6 problems

Let $G$ be a compact Lie group, let $MU_G$ denote $G$-equivariant complex cobordism, and let $KU_G$ denote equivariant complex K-theory. The relative smash product…

Length-spectrum obstruction conjecture. There is no Riemannian metric on $Q$ for which this quasi-isomorphism preserves the length filtration. Since the example has different compl…

Let $(Q,q_0)$ and $(Q',q'_0)$ be compact pointed Riemannian manifolds. For each $t\in\mathbf{R}$, let $F_{<t}C_*(\Omega_{q_0}Q;\mathbf{C})$ denote the subcomplex generated by loops…

Let $Q$ be a $d$-dimensional $\operatorname{Spin}^c$ manifold, let $\Lambda\subset T^*Q$ be a conic Lagrangian, and let $U\subset Q$ be open. Write…

Let $X$ be a compact Kähler Calabi–Yau manifold with integral Kähler class, and let $\operatorname{Fuk}(X)$ be its Fukaya category. Ganatra's conjecture. If $\operatorname{Fuk}(X)$…

Let $ku_p$ and $KU_p$ denote the connective and periodic $p$-complete complex $K$-theory spectra, respectively, and let $V(1)_*$ denote homotopy groups modulo $(p,v_1)$. Let…