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 …

This updated edition will continue to meet the needs for an authoritative comprehensive
analysis of the rapidly growing field of basic hypergeometric series, or q-series. It includes …

This is a complement to my previous article “Advanced Determinant Calculus”[C.
Krattenthaler, Advanced determinant calculus, Séminaire Lotharingien Combin. 42 …

A bstract Choi, Kim, Kim, and Nahmgoong have recently pioneered analyzing a Cardy-like
limit of the superconformal index of the 4d\(\mathcal {N}= 4\) theory with complexified …

We give a full list of known N= 1 supersymmetric quantum field theories related by the
Seiberg electric-magnetic duality conjectures for SU (N), SP (2 N) and G 2 gauge groups …

We prove a pair of transformations relating elliptic hypergeometric integrals of different
dimensions, corresponding to the root systems BC n and A n; as a special case, we recover …

An exact formula for partition functions in 3d field theories was recently suggested by
Jafferis, and Hama, Hosomichi, and Lee. These functions are expressed in terms of specific …

A bstract Recently an algorithm to dualize a theory into its mirror dual has been proposed,
both for 3d\(\mathcal {N}\)= 4 linear quivers and for their 4d\(\mathcal {N}\)= 1 uplift. This …

In this chapter we introduce the basic concepts of this thesis and give an impression of some
of the methods used to study them. Moreover we describe the connections to other parts of …

A bstract We propose new classes of 4d\(\mathcal {N}\)= 1 S-confining gauge theories, with
a simple gauge group, rank-two matter and cubic superpotentials. The gauge group can be …