I am a Master of Philosophy (Research) student at the University of Queensland under the supervision of Ole Warnaar.
My research interests lie in algebraic combinatorics, q-series, representation theory, special functions, and their interrelations.
Email: seamus.albion at uqconnect.edu.au
Honours Thesis: Generalised Selberg Integrals and Macdonald Polynomials
My honours thesis concerned the Selberg integral. In particular the close relationship between Knizhnik–Zamolodchikov equations, Macdonald polynomials, and generalised Selberg integrals. For those interested, here is a review article concerning the history and mathematics surrounding Selberg's integral.
Here is a copy of my thesis (pdf 15/06/18).
- The Macdonald Positivity Conjecture: A two-page expository report on Garsia–Haiman modules and the Macdonald Positivity Conjecture (pdf 31/10/2017)
- 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)
- 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 Jones Polynomial and Quantum Groups: A talk outlining
the relationship between the Jones polynomial and quantum groups presented in order to gain credit for my AMSI Summer School course. The talk was mostly based on Peter Tingley's "A minus sign" paper.
- The Littlewood–Richardson rule: Quantum Field Theory seminar (UQ) (May 2018)
- Three levels of hypergeometry: UQ Mathematics Students Society talks (May 2018) (slides)
- The Macdonald Positivity Conjecture: Representation Theory Presentation (UQ) (October 2017)
- A Brief History of the Rogers–Ramanujan Identities: UQ Mathematics Students Society talks (March 2017)
- 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 2017-2018 (website)
- 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
- Algebra and representation theory students (ARTS) seminar (UQ): Participant and speaker 2017-2018
- AMSIConnect student conference 2017 (UniMelb)
- President of the UQ Mathematics Students Society 2017
I have tutored (that is, been a teaching assistant for) the following courses at UQ:
- 2019 Semester 1: MATH3303 (Abstract Algebra & Number Theory) and MATH2400 (Mathematical Analysis)
- 2018 Semester 2: MATH4304 (Number Theory) and MATH2302 (Discrete Mathematics II)
- 2018 Semester 1: MATH2301 (Linear and Abstract Algebra and Number Theory) and MATH2400 (Mathematical Analysis)
- I was the tutor coordinator for MATH2400 in addition to teaching two tutorials.
- 2017 Semester 2: MATH2302 (Discrete Mathematics II)
- 2017 Semester 1: MATH2001 (Advanced Calculus and Linear Algebra II) and MATH1061 (Discrete Mathematics)
- Summer 2016/2017: MATH2001
- 2016 Semester 2: MATH1052 (Multivariate Calculus and ODEs)
- 2016 Semester 1: MATH1051 (Calculus and Linear Algebra I)
Sometimes I play saxophone with Jeremy Neale.
I also play clarinet in the UQ Symphony Orchestra. Our next performance is Rhapsody in Red, White and Blue @ QPAC, May 26th. You can listen to us perform
Symphonie fantastique by Hector Berlioz here.