6 problems

Let $X$ be a hyper-Kähler manifold and consider the Hilbert spaces of states arising from Rozansky–Witten theory on a manifold with boundary. Rozansky–Witten Hilbert-space conjectu…

Let $M$ be a 3-manifold, let $Z_n^{LMO}(M)$ denote the degree-$n$ part of the LMO invariant, and let $X$ be a hyper-Kähler manifold of dimension $4n$. Write $W_X^{RW}$ for the Roza…

Let $X$ be a K3 surface and let $A$ be an abelian surface. For a connected Jacobi diagram $\Gamma$, write $\beta_\Gamma(X^{[n]},\sigma^{[n]})$ for the associated Rozansky–Witten in…

Sawon's sign conjecture. For $2\leq k\leq n$, $\beta_{\Theta_k}<0$ if $k$ is even and $\beta_{\Theta_k}>0$ if $k$ is odd. Equivalently,

Let $M_3$ be a 3-manifold, let $G$ be the relevant group, and let … be the moduli space associated with the disk $D^2$, viewed conceptually as the cotangent bundle of the affine Gr…

Let $X$ be a non-compact space whose Rozansky–Witten invariant $Z_{\mathrm{RW}[X]}(M_3)$ computes invariants associated with a non-semisimple modular tensor category, denoted…