4 problems

Let $Y(t)$ be a path on the manifold of orthonormal $n$-frames, and let $\Delta$ be a tangent vector transported parallel along this path according to the parallel transport equati…

Let $X_K$ be a smooth connected scheme over $K$, let $x_0,x_1\in X(K)$, and let $F_{x_i}$ denote the corresponding fibre functors on the category under consideration. Write…

Let a swept surface carry sweeping functors arising from two-dimensional parallel transport, and consider their smooth limit. Let the group of diffeomorphisms of the swept surface…

Let $X$ be a smooth projective curve over $\overline{{\mathbb{Q}}}_p$. A vector bundle on $X_{{\mathbb{C}}_p}$ is semistable if every nonzero subbundle has slope at most its slope.…