5 problems

Let $\Gamma$ be a generic plane curve evolving under the curve-shortening flow, and let $\kappa$ denote its signed curvature. Write $n_\kappa(t)$ for the number of critical points…

Let $\Gamma$ be a generic plane curve evolving under the curve-shortening flow. Denote by $n_U(t)$ the number of critical points of its radial function relative to the fixed point…

Akopyan–Vysotsky conjecture.

Let $C$ be the unique compactification with rational components and no other singularities of the curve $\{x^n=y^{dn}\}$. Let … The algebra $A_n$ is the algebra acting on this homo…

Let $\gamma:[a,b]\rightarrow\mathbb{E}^2$ be an arbitrary continuous rectifiable parametric curve such that, for every $t\in(a,b)$, there is a non-zero derivative vector…