Scottish Mathematical Sciences Training Centre

Quantum integrable systems appear in many branches of mathematical physics (e.g. statistical
mechanics, quantum mechanics, high-energy physics and string theory) but also have overlap with
areas in pure mathematics in particular algebra and geometry. This short course will review some
recent developments of `modern usage’ of quantum integrable systems in different areas whose
selection is highly biased by the interests of the organisers. This short course is a first attempt to
gauge interest and might be followed in the future by more in depth courses.

Aims

To give several short lectures on various active research topics in quantum integrable systems which
go beyond a typical research seminar by spending more time to introduce ideas and notions and
presenting through tutorials an introduction to some of the techniques involved. We are not aiming
at being comprehensive but simply trying to showcase some recent developments in slightly more
depth than is possible in research seminars.

Programme

Lectures will take place 1 June - 6 July 2016 on Wed & Fri at 14:00-15:30. We will cover the following topics:

• Lectures 1-3 (A. Doikou, 1, 3 & 8 June): Braid groups, quantum algebras and Bethe ansatz
• Lectures 4-6 (C. Korff, 10, 15 & 17 June): Quantum Integrability & Quantum Schubert calculus
• Lectures 7-9 (R. Weston, 22, 24 & 29 June): The qKZ equation and Solvable Lattice Models
• Lectures 9-10 (P.-M. Adamopoulou, 1 & 6 July): The PDE/ODE-IM correspondence

Further details can be found in the programme under course content 2015-16.

Prerequisites

Starting point for each of the lecture series will be only a basic mathematical background and we will
attempt to explain all notions from scratch. A liking of algebra (in particular representation theory),
combinatorics and mathematical physics would be of an advantage but is not a must.