10 problems

Let $\gamma_t$, $t\in[0,1]$, be an eversion of a smooth circular wave front with no dangerous self tangencies: a family of generic oriented wave fronts in $\mathbb{R}^2$ whose endp…

Modified Low conjecture. Two events are causally unrelated if and only if the lifts of their fronts are unlinked in the appropriate sense.

Let a convex polygon billiard be a billiard in a convex polygonal table, and let $W_t(P)$ denote the billiard wave front at time $t$ from a point $P$ in the table. The wave front b…

Let a convex billiard table be a convex planar domain, and let $W_t(P)$ denote the billiard wave front at time $t$ from a point $P$ in the table. The wave front becomes dense if it…

Let a convex billiard table be a convex planar domain, and let $W_t(P)$ denote the billiard wave front at time $t$ from a point $P$ in the table. The wave front becomes dense if it…

Let $\mathbb{T}^d$ be the $d$-dimensional torus with $d>1$, equipped with a smooth Riemannian metric, and let $W_t(P)$ denote the wave front at time $t$ from a point…

Let $M$ be a $d$-dimensional Riemannian manifold with or without boundary, where $d\geq 2$, and let $W_t(P)$ denote the wave front at time $t$ from a point $P\in M$. The wave front…

The critical wave fronts are described by profiles depending on a reaction term $f$, with the relevant alternatives being either smooth continuation of the limiting profile after s…

Let $\Delta$ be a cooriented wave front whose Legendrian lift to $ST^*\mathbb{R}^2$ is embedded, hence a Legendrian knot. A vertex of $\Delta$ is an extremum of its curvature; cusp…

Calculus correspondence. The pedal evolution $Un\text{-}ped_{{\bf r},P}$ is $\mathcal{A}$-equivalent to the normal form of a Whitney umbrella $\times\mathbb{R}^{n-1}$ if and only i…