This collection of open problems has been circulated since 2018 when, encouraged by
Sean Prendiville, I prepared a draft for the Arithmetic Ramsey Theory workshop in …

Ajtai, Koml\'{o} s, Pintz, Spencer and Szemer\'{e} di proved that every $(r+ 1) $-
uniform``locally sparse''hypergraph $ H $ of average degree $ d\geq 1$ has an independent …

We show that if $ A $ is a set of mutually orthogonal exponentials with respect to the unit disk
then $| A\cap [-R, R]^ 2|\lesssim_\varepsilon R^{3/5+\varepsilon} $ holds. This improves the …

The Heilbronn triangle problem asks for the placement of $ n $ points in a unit square that
maximizes the smallest area of a triangle formed by any three of those points. In $1972 …

We prove that every n-vertex complete simple topological graph generates at least Ω (n)
pairwise disjoint 4-faces. This improves upon a recent result by Hubard and Suk. As an …

We develop a new simple approach to prove upper bounds for generalizations of the
Heilbronn's triangle problem in higher dimensions. Among other things, we show the …

Additive combinatorics is the study of the combinatorial properties of sets of numbers,
particularly with respect to the operations of addition and multiplication. This thesis is …

Using ideas from the geometry of compression, we improve on the current upper bound of
Heilbronn's triangle problem. In particular, by letting∆(s) denotes the minimal area of the …

The paper deals with the following optimisation problem: we need to locate points inside a
given subset of Euclidean space in such a way that the smallest possible area of triangles …

CS 164 & CS 266: Computational Geometry Week 10 Lecture 10b: Mesh generation Page 1 CS
164 & CS 266: Computational Geometry Week 10 Lecture 10b: Mesh generation David …