7 problems

Let $M^{2n}$ be a GKM$_4$ manifold with GKM graph $\Gamma$. A torus manifold is a manifold with an effective action of a torus whose dimension is half the manifold dimension, and a…

Let $X$ be a non-Fano variety containing a regular complex-algebraic Calabi–Yau hypersurface $Z_f$, let its Laurent smoothing be a pre-symplectic and pre-Kähler space, and let…

Let $X$ range over real $2n$-dimensional torus manifolds corresponding to a multifan $\mathcal S_X$. Let $h_k(\mathcal S_X)=\sum_{i=k}^n(-1)^{i-k}\binom{i}{k}e_{n-i}(\mathcal S_X)$…

Torus diffeomorphism conjecture. $B'$ is diffeomorphic to a $(k+1)$-dimensional torus.

No-positive-scalar-curvature conjecture for torus connected sums. The manifold $T^n\mathbin{\#}M^n$ admits no metric with scalar curvature $R>0$. This conjectural obstruction is us…

K-theory presentation conjecture. The ring $K^*(E(X))$ is a free $K^*(B)$-module of rank $m=\chi(X)$ and is isomorphic to $\mathfrak{S}/\mathfrak{J}$.

Minkowski-relation presentation conjecture. As a vector space, $\mathcal{F}^{2k}(X)$ is generated by the elements $\{x_I\}_{I\in K}$ subject to the Minkowski relations