12 problems

Let $p,q,t\in\mathbb C$ satisfy $M<|t|^{n+1}<1$. For fixed $w\in\mathbb T^n$, let $C_w$ be a contour inside the annulus … for infinitesimally small positive $\epsilon$, with the po…

Let $n$ be a positive integer, let $p,q,t$ satisfy $|p|,|q|,|t|<1$, and let $t_0,t_1,t_2,t_3,t_4,t_5$ be otherwise generic parameters satisfying … Let $C=C^{-1}$ be a contour conta…

Let $n$ be a positive integer. Let $z_i$, $i=1,dots,n$, $t_k$, $k=1,\dots,n+1$, and $f_j$, $j=1,\dots,n+2$, be independent complex variables, and set … With…

Let $N$ and $M$ satisfy $3N/2<M<3N$, and set $\tilde N=M-N$. Consider the electric $4d$ $\mathcal{N}=1$ theory with gauge group $SU(N)$, flavor symmetry…

Let $\mathcal{I}(b,\beta)$ be a general Romelsberger index, and let the hyperbolic limit mean $\beta\to0^+$ with $b\in]0,\infty[$ fixed. The estimate in question is understood with…

Let $\mathcal I(b,\beta)$ be a Romelsberger index in the hyperbolic limit $\beta\to0^+$ with $b\in]0,\infty[$ fixed, and let $r_G$ be the rank of the gauge group. Writing…

A four-dimensional supersymmetric gauge theory is described by an elliptic hypergeometric integral (EHI), and the total ellipticity condition is the corresponding mathematical cons…

Consider elliptic hypergeometric integrals on root systems and their higher-order analogues, including evaluation formulas and symmetry transformations. Conjecture on infinitely ma…

Consider exact formulas for elliptic hypergeometric integrals describing Seiberg duality transformations at the level of superconformal indices. Conjecture on elliptic hypergeometr…

Let $V(t_1,\ldots,t_8;p,q)$ be the elliptic hypergeometric integral function, regarded as an integral generalization of the meromorphic functions associated with discrete spin mode…

Let a family of meromorphic functions satisfy the novel two-index biorthogonality relation described in the source. Spiridonov's conjecture. These functions determine a new family…

Let $n$ be a positive integer and let $t_0,t_1,t_2,t_3,u_0,u_1,v_0,v_1,v_2,v_3$ be generic parameters satisfying the balancing condition … Write $\cR^{*(n)}_{\boldsymbol\lambda}$ f…