## Past Events

This is a repository of past events of various kinds.## Previous Seminars

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

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

Watch on YouTube.

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

Watch on YouTube.

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

Watch on YouTube.

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

Watch on YouTube.

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

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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

Watch on YouTube.

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

Watch on YouTube.

Field theories with polynomial tails, as in the case of the
φ^{8}, φ^{10}, and φ^{12} 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.

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

Watch on YouTube.

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.

Based on papers: https://aip.scitation.org/doi/10.1063/1.5099991, and https://www.nature.com/articles/s41467-021-21846-5

### 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 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

Watch on YouTube.

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

Watch on YouTube.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

Watch on YouTube.

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

Watch on YouTubeThe 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

Watch on YouTubeWe 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

Watch on YouTubeThe 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.

Watch on YouTube#### 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 (*s*EFT) 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

Watch on YouTube.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

Watch on YouTube.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

Watch on YouTube.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

Watch on YouTube.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

Watch on YouTube.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

Watch on YouTube.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

Watch on YouTube.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

Watch on YouTube.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

### 22nd October 2021, 10am BST

### 15th October 2021, 10am BST

### 8th October 2021, 10am BST

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### 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

### 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

### 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.

### New 'Jobs' Section at S@W

### 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!