Dávid R. Szabó

collaborators

4 papers

math.AG2026

Toric decomposition in algebraic groups

DÃ¡vid R. SzabÃ³

Over an arbitrary field $F$ , we construct $n + 1$ maximal tori $T_{1}, \dots, T_{n + 1}$ in $PGL_{n} (F)$ so that the product $T_{1} \dots T_{n + 1}$ is almost the…

math.AT2025

Constructing Highly Symmetric Compact Manifolds and Algebraic Varieties

DÃ¡vid R. SzabÃ³

For every algebraically closed field $k$ and natural number $r$ , we construct several algebraic varieties (over $k$ ) whose birational automorphism group contains every finite nilpo…

math.GR2025

Finite Class 2 Nilpotent and Heisenberg Groups

DÃ¡vid R. SzabÃ³

We present a structural description of finite nilpotent groups of class at most $2$ using a specified number of subdirect and central products of $2$ -generated such groups. As a co…

math.CO2025

Settling the no- $(k + 1)$ -in-line problem when $k$ is not small

Benedek KovÃ¡cs, ZoltÃ¡n LÃ³rÃ¡nt Nagy, DÃ¡vid R. SzabÃ³

What is the maximum number of points that can be selected from an $n \times n$ square lattice such that no $k + 1$ of them are in a line? This has been asked more than $100$ years ag…

Toric decomposition in algebraic groups

Constructing Highly Symmetric Compact Manifolds and Algebraic Varieties

Finite Class 2 Nilpotent and Heisenberg Groups

Settling the no-(k+1)-in-line problem when k is not small

Settling the no- $(k + 1)$ -in-line problem when $k$ is not small