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Throwing a Sofa Through the Window
We study several variants of the problem of moving a convex polytope $K$, with $n$ edges, in three dimensions through a flat rectangular (and sometimes more general) window.
Computational Geometry
On rich points and incidences with restricted sets of lines in 3-space
\medskip \noindent{\bf (3)} If $T$ is three-dimensional and nonlinear, the number of incidences between $L$ and a set of $m$ points in $R^3$ is $O\left(m^{3/5}n^{3/5} + (m^{11/15}n^{2/5} + m^{1/3}n^{2/3})s^{1/3} + m + n \right)$, provided that no plane contains more than $s$ of the points.
Combinatorics Computational Geometry 05D99, 14J99, 14N20, 52C10, 52C35, 52C45, 68R05
How to Find a Point in the Convex Hull Privately
We study the question of how to compute a point in the convex hull of an input set $S$ of $n$ points in ${\mathbb R}^d$ in a differentially private manner.
