Course Description
Bethe equations appear when you try to find eigenvalues of Hamiltonians from quantum integrable systems. There are many very different constructions of integrable systems but Bethe machinery seems to be universal, and it is rather unclear why. Maybe because of lack of understanding – we just do not know the better tools.
In my lectures I will try to explain some recent results about KdV-like systems. People suspected that Bethe equations have to be involved when you study eigenvalues but the situation was very unclear. Now we have some progress. New ideas ideologically not far from so-called AGT-conjecture. It means that the new approach uses the ideas from geometry of instanton manifolds.
No particular knowledge on representation theory is required.