Tuomas Orponen

activity

20102026

most citedOn restricted families of projections in R^3

52 citations · 367 across the 81 of their papers we have counts for

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5 papers · 1 filter

math.CO2026

Visibility problem in the plane

Tuomas Orponen, Alex Rutar

We disprove the visibility conjecture in the plane and prove the sharp upper bound for the almost-sure dimension of visible parts. Precisely, let $K \subset R^{2}$ be a co…

math.CO2025

Asymmetric sum-product theorems for Katz-Tao sets

Tuomas Orponen

I prove two variants of the $A B C$ sum-product theorem for $δ$ -separated sets $A, B, C \subset [0, 1]$ satisfying Katz-Tao spacing conditions. The main novelty is that the cardinality…

math.CO2024

Large cliques in extremal incidence configurations

Tuomas Orponen, Guangzeng Yi

Let $P \subset R^{2}$ be a Katz-Tao $(δ, s)$ -set, and let $L$ be a Katz-Tao $(δ, t)$ -set of lines in $R^{2}$ . A recent result of Fu and Ren gives a sharp…

math.CO2021

On the discretised $A B C$ sum-product problem

Tuomas Orponen

Let $0 < β \leq α < 1$ and $κ > 0$ . I prove that there exists $η > 0$ such that the following holds for every pair of Borel sets $A, B \subset R$ with $dim_{H} A = α$ …

math.CO2018★ 2 cited

A note on expansion in prime fields

Tuomas Orponen, Laura Venieri

Let $β, ε \in (0, 1]$ , and $k \geq exp (122 max {1/ β, 1/ ε})$ . We prove that if $A, B$ are subsets of a prime field $Z_{p}$ , and $∣ B ∣ \geq p^{β}$ , then there exists a sum of the…

Visibility problem in the plane

Asymmetric sum-product theorems for Katz-Tao sets

Large cliques in extremal incidence configurations

On the discretised ABC sum-product problem

A note on expansion in prime fields

On the discretised $A B C$ sum-product problem