13 problems

Let $C$ be an ellipse and let $O$ be an interior point that is not a focus of $C$. For each $n\geq 1$, the $n$-th caustic by reflection from $O$ is the envelope of the family of bi…

Caustics of iterates conjecture. For $0<r\leq 1/3$, the caustic of $R_r^{2m+1}$ is a $C^\infty$ curve with exactly four cusp singularities, with two of them occurring at…

The extended affine Weyl group Frobenius manifolds under consideration have caustic data analogous to that of the corresponding Coxeter group Frobenius manifolds. Caustic-data conj…

Starting from a planar tropical caustic, consider the connected components with infinitely many sides in the complement to the original caustic, and iterate the caustic constructio…

Let an elliptic billiard table be a smooth strictly convex closed curve in the Euclidean plane, and let $n\geq 1$. For a generic source of light inside the billiard table, consider…

Let $C$ be an oval, meaning a smooth strictly convex closed curve in the plane, and let an $n$-th caustic by reflection from an interior point $O$ be the envelope of billiard traje…

Let $f_0=x^3+y^3+z^3$, and consider the morsification obtained from the perturbation $x^3-3\varepsilon^2x+y^3-3\varepsilon^2y+z^3$ by splitting the critical points with coordinates…

Let $f$ be a real function singularity of type $E_7$ or $E_8$, and consider the complement of the caustic in the parameter space of a versal deformation of $f$. Homology conjecture…

Let $\gamma$ be a planar billiard table that is not an ellipse. For a light source chosen inside $\gamma$, let $\Gamma_n$ be the caustic by reflection after $n$ reflections, with…

Residue-vanishing conjecture. Cusp caustics lie at points $\vec x$ within curves on which the residues of the poles of $\mathbb S(\Lambda)$ vanish.

Ghost-source support conjecture. Cusp caustics always occur within the domain of support of ghost sources.

Ghost-source conjecture. Cusp caustics always coincide with ghost sources.

Let $r\in\{2,\ldots,\infty,w\}$, and consider billiard domains in a $C^r$ neighborhood of the circle. A billiard domain is said to preserve a $1/3$ and a $1/5$ caustic when its bil…