A wildly embedded 1-dimensional compact set in $S^3$ each of whose components is tame

Groups whose set of vanishing elements is exactly a conjugacy class

‎Let $G$ be a finite group‎. ‎We say that an element $g$ in $G$ is a vanishing element if there exists some irreducible character $chi$ of $G$ such that $chi(g)=0$‎. ‎In this paper‎, ‎we classify groups whose set of vanishing elements is exactly a conjugacy class‎.

A Tame Cantor Set

A Cantor set is a non-empty, compact set that has neither interior nor isolated points. In this paper a Cantor set K ⊆ R is constructed such that every set definable in (R, <,+, ·,K) is Borel. In addition, we prove quantifierelimination and completeness results for (R, <,+, ·,K), making the set K the first example of a modeltheoretically tame Cantor set. This answers questions raised by Friedma...

Sets Whose Difference Set Is Square-free

The purpose of this note is to give an exposition of the best-known bound on the density of sets whose difference set contains no squares which was first derived by Pintz, Steiger and Szemerédi in [PSS88]. We show how their method can be brought in line with the modern view of the energy increment strategy employed in problems such as Szemerédi’s Theorem on arithmetic progressions, and explore ...

A Compact Convex Set in £3 Whose Exposed Points Are of the First Category

A Point Set Whose Space of Triangulations Is Disconnected

In this paper we explicitly construct a triangulation of a 6-dimensional point configuration of 324 points which admits no geometric bistellar operations (or flips, for short). This triangulation is an isolated element in the graph of triangulations of the point configuration. It has been a central open question in polytope combinatorics in the last decade whether point configurations exist for...