second part we will explain the problem of describing the crust of NS with Skyrme crystals, and how a new set of periodic solutions, combined with quantum corrections, can help to solve this problem. Besides, the existence of these new solutions points towards the presence of a transition between different solutions near the crystal energy minimum.

### 30th March 2022 - 10am BST

#### Emine Şeyma Kutluk - Adiabatic Solutions in General Relativity as Null Geodesics on the Space of Boundary Diffeomorphisms

We use Manton approximation for general relativity on manifolds with spatial boundary; which results in a description of the slow-time dependent solutions as null geodesics on the space of boundary diffeomorphisms, with respect to a metric we prove to be composed solely of the boundary data. We show/conjecture how the solutions in the bulk space are fixed via the constraint equations of general relativity. Furthermore, we identify our resulting Lagrangian as a generalized version of the covariantized Lagrangian for continuum mechanics. We study the cases of 3+1 and 2+1 dimensions and show that for the solutions we propose, the -harder to untangle- Hamiltonian constraint becomes the real homogeneous Monge-Ampere equation in the special case of two spatial dimensions.

### 23rd March 2022 - 10am GMT

#### Prim Plansangkate - Quadric Ansatz for the mn-dKP Equation and related Einstein-Weyl Spaces

We consider two multi-dimensional generalisations of the dispersionless Kadomtsev-Petviashvili (dKP) equation. For one of these generalisations, we study solutions which are constant on a central quadric. The quadric ansatz leads to a second order ODE which is equivalent to Painleve I or II for the dKP equation, but fails to pass the Painleve test in higher dimensions. The second generalisation of the dKP equation leads to a class of Einstein-Weyl structures in an arbitrary dimension, which is characterised by the existence of a parallel weighted vector field, together with further holonomy reduction. We obtain an explicit local form for a family of Einstein-Weyl spaces belonging to this class, and depending on one arbitrary function of one variable.

### 16th March 2022, 10am GMT.

#### Kaushlendra Kumar - Yang-Mills solutions on Minkowski space via non-compact coset spaces

We compute solutions of Yang-Mills equation on Minkowski space by foliating different parts of it with non-compact coset spaces arising from the Lorentz group SO(1,3). The interior of the lightcone is foliated with hyperbolic space H3 which is isomorphic to SO(1,3)/SO(3), while the exterior of the lightcone isfoliated with de Sitter space dS3 which is isomorphic to SO(1,3)/SO(1,2). The equivariant reduction of the Yang-Mills system on these coset spaces yields a mechanical system with inverted potential admitting analytic solutions, including the "kink". We also present the energy-momentum tensor for these solutions.

### 9th March 2022, 10am GMT.

#### Calum Ross - Calorons and constituent monopoles

Calorons are instantons on ℝ3×S1, e.g. instantons with a periodic direction. Depending on the size of the circle they can look like instantons on ℝ4 or monopoles on ℝ3. The known examples, such as those due to Krann-van Baal and Lee-Lu, have an interpretation in terms of constituent monopoles. This picture can be formalised to give a construction of SU(2) calorons as a superposition of BPS monopoles and "rotated BPS" monopoles glued into a singular background. The singular background consists of Abelian Dirac monopoles with both positive and negative charges. I will sketch some of the basics about calorons and give an outline of this construction as well as how it can be generalised to G calorons, for G an arbitrary simple group. This is joint work with Lorenzo Foscolo.

### 2nd March 2022, 10am GMT.

#### Julien Garaud - Quartic bosonic metallic state and its topological properties

Superconductivity is an ordered quantum state with a long-range coherence of pairs of electrons, the Cooper pairs, which leads to zero resistivity and diamagnetism. I will present the recent observations of a new resistive state, coined quartic bosonic metal, characterized by the absence of long-range order between Cooper pairs but with order between pairs of pairs.

Unlike the superconductors, which break the U(1) gauge symmetry, this state spontaneously breaks the (discrete) time-reversal symmetry, and exhibits unconventional magnetic properties. I will demonstrate that the quartic bosonic metal state can be effectively accounted for, by a Faddeev-Skyrme-like model for the four-fermion order parameter. Its spectrum of topological excitations is rich, as it hosts domain-walls, magnetic-flux-carrying skyrmions, and most likely hopfions.

### 23rd February 2022, 10am GMT.

#### Bruno Barton-Singer - Long-range magnetic soliton interactions and the elliptical instability

The chiral magnet supports a range of solitons, such as the skyrmion (Q=-1) antiskyrmion (Q=+1) and skyrmionium (Q=0) solutions. When there is a magnetic field applied to the magnet at an arbitrary tilt, skyrmion and antiskyrmion solutions are known to still be stable. Only the interaction potential between two skyrmions in untilted field has been calculated explicitly up until now. Separately, the stability regions of these solitons have been numerically observed but not much explained.

In this talk I will discuss the interaction potential between skyrmions and antiskyrmions in tilted field and the interaction potential in untilted field between more novel configurations. Along the way I will also discuss how we can model the elliptical instability' of magnetic solitons and thus approximate some boundaries in the phase diagram of the chiral magnet.

### 16th February 2022, 10am GMT.

#### Bjarke Gudnason and Chris Halcrow - A Smörgåsbord of Skyrmions

We study static solutions of the standard Skyrme model with a pion mass. Using approximately 105 pseudo-random initial configurations made of single Skyrmions in the non-symmetrized product Ansatz and an automatic detection of repeated solutions, we find 409 local energy minimizers (Skyrmions) of the model with baryon numbers 1 through 16, of which 385 are new. In particular, we find new solutions for baryon numbers 5, 8, 9, 10, 11, 12, 13, 14, 15, and 16. Our results for the number of solutions per baryon number suggest that this number could grow either polynomially or exponentially. We identify new families of solutions: sheets of Skyrmions in synchronized and antisynchronized hexagonal layers (which we call graphene); chains of 2- and 3-tori; chain-like solutions containing a hinge and many clustered Skyrmions. Contrary to common lore, only the B=12 global energy minimizer is made of alpha particles or some chunk of a cubic crystal, whereas the B=9,11,14,15 minimizers contain the B=7 icosahedrally symmetric Skyrmion as a component. The B=10,13,16 are symmetric graphene-like solutions. We find B=5 and B=8 minimizers with numerically indistinguishable energies. The B=8 candidates are the chain of two cubes, which is a chunk of the cubic Skyrme crystal and the fullerene-type ball found originally by the rational map approximation. The B=5 global minimizer is either the well-known D2d symmetric fullerene or a new C2v symmetric solution. Finally, our findings show a large number of solutions have no discrete symmetries or just one symmetry, contrary to the common lore that Skyrmions are highly symmetric configurations.

### 9th February 2022, 10am GMT.

#### Steven Cotterill - Predicting the stability of vortons

In this talk I will be discussing the stability of loops of superconducting cosmic string, known as vortons, to non-axially symmetric perturbations. By calculating a few integrated quantities of straight string solutions we can accurately predict the stability properties of vortons, if they are large enough that the effects of curvature can be neglected. Using this analysis, we have predicted the existence of stable vortons and performed supporting 3D simulations by perturbing our constructed solutions.

### 8th December 2021, 10am GMT.

#### Paul Sutcliffe - Boundary metrics on soliton moduli spaces.

The geodesic approximation to soliton dynamics is extended to situations in which the standard metric is infinite, by considering boundary metrics on soliton moduli spaces. Examples are presented, including a hyperbolic analogue of the Atiyah-Hitchin manifold, relevant to the scattering of a pair of hyperbolic monopoles.

### 24th November 2021, 10am GMT.

#### Alberto Alonso Izquierdo - Scattering between wobbling kinks

The kink-antikink scattering in the φ4-model involves fascinating properties. One of them is the presence of a fractal structure embedded in the final versus initial velocity diagram. The kink reflection processes included in this regime involve n-bounce events where the kink and the antikink collide and bounce back a finite number of times before escaping away. The excitation of the shape modes of the colliding kinks makes that the subsequent collisions in an n-bounce event involve the scattering between wobbling kinks or wobblers. In this talk we shall discuss the scattering between wobblers in the standard φ4 model in two different scenarios, which give rise to constructive or destructive interference between the shape modes at the collision.

### 17th November 2021, 10am GMT.

#### Jose Queiruga - Excitations of global vortices

In this talk I will discuss the spectrum of linearized excitations of global vortices in 2+1 dimensions. After identifying the existence of localized excitation modes, the decay time scale of the first two will be compared with the results given by the numerical evolution of the full non-linear equations. I will show numerically how the interaction of vortices with an external source of radiation or other vortices can excite these modes dynamically. I will also explore the evolution of a network of vortices in an expanding (2+1) dimensional background, in particular, in a radiation dominated universe and analyze the excitation of the internal modes.

### 10th November 2021, 1pm GMT.

#### Uri Kol - Duality and Infrared Phenomena in Einstein's Gravity

In this talk I will describe a phenomenon akin to Electric-Magnetic duality in Einstein's gravity. I will show that a new type of "magnetic" dual gravitational charges generate redundant symmetry transformations which are not part of the standard group of diffeomorphisms. The new gauge symmetry of the metric reveals, in turn, a wide class of IR phenomena including: monopole solutions, double copy structure of scattering amplitudes and more.

### 3rd November 2021, 1pm GMT.

#### Masaru Hongo - Instanton, inhomogeneous phase, and Nambu-Goldstone mode in chiral magnets

Watch on YouTube. View the slides.

The Dzyaloshinskii-Moriya (DM) interaction, described by a term proportional to the vector product of neighboring spins, is a specific interaction for spin systems to favor inhomogeneous order. In this talk, I will present some interesting analytic results for chiral magnets (or spin systems with the DM interaction) after demonstrating how we can implement the DM interaction into the O(3) nonlinear sigma model. By considering several types of the DM interaction, I will explain various instanton solutions [1] and the inhomogeneous ground states (helical and spiral phases) together with the energy spectrum of the Nambu-Goldstone modes [2].
Ref.
[1] M. Hongo, T. Fujimori, T. Misumi, M. Nitta, N. Sakai, Phys.Rev.B 101 (2020) 10, 104417
[2] M. Hongo, T. Fujimori, T. Misumi, M. Nitta, N. Sakai, Phys.Rev.B 104 (2021) 13, 134403

### 27th October 2021, 1pm BST.

#### Jan Albert - The Abrikosov vortex in curved space

It is known that when coupled to gravity, 't Hooft-Polyakov monopoles can hold a Schwarzschild black hole at their core, realizing a hairy magnetic black hole. In this talk we will try to construct a similar object with Abrikosov vortices. So we will study the Abrikosov vortex in curved space, first in the asymptotically flat case and later in AdS, discussing both singular and non-singular solutions. We will end with some comments on the interpretation of these objects in the context of AdS/CFT, touching on the story of the holographic superconductor.

### 13th October 2021, 10am BST.

#### Juan Carlos Criado - Electroweak skyrmions in the HEFT

We will see how skyrmions, topological solitons originally found in an effective theory for pions, may arise also in the electroweak sector, including a dynamical Higgs boson. A powerful tool for studying them, with applications in many other non-perturbative problems, are neural networks. We will discuss their use in computing the skyrmion solutions and the shape of the energy functional. This allows to find which effective operators can stabilize them. Finally, we will consider some phenomenological aspects of skyrmions: the collider signatures of their stabilizing operators, and their potential as Dark Matter candidates.

### 6th October 2021, 10am BST.

#### Kenji Fukushima - Deformation of Skyrmions under a magnetic field and the domain-wall formation

In a nuclear system with chiral symmetry and a magnetic field, SU(2) symmetry is explicitly broken down to U(1), and the baryon number winding should be changed accordingly. I will first discuss deformation of isolated baryons in a magnetic field and explain two interesting observations; the magnetic assisted confinement and the mass splitting between protons and neutrons by a topological term. I will next discuss the Skyrme Crystals under a magnetic field and show two solutions. One corresponds to deformed nuclear matter and the other to the uniform pionic domain wall. I will finally show the phase diagram as a function of the density and the magnetic field.

### SIG IX Schedule

This is a copy of the SIG IX schedule from the SIG website.

All times are European Central Summer Time (Brazil Standard time -5 (6 am/10 am), British Summer Time -1 (10 am/14 pm), China Standard Time + 6 (5 pm/9 pm) and Japan Standard Time + 7 (6 pm/10 pm).

Recordings of the talks will appear on this webpage, as well as the official SIG page.

To join a seminar, enter the usual Solitons at Work Zoom room.

#### Monday 28th June

10.50: Welcome by Kasia Oles and Andrzej Wereszczynski
11.00: Wormholes and Solitons, Nick Manton [Watch].
15.00: Self-Duality: applications of Skyrme theory to nuclear matter, Luiz Ferreira [Watch].

#### Tuesday 29th June

11.00: Collective coordinate model of kink-antikink collisions in phi^4 theory by Kasia Oles, Tom Romanczukiewicz and Andrzej Wereszczynski [Watch].
15.00: Short talks:

• Yasha Shnir, "Spinning Q-balls and boson stars" [Watch].
• Carlos Naya, "Skyrmion tubes in liquid crystals" [Watch].
• Andy Royston, "Simulating magnetic monopole-defect dynamics" [Watch].
• Andreas Fring, "Degenerate and nonlocal soliton solutions from PT-symmetry" [Watch].
• Paul Leask, "The baby Skyrme crystal" [Watch].

#### Wednesday 30th June

11.00: Topological Defects in Multicomponent Ginzburg Landau Theory, Martin Speight [Watch].
15.00: The geometry of chiral skyrmion dynamics, Bernd Schroers [Watch].

#### Thursday 1st July

11.00: Skyrmions from instantons, Josh Cork, Chris Halcrow, Derek Harland and Tom Winyard [Watch].
15.00: Skyrme crystals - nuclear matter and neutron stars, Alberto Garcia Martin-Caro and Miguel Huidobro [Watch].

#### Friday 2nd July

11.00: Near-BPS (baby) Skyrmions as an approach to nuclear physics, Bjarke Gudnason [Watch].
15.00: Quantum corrections to the ANO vortex, Herbert Weigel [Watch].
16.30: Closing remarks by Nick Manton [Watch].

### 26th May 2021, 10am BST.

#### Calum Ross - Magnetic Impurities, Integrable Vortices and the Toda Equation

The five known integrable Abelian vortex equations are generalised to include magnetic impurities. Exploring this leads to a Tong-Wong type product group gauge theory of coupled vortices. For a suitable choice of charge matrix these coupled vortex equations reduce to either the integrable Toda equation or an opposite sign version. I will sketch this construction and highlight the integrable cases.

### 19th May 2021, 10am BST.

#### Daniel Jimenez - Exciting the kink

In many field theories, solitonic solutions admit localized excitations with unnaturally long lifetimes in their spectrum of perturbations. These bound states may play a significant role in the dynamics of solitons, and in particular, they could shed light on some aspects concerning the evolution of cosmic string networks. As a starting point, we investigate the properties of this type of excitations in the simple case of the (lambda phi^4) theory in 1+1 dimensions. This talk will be devoted to a detailed characterization of the shape mode perturbation of the kink solution. We study its decay rate and its level of excitation in Minkowski spacetime as well as in two cosmological settings: the formation of kinks in a phase transition and the interaction of the kink with a thermal bath.

### 12th May 2021, 10am BST.

#### Andreas Fring - Non-Hermitian gauge field theories and BPS limits

We present an overview of some key results obtained in a recent series devoted to non-Hermitian quantum field theories for which we systematically modify the underlying symmetries. Particular attention is placed on the interplay between the continuous symmetry group that we alter from global to local, from Abelian to non-Abelian, from rank one to generic rank N, and the discrete anti-linear modified CPT-symmetries. The presence of the latter guarantees the reality of the mass spectrum in a certain parameter regime. We investigate the extension of Goldstone's theorem and the Higgs mechanism, which we demonstrate to work in the conventional fashion in the CPT-symmetric regime, but which needs to be modified technically at the standard exceptional points of the mass spectrum and entirely fails at what we refer to as zero exceptional points as well as in the broken CPT-symmetric regime. In the full non-Hermitian non-Abelian gauge theory we identify the t'Hooft-Polyakov monopoles by means of a fourfold Bogomol'nyi-Prasad-Sommerfield (BPS) limit. We investigate this limit further for other types of non-Hermitian field theories in 1+1 dimensions that possess complex super-exponential and inverse hyperbolic kink/anti-kink solutions and for 3+1 dimensional Skyrme models for which we find new types of complex solutions, that all have real energies due to the presence of different types of CPT-symmetries.

### 5th May 2021, 10am BST.

#### Sven Bjarke Gudnason - 1/2-BPS vortex strings in N=2 supersymmetric U(1)N gauge theories

Strings in N=2 supersymmetric U(1)N gauge theories with N hypermultiplets are studied in the generic setting of an arbitrary Fayet-Iliopoulos triplet of parameters for each gauge group and an invertible charge matrix. Although the string tension is generically of a square-root form, it turns out that all existing BPS (Bogomol'nyi-Prasad-Sommerfield) solutions have a tension which is linear in the magnetic fluxes, which in turn are linearly related to the winding numbers. The main result is a series of theorems establishing three different kinds of solutions of the so-called constraint equations, which can be pictured as orthogonal directions to the magnetic flux in SU(2)R space. We further prove for all cases, that a seemingly vanishing Bogomol'nyi bound cannot have solutions. Finally, we write down the most general vortex equations in both master form and Taubes-like form. Remarkably, the final vortex equations essentially look Abelian in the sense that there is no trace of the SU(2)R symmetry in the equations, after the constraint equations have been solved.

### 28th April 2021, 4pm BST.

#### Bob Decker - Kink-Antikink Initial Conditions and Interactions for Field Theories with Polynomial Tails

Field theories with polynomial tails, as in the case of the φ8, φ10, and φ12 theories, present new challenges for the computer simulation of interactions involving kinks and antikinks. In particular, a naive sum ansatz of a single kink and antikink is shown to be an inadequate choice on which to base initial conditions. The results contained in a recent paper (and two preceding ones) in which the authors investigate such simulations and methods for generating good initial conditions, will be presented. The meaning of "good" in this context is one primary focus of the talk. It is shown that constrained minimization processes are needed to distill the best possible initial conditions from various ansatze. Some results of resonance windows for these theories will also be discussed.

The talk will be based on our papers:
Phys. Rev. D 99, 016010 (2019), https://arxiv.org/abs/1810.03590
Phys. Rev. Lett. 122, 171601 (2019), https://arxiv.org/abs/1811.07872
Commun. Nonlinear Sci. Numer. Simulat. 97 (2021) 105748, https://arxiv.org/abs/2005.00154

### 21st April 2021, 4pm BST.

#### Noah Kent - Target skyrmions, topological stability, and hopfions in experimental chiral ferromagnetic systems

Topologically non-trivial structures in ferromagnetic systems have garnered significant interest in recent years due to their technological potential and interesting mathematical properties. In this talk I will discuss the experimental realization and identification of target skyrmions and hopfions in chiral ferromagnetic Ir/Co/Pt multilayer heterostructures. I will detail how micromagnetic energies are tuned in experimental chiral ferromagnetic systems, how these nanostructures are made with nanofabrication, and how they are identified using multiple types of x-ray magnetic circular dichroism microscopies.

Throughout this talk, I hope to identify some differences between topological theory and scientific experiment; for example in a real magnetic system the stability of topologically non-trivial structures is very important as topological transformations are possible at accessible energies due to the finite scale of the system and discrete nature of the magnetization.

### 7th April 2021, 10am BST.

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

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

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

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

It has been proposed by Komargodski in arxiv.org/abs/1812.09253 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

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

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

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

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

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

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

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

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

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

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.

#### 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

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

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

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

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

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

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

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

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

### 12th February 2021, 10am GMT

Topic: Malomed's talk

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

Initial presenter: Father Christmas

### 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

### Henan University Short Course: July 2021

#### Sven Bjarke Gudnason - CUDA C programming for scientific computing

In these lectures, I will introduce scientific computations in the C language at double precision and how to structure your code in a modular fashion using functions and structs. Then I will teach how to write code in CUDA C for scientific computation, specifically:
-how to set up computations
-how to define overloaded operators
-how to handle the memory in a efficient way
-how to write kernels and kernel wrappers
-how to perform parallel computations on arrays of data
-how to avoid warp divergence
-how to perform atomic computations
-how to visualize an ongoing calculation on the GPU
-how to make a simple example using cuDNN for deep neural networks
Finally, I will give homework at every lecture and students can briefly present their results at the next lecture.

First lecture: Wednesday 7th July at 9:00 (BST) [Watch]
Second lecture: Wednesday 14th July at 9:00 (BST) [Watch]
Third and final lecture: Tuesday 20th July at 9:00 (BST) [Watch]

### Henan University short course: November 2020 - May 2021

#### Nuno Romão - Moduli Spaces in Gauge Theory

This course will cover rigorous aspects of gauge theory - a branch of differential geometry that has been a major stage for cross-fertilisation between mathematics and physics over the last few decades. The focus will be on mathematical objects called moduli spaces that play a pivotal role in this subject. They arise as spaces of orbits (in some set of "fields", in physical terminology) under infinite-dimensional groups of symmetries.
The lectures will be organised in two blocks. In Part I, the language of connections in fibre bundles will be introduced from scratch, together with other topics that are essential to lay out the foundations of gauge theory. In Part II, we will apply this machinery to the specific setting of the vortex equations, which are a system of PDEs on complex manifolds that form a prototype of the intriguing notion of self-duality, permeating much of modern geometry. The moduli spaces that we shall mostly be concerned with classify (or parametrise) equivalence classes of solutions to the vortex equations. These spaces will be described concretely in some simple examples, incorporating recent research. After this, we will be able to ask and answer some questions regarding their intrinsic geometry and topology, and along the way discuss a few applications.

Part I: Introduction to gauge theory
The sessions (2h15m each, no breaks) will start at 9:30am GMT(UTC) on Tuesdays 24th November and 1st, 8th December 2020; and then on Monday 14th, Tuesday 22nd December 2020.
Part II: Moduli of symplectic vortices
The sessions (2h15m each, no breaks) will start at 7:00am GMT(UTC) on Wednesday 3rd March and continue every Wednesday for about 10 weeks.

If you are interested in attending this short course organized by Henan University, please contact n.m.romao (at) gmail (dot) com for details.

### 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

### Vortex Moduli - ICTS Bangalore

There is an interesting research program happening soon. "Vortex Moduli" at ICTS Bangalore is taking place from 6th-17th February 2023. Registration closes on 15th January 2023, but the organisers advise everyone to apply much earlier because of current delays with visa processing. For more details, check out this link.You might recognise Nuno Romão and Martin Speight from previous talks at Solitons at Work. Both are giving mini-courses at the event.

### PhD studentship in spinor-BECs, University of East Anglia (Deadline: 27 November, 2022)

Hayder Salman and Magnus Borgh have an opening for a PhD student in spinor-BECs at the University of East Anglia, starting in October 2023. Interested applicants are welcome to contact Magnus Borgh. For more details, see S@W Jobs.

### JSPS Fellowship for Foreign (UK-based) Researchers

There is an opening for a JSPS pre/postdoc fellowship for researchers based in the UK, promoting academic exchange between Japan and the UK or Ireland. For more details, see S@W Jobs.

### Lecturer in Physics, University of Kent

There is an opening for a lecturer position at the University of Kent, UK, in the Physics of Quantum Materials Group. For more details, see S@W Jobs.

### GMNM conference website launched

The Geometric Models of Nuclear Matter conference website has been launched. The conference will take place from the 20th - 22nd of July. You can view the conference website here! From the website:

"This conference will be an in person event based at the University of Kent in Canterbury. The theme of the conferences is intentionally broad, focussing on topological solitons and their applications in physics. We welcome any talks within this loose brief.

While we will be making the talks available online through the solitons at work network, all speakers will be in person. This is due to the numerous years without in person interaction due to the pandemic. We look forward to welcoming you to the university and seeing some faces we haven't seen in some time.

We would like to thank the London Mathematical Society (LMS) for funding this meeting. We would also like to thank the University of Kent for hosting the event."

### SIG X announced

This is the first announcement of the SIG X workshop that will be held both in-person and online, on June 27th - July 01, 2022. As you may know, the idea of this workshop is to increase collaboration and hence there will only be few talks a day. In first week there will be one talk a day with a more overview/introduction flavor, whereas in the second week there will be two talks per day, as usual. However, after each of the talks there will be a longer informal discussion related to the topic of the talk which can be attended both in-person and online. To increase discussion, we will also open other discussion rooms. The preliminary list of the talks (with topics) is at our website, which will be regularly updated. If you would like to participate in the workshop, please send an email to Kasia Oles at katarzyna.slawinska (at) uj.edu.pl.

### New book on Skyrmions as nuclei

An exciting new book "Skyrmions - A Theory of Nuclei" has just been published by Nick Manton, see this link for more details.

### Postdoctoral Research Associate in Mathematical Physics

Postdoc opportunity in topological solitons available at the University of Edinburgh from 1st September 2022, see the announcement under jobs.

### Tune-up

The engine of the website got a tune-up and a change of oil, it should now be running faster than ever.

### Postdoc Positions at Henan University

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

### Fall seminars starting soon!

We have been working on a line-up of seminars for the fall and are ready with seminars from October 6th!

### Senior Research Associate Position at University of East Anglia

There is an opening for a postdoctoral position (Senior Research Associate) at the University of East Anglia in Norwich, UK. For more details, see S@W Jobs.

### Conference at Henan University

Recordings and pictures are now available on the conference website.

### Conference at Henan University hit by typhoon

Due to heavy rainfalls, the conference program has changed, please look at the updated version. There is a 7 hour time difference between the times on the conference website and BST times, so the 9am talk will be at 2am in the UK and the afternoon 2pm talk will be at 7am in the UK.

### Conference at Henan University

There will be a hybrid conference on "Instantons, Holography, Strong Interactions and Nuclear Physics" taking place at Henan University on July 21-23, with all talks being available in the usual zoom meeting room used by the S@W network. For more information, see the conference website. There is a 7 hour time difference between the times on the conference website and BST times, so the 9am talk will be at 2am in the UK and the afternoon 2pm talk will be at 7am in the UK.

### SIG IX video recordings

In case some of you have missed a seminar of the SIG IX conference, the videos have been recorded and are available here as well as on the official SIG IX conference website.

### Henan University Short Course on CUDA C programming for scientific computing

Henan University is organizing a short course on "CUDA C programming for scientific computing" taught by Sven Bjarke Gudnason (Henan U.). For more details and the video recordings, see Training.

### 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. The second part starts on 3rd March 2021.
Part I was an introduction to gauge theory in fiber bundles, and Part II will cover moduli of symplectic vortices. For more details, see Training.

### 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 (https://jobs.kent.ac.uk/CEMS-031-21) with deadline is 7th March 2021 and a 3-year lectureship in Pure Mathematics (https://jobs.kent.ac.uk/Vacancy.aspx?ref=CEMS-032-21) 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: http://www1.maths.leeds.ac.uk/~pmtcjh/LMSsoliton/.

### 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.

### SIG IX announced.

This is the first announcement of the SIG IX workshop that will be held online, on June 28th - July 02, 2021. As you may know, the idea of this workshop is to increase collaboration. So, as usual, there are only two talks per day. However, after each of the talks there will be a longer informal discussion related to the topic of the talk. To increase discussion, we will also open other discussion rooms, which can be proposed by the participants before or during the workshop. We hope these rooms will grow naturally in the duration of the workshop. The preliminary list of the talks (with topics) is at our website at the following address http://th.if.uj.edu.pl/~wereszcz/sig9.html which will be regularly updated. There will also be a session devoted to shorter (20 min) talks, which is a perfect opportunity for advertising recent work, or discussing a topics that you don't usually talk about. If you would like to participate in the workshop, please send an email to Kasia Oles at katarzyna.slawinska (at) uj.edu.pl.

### 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!

## Old Jobs

### PhD studentship in spinor-BECs, University of East Anglia (Deadline: 27 November, 2022)

Topological defects and phase transitions are phenomena that occur ubiquitously across otherwise very dissimilar physical systems, from superfluids to cosmology. Spinor Bose-Einstein condensates (BECs), which allow full freedom to the atoms' quantum-mechanical spin, open up the possibility to study topological objects and their role in quantum phase transitions in experimentally highly accessible atomic systems. Experiments are now increasingly turning to spin-2 BECs, where non-Abelian defects are possible. For such defects, adding charges A + B is not the same as B + A, leading to new dynamics.

The central aim of this PhD project is to theoretically determine the phase diagram of spin-2 BECs under experimentally relevant constraints and to use this as a basis for determining the universal scaling properties of quantum phase transitions in spinor BECs. In particular we will determine the production and impact of non-Abelian vortices. On the same basis we will also numerically simulate defect production and dynamics at interfaces between topologically distinct phases.

As a PhD student on this project, you will employ mean-field theory to model the spinor condensate. The resulting non-linear equations can in general only be solved numerically. Research results will be obtained using UEA's high-performance computer cluster, including GPU computation. Developing and refining numerical tools will be integral to the project. This work will be performed in collaboration with other researchers at UEA.

We are looking for an enthusiastic candidate eager to work in this rapidly developing area of atomic physics and superfluidity, with links to condensed-matter physics and cosmology. A background involving quantum physics is essential. You must also be comfortable working with computers and have some familiarity with programming. Knowledge of numerical analysis is desirable. As a student you will take part in existing collaborations with experimenters.

For more details and application click here.

### JSPS Fellowship for Foreign (UK-based) Researchers

JSPS London Pre/Postdoctoral Fellowship for Foreign Researchers (Short Term)
Application Deadline: Monday 7th November, 2022
Fellowships must start between: 1st April 2023 to 31st March 2024

Japan Society for the Promotion of Science (JSPS) is the leading research funding agency in Japan, established by the Japanese Government for the purpose of contributing to the advancement of science. Our Pre/Postdoctoral Fellowship for Foreign Researchers (Short Term) provides the opportunity for short-term visits for UK, European, North American and Canadian researchers ordinarily based in the UK or Ireland to do cooperative research with leading research groups at Japanese Universities and Institutions. The programme is designed to provide researchers with first-hand experience of the research and living environment in Japan, whilst expanding academic exchange between Japan and the UK or Ireland. Researchers from any field; Computer, Engineering, Health, Biological, Life, Natural and Physical Sciences, Mathematics, Humanities and Social Sciences etc. are eligible to apply. Awards will cover visits of 1 to 12 months.

Eligible applicants also need to be either within 2 years of finishing their PhD at the time of applying to start their fellowship in Japan or have obtained their PhD at a university outside of Japan within the last 6 years (on or after 2nd April 2017).

Please visit the JSPS London website here for further information.

### Lecturer in Physics, University of Kent (Deadline: 30 September, 2022)

The University of Kent's Division of Natural Sciences, School of Physics & Astronomy is seeking to appoint a dedicated academic who is keen to make a strong contribution to research, innovation and teaching within the School. The successful candidate will contribute to and support research in the Physics of Quantum Materials Group (PQM). We particularly welcome applicants with a track record of research in Quantum Technologies that complements the current activities of the group (for instance, at the interface between Condensed Matter Physics and Quantum Technologies).

The position of Lecturer in a UK university is roughly equivalent to an Assistant Professor in the USA. The deadline for applications is on 30 September 2022. Interested candidates are encouraged to contact Dr S Ramos (Head of School, Physics & Astronomy). They may also wish to contact Dr. J. Quintanilla (Group Leader, Physics of Quantum Materials). Follow the links for contact details. The post is based at the School of Physics & Astronomy in the historic city of Canterbury, England.

Further details and information on how to apply can be found in the official job announcement.

### Postdoctoral Research Associate in Mathematical Physics (Deadline: 5th April, 2022)

Applications are invited for the post of Postdoctoral Research Associate in Mathematical Physics to work with Bernd Schroers in the School of Mathematics at the University of Edinburgh. Candidates should preferably have some research experience related to topological solitons and their applications in physics, and ideally have an active interest in magnetic skyrmions. The post is available from 1st September 2022 for a 24 months fixed-term, full-time contract, with a possible extension by a further year.
The successful candidate will join the Maxwell Institute (https://www.maxwell.ac.uk), the joint mathematical research institute of the University of Edinburgh and Heriot-Watt University, and become a member of the Edinburgh Mathematical Physics Group (https://empg.maths.ed.ac.uk) whose research interests include string theory, gauge theory, solitons, integrable systems, non-commutative geometry, classical and quantum gravity. The post will allow its holder ample opportunities to develop and pursue their own research interests in mathematical physics.

Further information and the link to the online application form: click here

Applicants should upload a CV with a list of publications and a brief research statement (two pages) when applying for the post online. In addition, they should arrange for at least two letters of reference to be sent directly to references@maths.ed.ac.uk quoting the reference number 3612.