## 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

### Papers and preprints

- S. P. Albion, E. M. Rains and S. O. Warnaar,
*Elliptic*A_{n}*Selberg integrals*(in preparation) - S. P. Albion,
*Proof of some Littlewood identities conjectured by Lee, Rains and Warnaar*arXiv:2108.12766 (pdf 14/12/2021) (more up-to-date than the arXiv), submitted. - S. P. Albion, E. M. Rains and S. O. Warnaar,
*AFLT-type Selberg integrals*, (pdf 26/10/2021), arXiv:2001.05637, Communications in Mathematical Physics**388**(2021), 735–791.

Also see this list on the arXiv.

### Other writing

- MPhil thesis:
*Selberg integrals of Alba–Fateev–Litvinov–Tarnopolsky type*(pdf 24/09/2020)

### Talks

*2-core Littlewood identities*: JMM 2022 AMS Special Session on Early Career Number Theory Research with Combinatorics, Modular Forms, and Basic Hypergeometric Series, January 8th, 2022 (virtual)*Elliptic A*: SFB Statusseminar, December 1st, 2021_{n}Selberg integrals*2-core Littlewood identities:*SFB meeting, JKU Linz, August 9th, 2021 (slides)*Selberg integrals and symmetric functions:*Arbeitsgemeinschaft Discrete 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)

### Academic Activities

*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, Slovenia) 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

At UQ I was a teaching assistant/tutor for several undergradute course including MATH2302 (Discrete Mathematics II) and MATH3303 (Algebra).### Music

When I'm not doing mathematics I'm usually thinking about music.

I play saxophone with Jeremy Neale, and have played saxophone for Rinse and
The John Steel Singers. You can hear me on SPOD's song *Golden Gaytime*.

I used to play clarinet in the UQ Symphony Orchestra. For a list of works I performed with them click here.