I am a Research Felow at University College London within Lorenzo Foscolo's group in the Mathematics department.

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.

Before joining UCL I was a temporary Lecturer in Physics at University College Cork for the 2020-2021 academic year. In the first semester I taught PY2101 Classical Mechanics, in the second semester I taught PY3104 Statistical Thermodynamics and part of PY4126 Radiative Processes.

In 2019-2020 I was a postdoctoral researcher in the Topological Sciences group at Keio university. While in Japan I primarily worked on magnetic solitons, particularly questions about the interaction of magnetic skyrmions and the phase diagram of chiral magnets.

I did my PhD student in the mathematical physics group at Heriot-Watt University under the supervison of Bernd Schroers. While in Edinburgh I was a member of the Edinburgh Mathematical Physics Group. I have an MPhys in Theoretical Physics from Lancaster University and a MASt in Applied Mathematics from the University of Cambridge. At Lancaster I wrote a Master's project on Physical Applications of Products of Geometric Distributions and while at Cambridge I wrote a Part III Essay on the Geometry of Supersymmetric and Super-Conformal Quantum Mechanics.

During the academic years 2016-2017 and 2017-2018 I organised the PhD student seminar series within MACS at Heriot-Watt. This is a weekly informal seminar series held in CM/T.01 on Fridays, offering PhD students to present their work or a topic that they are interested in to their peers.

University College London Email: calum.ross[at]ucl[dot]ac[dot]uk

Magnetic Zero-Modes, Vortices and Cartan Geometry (with Bernd Schroers). Letters in Mathematical Physics, 108: 949, 2018 online version. arXiv:1705.09632.

Hyperbolic vortices and Dirac fields in 2+1 dimensions (with Bernd Schroers). J Phys A 51: 295202, 2018 online version. arXiv:1803.11120.

Linked and knotted synthetic magnetic fields (with Callum Duncan, Niclas Westerberg, Manuel Valiente, Bernd Schroers and Patrik Ohberg). Phys. Rev. A 99, 063613, 2019 online version. arXiv:1808.03655.

Magnetic Skyrmions at Critical Coupling (with Bruno Barton-Singer and Bernd Schroers). Communications in Mathematical Physics 375, pages2259–2280(2020) available online here. arXiv:1812.07268.

Skyrmion Interactions and Lattices in Chiral Magnets: Analytical Results (with Norisuke Sakai and Muneto Nitta). JHEP 02 (2021) 095 online version. arXiv:2003.07147.

Exact Phase Structure of One Dimensional Chiral Magnets (with Norisuke Sakai and Muneto Nitta). JHEP 12 (2021) 163 online version. arXiv:2012.08800.

Magnetic Impurities, Integrable Vortices and the Toda Equation (with Sven Bjarke Gudnason). Letters in Mathematical Physics, 111: 100, 2021 online version. arXiv:2105.01332.

Cartan Connections and Integrable Vortex Equations. Journal of Geometry and Physics, 2022 online version. arXiv:2112.08328

Domain Wall Skyrmions in Chiral Magnets (with Muneto Nitta). arXiv:2205.11417

Calorons and constituent monopoles (with Lorenzo Foscolo). arXiv:2207.08705

Building ideal paraxial optical skyrmions using rational maps (with Claire Cisowski and Sonja Franke-Arnold).arXiv:2207.12741

July 2022 Calorons and Constituent Monopoles at the Geometric Models of Nuclear Matter conference.

March 2022 Calorons and Constituent Monopoles as part of the Solitons at Work seminar series. A recording of the talk is available here.

February 2022 Cartan Connections and Integrable Vortex Equations in the DAMTP Mathematical Physics Seminars in Cambridge

November 2021 Periodic Instantons with Small Period in the Algebra, Geometry and Number Theory seminar at the University of Bath.

November 2021 Integrable Vortices and Flat Connections in the Leeds Geometry Seminars at the University of Leeds.

May 2021 Magnetic Impurities, Integrable Vortices and the Toda Equation as part of the Solitons at Work seminar series. A recording of the talk is available here.

November 2020 Mathematical models of topological solitons at an internal UCC physics seminar.

September 2020 Magnetic Skyrmions in solvable chiral magnets as part of the Geometric Models of Nuclear Matter Digital Seminar Series.

January 2020 Magnetic Skyrmions from Gauged CP^1 Models at the CP^N model: recent developments and future directions workshop at Keio University.

May 2019 Magnetic Skyrmions at Critical Coupling as a condensed matter theory seminar at the University of Mainz.

April 2019 Magnetic Skyrmions at Critical Coupling at the Keio Topological Science Project Seminars.

February 2019 Magnetic Skyrmions at Critical Coupling at the DAMTP Mathematical Physics Seminars in Cambridge.

July 2018 Hyperbolic vortices and flat connections at the LEEDS workshop on topological solitons in Leeds.

January 2018 Vortices, Cartan connections and Magnetic Zero-Modes at the local EMPG Seminars.

June 2017 Magnetic Zero-Modes, Vortices and Cartan connections at the Sen Conjecture and Beyond workshop.

April 2017 Metric structure of the moduli space of solutions to the self-duality equations at the BIG Workshop on Higgs Bundles.

September 2016 Solutions of the Perturbed Freund Equations at the second Geometric Models of Nuclear Matter Conference.

March 2016 Topological Electromagnetism and the Seiberg-Witten Equations at the 46th NBMPS.

2020/2021 Lecturer for PY2101 Classical Mechanics.

2020/2021 Lecturer for PY3104 Statistical Thermodynamics, a syllabus for the course is available here.

2020/2021 Lecturer for PY4126 Radiative Processes.

2016/2017 tutorials for the SMSTC Geometry and Topology stream.

2016/2017 tutorials for F17XB Maths for Engineers and Scientists 2.

2017/2018 tutorials for F17CC Introduction to University Maths. The course webpage is here.

2017/2018 tutorials for SMSTC Geometry and Topology stream

2017/2018 tutorials for F18XD Maths for Engineers and Scientists 4. The webpage for the course is here.

2018/2019 tutorials for F17CC Introduction to University Maths. The course webpage is still in the same place.

In September 2020 I gave two lectures on topological solitons as part an NBMPS lecture series funded by the LMS. The notes and slides will be made available on the NBMPS page and here. The Lecture slides are here and here. The videos of the lectures have gone up on the LMS youtube channel lecture 1 here and lecture 2 here.

Another set of LMS funded Solitons lectures put on by the Yorkshire Durham Geometry Day are available here. They cover complimentary topics to my lectures, including; vortices, instantons and the Nahm transform, and nuclear Skyrmions.

While a PhD student at Heriot-Watt I was invloved as an organiser and a participant in a variety of reading groups.

January 2017 - September 2017: I organised a reading group on String Theory and D-Branes following Richard J. Szabo. An Introduction to String Theory and D-Brane Dynamics (With Problems and Solutions). ICP, 2 edition, 2011. Notes from this reading group are included in the notes section below.

October 2017 - January 2018: I participated in a reading group renormalisation and effective field theories following the book by Costello. Following this reading group we decided to start a short seminar series, the details of which are here.

October 2018 - March 2019: I organised a reading group on Statistical Field Theory following David Tongs Lecture notes .

The reading group moved online in 2020 and I started to participate again.

October 2020 - April 2021: I organised a reading group on Yang-Mills Equations over Riemann Surfaces following the seminal paper by Atiyah and Bott. A partial webpage for this reading group is available here.

June 2022-July 2022: I was involved in a reading group on Nahm's equations and hyperkähler quotient constructions. A partial webpage is available here.

Here are a selection of notes that I made to remind myself about interesting topics that I started reading about. N.B some of the links might be dead as I have migrated files from my Heriot Watt webpage.

- Notes on moment maps and the Hyperkähler structure of the moduli space of solutions to Hitchin's Self-duality equations.
- Notes on String Theory relating to the reading group we are having. The plan was that everyone would contribute to these notes but in the end it was just me. There are a couple of gaps where I did not have time to tex up some of the computations that we discussed.
- Notes for a talk I gave on classical bosonic membrane dynamics as part of our D-Brane reading group.
- Notes on rational maps that I made to remind myself of their properties and relation to vortices.
- Martin Wolf from the university of Surrey gave a short introductory course on Twistor theory at Heriot-Watt from 27/11/17-30/11/17. The lectures contained many exercises and some of us spent some time solving them. The exercises and our sketch solutions are here.
- Some notes on Monopoles, mini-twistors and spectral curves that I made ( am still making) while reading papers about the topics so that I could keep some conventions to hand.