Krystal Taylor

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20232026

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math.CA2025

Interior of distance trees over thin Cantor sets

Yeonwook Jung, Krystal Taylor

It is known that if a compact set $E$ in $R^{d}$ has Hausdorff dimension greater than $(d + 1) /2$ , then its $n$ -chain distance set $$Δ^n(E) = \left\{\left(\left|x^1-x^2\right|…

math.CA2025

Triangles in the Plane and arithmetic progressions in thick compact subsets of $R^{d}$

Samantha Sandberg-Clark, Krystal Taylor

This article focuses on the occurrence of 3-point configurations in subsets of $R^{d}$ of sufficient thickness. We prove that a compact set $A \subset R^{d}$ contains…

math.NT2025

Counting Lattice Points near Korányi Spheres via Generalized Radon Transforms

Rajula Srivastava, Krystal Taylor

In this note, we study a lattice point counting problem for spheres in Heisenberg groups, incorporating both the non-isotropic dilation structure and the non-commutative group law.…

math.CA2025

Point configurations in sets of sufficient topological structure and a topological {E}rdős similarity conjecture

Alex McDonald, Krystal Taylor

We explore the occurrence of point configurations within non-meager (second category) Baire sets. A celebrated result of Steinhaus asserts that $A + B$ and $A - B$ contain an interval…

Interior of distance trees over thin Cantor sets

Triangles in the Plane and arithmetic progressions in thick compact subsets of Rd

Counting Lattice Points near Korányi Spheres via Generalized Radon Transforms

Point configurations in sets of sufficient topological structure and a topological {E}rdős similarity conjecture

Triangles in the Plane and arithmetic progressions in thick compact subsets of $R^{d}$