9 problems

Let $X_0$ and $X_1$ be noncollapsed $RCD(K,n)$ spaces with nonempty boundaries $\partial X_0$ and $\partial X_1$, where the boundaries are understood in the sense of Gigli and Pasq…

Closure conjecture. The set $\mathcal A$ is closed under gluing: if $A,B\in\mathcal A$ admit a gluing, then

Largeness conjecture. Every gluing

Let $(\hat\gamma,\hat k)$ denote boosted subextremal Kerr black hole initial data with parameters $\hat{\mathfrak{m}}$ (mass) and $\hat{\mathfrak{a}}$ (specific angular momentum).…

Let $X\in\operatorname{Alex}_{\amalg}^n(\kappa)$ satisfy the paper's condition, let $Y$ be a connected length metric space, and let $f\colon X\to Y$ be a 1-Lipschitz onto map. Glui…

RCD gluing conjecture. The glued metric measure space

Alexandrov gluing conjecture. The gluing produces an Alexandrov space $Y$ if and only if the gluing is by isometry and, for every $p\in Y$, $T_p(Y)$ is a metric cone over…

Let $(S,M,A)$ be a graded marked surface with a full arc system $A$. Say that it has enough marked intervals when … and, for each $k$, the inclusion $\iota_k:(D^2_k,M_k)\to(S,M)$ i…

Let $G$ be a complex reductive group and let $X$ be a smooth complex projective curve. Let $\mathcal Shv_{\mathcal N}(Bun_G(X))$ be the Betti category of nilpotent sheaves. Automor…