Seamus Albion

I am a PhD student at the University of Vienna where my advisor is Christian Krattenthaler. As such I am a member of the combinatorics group and the Vienna School of Mathematics. Before coming to Vienna I did my undergraduate and MPhil at the University of Queensland where my advisor was Ole Warnaar.

My research interests (at this stage) lie in special functions and combinatorics.

Email: seamus.albion at univie.ac.at

Preprints

S. Albion, T. Eisenkölbl, I. Fischer, M. Gangl, H. Höngesberg, C. Krattenthaler and M. Rubey, A generalization of conjugation of integer partitions, arXiv:2407.16043 (pdf).
S. P. Albion, E. M. Rains and S. O. Warnaar, Elliptic A_n Selberg integrals, arXiv:2306.02442 (pdf).

Publications

S. P. Albion, I. Fischer, H. Höngesberg and F. Schreier-Aigner, Skew symplectic and orthogonal characters through lattice paths, European Journal of Combinatorics 122 (2024), article 104000. arXiv:2305.11730 (pdf)
S. P. Albion, Proof of some Littlewood identities conjectured by Lee, Rains and Warnaar, Proceedings of the American Mathematical Society, Series B 11 (2024) 133–146. arXiv:2108.12766 (pdf)
S. P. Albion, Universal characters twisted by roots of unity, Algebraic Combinatorics 6 (2023), 1653–1676. arXiv:2212.07343 (pdf) (journal webpage)
S. P. Albion, E. M. Rains and S. O. Warnaar, AFLT-type Selberg integrals, Communications in Mathematical Physics 388 (2021), 735–791. arXiv:2001.05637 (pdf)

Also see this list on the arXiv.

Other writing

Character factorisations, z-asymmetric partitions and plethysm, Proceedings of FPSAC 2024 (Bochum), Séminaire Lotharingien de Combinatoire 91B (2024), Article 22, 12pp.
2-core Littlewood identities, Oberwolfach Reports 57/2022
MPhil thesis: Selberg integrals of Alba–Fateev–Litvinov–Tarnopolsky type (pdf)

Selected talks

Character factorisations and the Littlewood map: 67th Conference of the Australian Mathematical Society, University of Queensland, Brisbane, Australia, December 5th, 2023
(Elliptic) A_n Selberg integrals: Arbeitsgemeinschaft Diskrete Mathematik, TU Wien & Universität Wien, October 17th, 2023 (board talk)
Character factorisations and the Littlewood map: 90th Séminaire Lotharingien de Combinatoire (Bad Boll, Germany), September 3rd, 2023
Universal character factorisations: Séminaire Combinatoire et Théorie des Nombres, Université Lyon 1, February 28th, 2023 (slides)
Universal character factorisations: Arbeitsgemeinschaft Diskrete Mathematik, TU Wien & Universität Wien, January 17th, 2023 (slides)
2-core Littlewood identities: Oberwolfach workshop Enumerative Combinatorics, December 13th, 2022
2-core Littlewood identities: JMM 2022 AMS Special Session on Early Career Number Theory Research with Combinatorics, Modular Forms, and Basic Hypergeometric Series, April 9th, 2022
2-core Littlewood identities: Séminaire Lotharingien de Combinatoire 87, Domaine de la Barollière, Saint-Paul-en-Jarez, France April 5th, 2022
Elliptic A_n Selberg integrals: SFB Statusseminar, December 1st, 2021
2-core Littlewood identities: SFB meeting, JKU Linz, August 9th, 2021 (slides)
Selberg integrals and symmetric functions: Arbeitsgemeinschaft Diskrete Mathematik, TU Wien & Universität Wien, June 29th, 2021 (notes)
What is a honeycomb?: MathWiSe seminar, October 9th, 2020 (website)
What is Dyson's contribution to q-series?: MathWiSe seminar, July 9th, 2020 (website)
Selberg integrals and the AGT conjecture: AustMS 2019 Mathematical Physics session, December 2019 (Monash) (slides)
AFLT-type Selberg integrals: UQ Pure Mathematics Seminar, November 2019.
Selberg integrals and symmetric functions: Talk at AEC Sommerschool 2019 (slides).
U-turn alternating sign matrices: Quantum Field Theory seminar (UQ) (notes)
The Selberg integral and Macdonald polynomials: AustMS 2018 Representation theory session, Adelaide 2018. I also gave talk for the UQ Pure Mathematics seminar (March 2019). (slides)
From symmetric functions to hypergeometric integrals: AustMS student conference, December 2018 (UniSA) (slides)
Kazhdan–Lusztig theory: Quantum Field Theory seminar (UQ) (October 2018)
Generalised Selberg integrals and Macdonald polynomials: This was my honours presentation. I also gave an abridged version of this talk at the AMSI Winter School. (May/July 2018) (slides)
The Littlewood–Richardson rule: Quantum Field Theory seminar (UQ) (May 2018)

Some events

90th Séminaire Lotharingien de Combinatoire (Bad Boll, Germany) September 3–6, 2023
Elliptic Integrable Systems, Representation Theory and Hypergeometric Functions, (University of Tokyo, Japan) July 31–August 4, 2023 (website) (poster I presented)
FPSAC 2023 (UC Davis, USA) July 17–21, 2023
Workshop Enumerative Combinatorics (Oberwolfach, Deutschland) December 12–16, 2022
88th Séminaire Lotharingien de Combinatoire (Strobl, Austria) September 4–7, 2022
Algorithmic and Enumerative Combinatorics (Vienna, Austria) July 4–8, 2022
Workshop on Integer Partitions at the Nesin Matematik Köyü (Nesin Mathematics Village) (Şirince, Türkiye) May 30–June 5, 2022
87th Séminaire Lotharingien de Combinatoire (Saint-Paul-en-Jarez, France) April 3–6, 2022
Hypergeometry, Integrability, and Lie Theory (online, website) 7th – 11th December, 2020
New connections in integrable systems (online, website) September 29th – October 2nd, 2020
Australian Mathematical Society annual conference (Monash, Melbourne) 3rd-6th December, 2019
Algorithmic and Enumerative Combinatorics Sommerschool 2019 (Hagenberg, Austria) 29th July-2nd August, 2019
15th Symposium on Orthogonal Polynomials, Special Functions, and Applications (Hagenberg, Austria), 22nd-26th July, 2019
Formal Power Series and Algebraic Combinatorics 2019 (Ljubljana, Slovenija) 1st-5th July, 2019
Australian Mathematical Society annual conference (Adelaide) 4th-7th December, 2018
Australian Mathematical Society student conference (Adelaide) 28th-30th November, 2018
Rainsfest (UQ): A one-day workshop celebrating Eric Rains' birthday (website).
Quantum Field Theory Seminar (UQ): Participant and speaker 2017-2019
AMSI Winter School 2018 (UQ): The theme was curvature, and included short courses on conformal geometry, heat flow, and more.
AMSI Summer School 2018 (Monash): Courses in low-dimensional topology and mathematical relativity

Teaching

In Summer Semester 2022 I taught an exercise class for the course Diskrete Mathematik at the University of Vienna. At UQ I was a teaching assistant/tutor for several undergradute course including MATH2302 (Discrete Mathematics II) and MATH3303 (Algebra).