10 problems

Let $M$ be a closed oriented aspherical manifold. Its tangent bundle is denoted by $TM$, and a flat structure on $TM$ means that it is induced by a representation of the fundamenta…

A flat Hilbertian bundle of determinant class is a flat Hilbertian vector bundle whose relevant operators are of determinant class. The Poincaré–Reidemeister metric is the metric o…

Kählerness conjecture. If $X$ is Kähler, then $F$ is a Kähler form on ${{\cal M}_{\cal N}}$.

Beilinson–Cheeger–Chern class conjecture. For all $p \geq 1$ and $n \in {\mathbb N} \cup\{\infty\}$,

Let $X$ be a smooth complex quasi-projective variety with base point $x$, and let … be Lie irreducible with quasi-unipotent monodromy at infinity. Let $(V_\rho,\nabla_\rho)$ be the…

Let $X$ be a smooth complex quasi-projective variety and let $\mathbb V$ be a local system of geometric origin on $X$. Let $(V,\nabla)$ be the associated algebraic flat vector bund…

Let $X$ be a smooth complex quasi-projective variety with base point $x$, and let … be a properly rigid representation with quasi-unipotent monodromy at infinity. Let…

Let a flat bundle over a complex curve have Lyapunov exponents, and let the degree refer to the degree of a holomorphic subbundle of the bundle. Let the monodromy group be the subg…

Milnor's conjecture. For every prime $p$, the classifying spaces ${\mathrm B}G$ and ${\mathrm B}G^{\delta}$ are $p$-adically equivalent.

Let $K$ be a compact Riemannian manifold, let $g:\pi_1(N)\to\operatorname{Iso}(K)$ be a homomorphism, and let $h:K\to\operatorname{Hom}_c(\pi_1(N),U(p,q))$ be a continuous $g$-cocy…