General theory of elliptic hypergeometric functions. Exactly computable integrals, in particular, elliptic beta integrals. Classical and quantum integrable systems. Superconformal indices and
Seiberg duality. Self-similar potentials in quantum mechanics.

Main publications:

V. P. Spiridonov, “Essays on the theory of elliptic hypergeometric functions”, Russian Math. Surveys, 63:3 (2008), 405–472

V. P. Spiridonov and G. S. Vartanov, “Elliptic hypergeometry of supersymmetric dualities”, Commun. Math. Phys., 304 (2011), 797-874

V. P. Spiridonov, “Theta hypergeometric integrals”, St. Petersburg Math. J., 15:6 (2004), 929–967

S. E. Derkachov and V. P. Spiridonov, “Yang-Baxter equation,
parameter permutations, and the elliptic beta integral”, Russian Math. Surveys, 68:6 (2013), 1027–1072