8 problems

Let $M$ be a compact manifold of dimension $m$, let $P:M\rightarrow\mathbb{R}^d$ be smooth, and let $\mathfrak{F}$ be the quasi-stratification of $M$ by the level sets…

Let $G$ be an ordered vector field, let $H$ be the fixed invariant one-dimensional set, and let $T_1,\ldots,T_k$ be the periodic orbits in $Ess(G)$. Choose tubular neighborhoods…

Let $(g,J)$ be a compatible almost Hermitian structure, and define … A biharmonic almost complex structure is a zero of $B$. Transversality conjecture. The map $B$ is transverse to…

Generic density conjecture. For any $A>0$ and $K$, ${\cal G}_{2}(3A/2,K)$ is dense in ${\cal G}_{3/2}(3A/2,K)\cap {\cal G}_{2}(A,K)$.

Let $f_1:X_1\to Y_1$ and $f_2:X_2\to Y_2$ be morphisms of schemes, and let … be their product. For $i=1,2$, let $F_i\in\mathbf{T}(X_i)$, and let $F_1\boxtimes F_2$ denote their ext…

Let $M$ be an open smooth $n$-manifold with a Riemannian metric $g$, and let $\alpha:N\subset M$ be a smooth compact codimension-one submanifold. An isotopy $A:N\times[0,1]\to M$ i…

Higher-jet transversality codimension conjecture. The set $\tilde A$ is a countable union of smooth submanifolds of codimension more than $n=\dim X$ in $J^{p+1}(X,Y)$.

Let $\Bbbk$ be an algebraically closed field of characteristic 0, let $X/\Bbbk$ be a projective variety, let $\sigma \in \operatorname{Aut}_{\Bbbk} X$, and let $Z \subseteq X$ be a…