This is a brief survey of the main results of the theory of elliptic hypergeometric functions--a
new class of special functions of mathematical physics. A proof is given of the most general …

A comprehensive review of the discrete quantum mechanics with the pure imaginary shifts
and the real shifts is presented in parallel with the corresponding results in the ordinary …

We study compactifications of the 6d E‐string theory, the theory of a small E8 instanton, to
four dimensions. In particular we identify N= 1 field theories in four dimensions …

A bstract Conformal blocks are the central ingredient of the conformal bootstrap programme.
We elaborate on our recent observation that uncovered a relation with wave functions of an …

We survey results on Galilei-and Poincaré-invariant CalogeroMoser and Toda N-particle
systems, both in the context of classical mechanics and of quantum mechanics. Special …

We degenerate the finite gap solutions of the KdV equation from the general formulation
given in terms of abelian functions when the gaps tend to points, to get solutions to the KdV …

A bstract We show that the 4d\(\mathcal {N}\)= 1 SU (3) N f= 6 SQCD is the model obtained
when compactifying the rank one E-string theory on a three punctured sphere (a trinion) with …

We consider supersymmetric surface defects in compactifications of the $6 d $ minimal $(D_
{N+ 3}, D_ {N+ 3}) $ conformal matter theories on a punctured Riemann surface. For the …

We present explicit generators D,..., Dn of an algebra of commuting difference operators in n
variables with trigonometric coefficients. The algebra depends, apart from two scale factors …

In this work we study the quantisation of the Seiberg-Witten curve for the E-string theory
compactified on a two-torus. We find that the resulting operator expression belongs to the …