9 problems

Cohomotopy theory assigns cohomology classes to charges carried by branes in M-theory. Cohomotopy conjecture. Cohomotopy theory is conjectured to be the actual cohomology theory of…

Let $X$ be a space equipped with a $\mathbb{Z}$-graded cochain complex and a Morse function $h$. For a compatible circle action, let the equivariant Poincaré polynomial be…

Let $X_1=(X,\omega_1)$ and $X_2=(X,\omega_2)$ be symplectic manifolds on the same underlying manifold, where $omega1$ and $omega2$ are connected by a path of symplectic forms. For…

Let $X$ be a symplectic manifold, and let $g_0,g_1:X\rightarrow X$ be symplectomorphisms. The maps $(g_0)_*$ and $(g_1)_*$ are induced on the groups $SH_{\bullet}^M(Y,X)$ associate…

Let $K^{-n}(X):=\widetilde{K}(\Sigma^n X_{+})$ for $n\geq 0$, where $\Sigma^n$ denotes the $n$-th reduced suspension and $K^0(X)$ is the Grothendieck group of structural vector bun…

A cohomology theory has a divisible group with formal and étale components. Globalness conjecture. The globalness of a cohomology theory is completely determined by the formal comp…

Naive categoricity conjecture for Betti cohomology. The description of a Weil cohomology theory with $\mathbb Q$-coefficients that factors through $\operatorname{Mot}/K$ is categor…

Let $\operatorname{Kt}_F$ be Kottwitz's $F$-linear tensor category for a local or global field $F$, and let there be natural functors … For a variety $X$ over…

Let $\mathbb{TR}$ be a candidate (co)homology theory on dg-categories over $\mathbf{F}_{p}$, with $\mathsf{dg}\mathsf{Cat}_{\mathbf{F}_{p}}$ the category of dg-categories over…