-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathresearch.html
171 lines (136 loc) · 12 KB
/
research.html
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
<!DOCTYPE html>
<html lang="en-UK">
<head>
<title>Research</title>
<!-- <meta charset="UTF-8">
</head>
<head>-->
<meta charset="UTF-8" name="viewport" content="width=device-width, initial-scale=1">
<style>
* {box-sizing: border-box;}
body {
margin: 1;
font-family:'Times New Roman', serif
}
.header {
overflow: hidden;
background-color: lightgrey;
padding: 20px 10px;
}
.header a {
float: left;
color: black;
text-align: center;
padding: 12px;
text-decoration: none;
font-size: 18px;
line-height: 25px;
border-radius: 4px;
}
.header a.logo {
font-size: 25px;
font-weight: bold;
}
.header a:hover {
background-color: lightgrey;
color: black;
}
.header a.active {
background-color: dodgerblue;
color: white;
}
.header-right {
float: right;
}
@media screen and (max-width: 500px) {
.header a {
float: none;
display: block;
text-align: left;
}
.header-right {
float: none;
}
}
.center {
display: block;
margin-left: auto;
margin-right: auto;
}
</style>
</head>
<body style="background-color:lightgrey;">
<div class="header">
<!--<a href="#default" class="logo">CompanyLogo</a>-->
<h1>Calum Ross</h1>
<div class="header-right">
<a href="https://cdross1.github.io">Home</a>
<a class="active" href="https://cdross1.github.io/research">Research</a>
<a href="https://cdross1.github.io/teaching">Teaching</a>
<a href="https://cdross1.github.io/notes">Notes</a>
<a href= "https://cdross1.github.io/outreach">Outreach</a>
</div>
</div>
<!--<div style="text-align:center:20px">
<h1>Calum Ross</h1>
</div>-->
<hr>
</body>
<body>
<img src="calum_snow.jpg" alt="" width="500" height="380" class="center" >
<h2> Research </h2>
<p>My research interests relate to Topological Solitons and their links to geometry, Differential Geometry and Gauge Theory. In particular my PhD work focused on studying a geometric interpretation of integrable vortex equations. I have continued working on this as well as studying the relationship between vortices and BPS monopoles. More recently I have worked on solvable models of magnetic skyrmions, as well as domain walls in one dimensional chiral magnets. Three of the main areas of my research are highlighted below. </p>
<h4>Gauge Theoretic Solitons</h4>
<p>Topological solitons are particle like lumps of energy that occur in many nonlinear classical field theories. The most famous examples include <em>magnetic vortices</em>, <em>nuclear and magnetic skyrmions</em>, <em>instantons</em>, and <em>kinks</em>. The topology in the name arises because the topology of the space of finite energy, non-singular, field configurations. Roughly speaking, we call a soliton topological if it cannot be continuously deformed to the vacuum. Usually this topology takes the form of the configuration having an associated degree or winding number counting, with sign, the number of zeros that the fields have.
My work on topological solitons has primarily focussed on vortices, instantons and monopoles. Typically studying solvable models and exploring the relationship between the solitons and geometric structures. </p>
<h4>Chiral Magnets</h4>
<p>Chiral magnets are examples of materials where the parity symmetry is broken. Magnetic systems are well known to possess examples of solitons, most famously domain walls, and chiral magnets are also host to a plethora of magnetic solitons. In particular magnetic skyrmions, which are "knotted" configurations in the magnetisation vector field of the magnetic materials.
I have studied solvable models of a variety of magnetic solitons, particularly magnetic skyrmions and kinks on domain walls known as <em>Domain wall skyrmions</em>.</p>
<h4>Solitons in Physical Systems</h4>
<p>As well as the mathematical properties of solitons I am also interested in solitons that can be realised in physical systems. This includes <em>optical skyrmions</em>, which are skyrmion configurations occurring in the polarisation field of lasers, and linked and knotted synthetic gauge fields realised in ultracold atomic gasses. </p>
<h2>Publications</h2>
<p>An up to date list of my publications can be found on <a href="https://arxiv.org/a/ross_c_1.html"> arXiv</a>. Below I have split them up into rough subject areas, though there is a lot of overlap between different sections.</p>
<h3>Vortices and Geometry</h3>
<p>Magnetic Zero-Modes, Vortices and Cartan Geometry (with Bernd Schroers). Letters in Mathematical Physics, 108: 949, 2018 <a href="https://link.springer.com/article/10.1007/s11005-017-1023-2">online version</a>. <a href="https://arxiv.org/abs/1705.09632">arXiv:1705.09632</a>. </p>
<p>Hyperbolic vortices and Dirac fields in 2+1 dimensions (with Bernd Schroers). J Phys A 51: 295202, 2018 <a href="http://iopscience.iop.org/article/10.1088/1751-8121/aac597" >online version</a>. <a href="https://arxiv.org/abs/1803.11120">arXiv:1803.11120</a>. </p>
<p>Magnetic Impurities, Integrable Vortices and the Toda Equation (with Sven Bjarke Gudnason). Letters in Mathematical Physics, 111: 100, 2021 <a href="https://doi.org/10.1007/s11005-021-01444-8">online version</a>. <a href="https://arxiv.org/abs/2105.01332">arXiv:2105.01332</a>. </p>
<p>Cartan Connections and Integrable Vortex Equations. Journal of Geometry and Physics, 2022 <a href="https://doi.org/10.1016/j.geomphys.2022.104613">online version</a>. <a href="http://arxiv.org/abs/2112.08328">arXiv:2112.08328</a></p>
<h3>Solitons in Ultracold Atoms and Optical Systems</h3>
<p>Linked and knotted synthetic magnetic fields (with Callum Duncan, Niclas Westerberg, Manuel Valiente, Bernd Schroers and Patrik Ohberg). Phys. Rev. A 99, 063613, 2019 <a href="https://journals.aps.org/pra/abstract/10.1103/PhysRevA.99.063613" >online version</a>. <a href="https://arxiv.org/abs/1808.03655">arXiv:1808.03655</a>. </p>
<p>Building Paraxial Optical Skyrmions Using Rational Maps (with Claire Cisowski and Sonja Franke-Arnold). Adv. Photonics Res., 4: 2200350, 2023 <a href="https://onlinelibrary.wiley.com/doi/10.1002/adpr.202200350"> online version </a>. <a href="http://arxiv.org/abs/2207.12741">arXiv:2207.12741</a></p>
<h3>Solitons in Chiral Magnets</h3>
<p>Magnetic Skyrmions at Critical Coupling (with Bruno Barton-Singer and Bernd Schroers). Communications in Mathematical Physics 375, pages 2259–2280(2020) available online <a href= "https://link.springer.com/article/10.1007%2Fs00220-019-03676-1 "> here</a>. <a href="https://arxiv.org/abs/1812.07268">arXiv:1812.07268</a>.</p>
<p>Skyrmion Interactions and Lattices in Chiral Magnets: Analytical Results (with Norisuke Sakai and Muneto Nitta). JHEP 02 (2021) 095 <a href="https://doi.org/10.1007/JHEP02(2021)095">online version</a>. <a href="https://arxiv.org/abs/2003.07147">arXiv:2003.07147</a>. </p>
<p>Exact Ground States and Domain Walls in One Dimensional Chiral Magnets (with Norisuke Sakai and Muneto Nitta). JHEP 12 (2021) 163 <a href="https://doi.org/10.1007/JHEP12(2021)163">online version</a>. <a href="https://arxiv.org/abs/2012.08800">arXiv:2012.08800</a>. </p>
<p>Domain Wall Skyrmions in Chiral Magnets (with Muneto Nitta). Phys. Rev. B 107, 024422, 2023 <a href="https://journals.aps.org/prb/abstract/10.1103/PhysRevB.107.024422" >online version</a>. <a href="http://arxiv.org/abs/2205.11417">arXiv:2205.11417</a></p>
<p>Domain-wall skyrmion chain and domain wall bimerons in chiral magnets (with Yuki Amari and Muneto Nitta). Phys. Rev. B 109, 104426, 2024 <a href="https://journals.aps.org/prb/abstract/10.1103/PhysRevB.109.104426">online version</a>. <a href ="https://arxiv.org/abs/2311.05174"> arXiv:2311.05174</a></p>
<h3>Instantons and Monopoles</h3>
<p>Calorons and constituent monopoles (with Lorenzo Foscolo). Communications in Mathematical Physics (2023) available online <a href= "https://doi.org/10.1007/s00220-023-04827-1 "> here</a>. <a href="http://arxiv.org/abs/2207.08705">arXiv:2207.08705</a></p>
<p>The Asymptotic Structure of the Centred Hyperbolic 2-Monopole Moduli Space (with Guido Franchetti). SIGMA 19 (2023), 043 <a href="https://doi.org/10.3842/SIGMA.2023.043"> online version </a>. <a href="https://arxiv.org/abs/2302.13792">arXiv:2302.13792</a></p>
<!--<h4>Preprints</h4>-->
<!-- <h4>In preparation</h4> -->
<h2>Talks</h2>
<p>July 2024, Domain Wall Skyrmions at the <a href ="https://cdross1.github.io/ehu_solitons">Topological Solitons at Edge Hill</a> event held at Edge Hill University </p>
<p>May 2024, Vortices and Cartan Geometry at the <a href = "https://graemewilkin.github.io/seminar/index.html">York Geometry, Analysis and Mathematical Physics</a> seminar.</p>
<p>June 2023, Instantons and constituents at <a href = "https://sig.fais.uj.edu.pl/main">SIG XI </a></p>
<p>October 2022, A Gluing Construction for Calorons in the <a href="https://drbenlambert.github.io/GeometrySeminar22-23S1.html"> Leeds Geometry Seminars</a> at the University of Leeds.</p>
<p>July 2022 Calorons and Constituent Monopoles at the <a href="https://www.kent.ac.uk/smsas/personal/skyrmions/GMNM2022/">Geometric Models of Nuclear Matter conference</a>.</p>
<p>March 2022 Calorons and Constituent Monopoles as part of the <a href="http://solitonsatwork.net/?display=seminars">Solitons at Work</a> seminar series. A recording of the talk is available <a href= "https://youtu.be/RNe4AJbX_aY"> here</a>.</p>
<p>February 2022 Cartan Connections and Integrable Vortex Equations in the <a href="http://www.talks.cam.ac.uk/talk/index/169931"> DAMTP Mathematical Physics Seminars </a> in Cambridge</p>
<p>November 2021 Periodic Instantons with Small Period in the <a href = " https://people.bath.ac.uk/masadk/seminar/geom/">Algebra, Geometry and Number Theory seminar</a> at the University of Bath.</p>
<p>November 2021 Integrable Vortices and Flat Connections in the Leeds Geometry Seminars at the University of Leeds.</p>
<p>May 2021 Magnetic Impurities, Integrable Vortices and the Toda Equation as part of the <a href="http://solitonsatwork.net/?display=seminars">Solitons at Work</a> seminar series. A recording of the talk is available <a href="https://www.youtube.com/watch?v=I1C3txYpbrg"> here</a>.</p>
<p>November 2020 Mathematical models of topological solitons at an internal UCC physics seminar.</p>
<p>September 2020 Magnetic Skyrmions in solvable chiral magnets as part of the <a href ="http://www1.maths.leeds.ac.uk/~pmtcjh/GMNM/"> Geometric Models of Nuclear Matter Digital Seminar Series</a>.</p>
<p>January 2020 Magnetic Skyrmions from Gauged CP^1 Models at the <a href="https://indico.rcnp.osaka-u.ac.jp/event/1394/overview">CP^N model: recent developments and future directions</a> workshop at Keio University. </p>
<p>May 2019 Magnetic Skyrmions at Critical Coupling as a condensed matter theory <a href="https://www.sinova-group.physik.uni-mainz.de/seminar/">seminar</a> at the University of Mainz. </p>
<p>April 2019 Magnetic Skyrmions at Critical Coupling at the <a href="https://sites.google.com/site/keiotopsci/seminars ">Keio Topological Science Project Seminars</a>. </p>
<p>February 2019 Magnetic Skyrmions at Critical Coupling at the <a href="http://www.talks.cam.ac.uk/talk/index/117988">DAMTP Mathematical Physics Seminars</a> in Cambridge. </p>
<p>July 2018 Hyperbolic vortices and flat connections at the <a href="http://www1.maths.leeds.ac.uk/~pmtdgh/leeds/programme.html">LEEDS</a> workshop on topological solitons in Leeds.</p>
<p>January 2018 Vortices, Cartan connections and Magnetic Zero-Modes at the local <a href="https://empg.maths.ed.ac.uk/HTML/CurrentSeminars.html">EMPG</a> Seminars.</p>
<p>June 2017 Magnetic Zero-Modes, Vortices and Cartan connections at the <a href="http://ckottke.ncf.edu/senworkshop/">Sen Conjecture and Beyond</a> workshop.</p>
<p>April 2017 Metric structure of the moduli space of solutions to the self-duality equations at the <a href="http://wwwf.imperial.ac.uk/~at515/bigworkshop.html">BIG Workshop</a> on Higgs Bundles. </p>
<p>September 2016 Solutions of the Perturbed Freund Equations at the second <a href="https://www.kent.ac.uk/smsas/personal/skyrmions/GMNMC2016.html">Geometric Models of Nuclear Matter Conference</a>. </p>
<p>March 2016 Topological Electromagnetism and the Seiberg-Witten Equations at the <a href="http://www.macs.hw.ac.uk/~anatolyk/NBMPS46.html">46th NBMPS</a>. </p>
</body>
</html>