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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.

ICMS

Fifth Floor

Bayes Centre

47 Potterrow

Edinburgh

EH8 9BT

Tel : 0131 650 9816

Fax : 0131 651 4381

Mail : johanna.mcbryde@icms.org.uk