7 problems

Let $G$ be a compact Hausdorff topological group, and define its Witten zeta function by … where the sum runs over the finite-dimensional irreducible representations of $G$. Kuroka…

Higher-genus gauge/string duality conjecture. The torus gauge/string duality should admit a generalization to every genus $g\geqslant 2$, involving not only the expansion of the he…

Let $\{g_n\}_{n\geq 0}$ be the sequence defined earlier in the paper through the rank-three Witten zeta function of type $G$. Nonvanishing conjecture for $g_n$. If…

Let $n$ be a positive integer, let $f_B(x)=(1+x)(1+2x)$ and $f_G(x)=(1+x)(1+2x)(1+3x)(2+3x)$, and let $E_{2k}(\tau)$ denote the Eisenstein series for $\tau$ in the upper half-plane…

Optimality conjecture. In the theorem, all stated inequalities for orders of vanishing are actually equalities. The theorem establishes the displayed lower bounds for compact simpl…

Let $\MZV(w,\le l)$ be the $\Q$-vector space generated by multiple zeta values of weight $w$ and depth at most $l$, and let $\gz_\slfour$ denote the Witten multiple zeta function a…

The span conjecture. The space $V_w$ coincides with the $\mathbb{Q}$-vector space spanned by all weight-$w$ alternating Euler sums of depth at most two.