平面上的近似入射几何。

IF 1.2 3区数学 Q1 MATHEMATICS

Research in the Mathematical Sciences Pub Date : 2025-01-01 Epub Date: 2025-09-05 DOI:10.1007/s40687-025-00552-4

Tuomas Orponen

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引用次数: 0

摘要

这些是2024年6月在班夫开设的一门迷你课程的讲义。他们讨论了在P∧R 2和L∧A（2,1）上的各种假设下δ -事件数I δ （P， L）的边界问题：= {(P， R)∈P × L: P∈[R] δ}。主要的焦点将放在与Furstenberg集合问题相关的假设上。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Approximate incidence geometry in the plane.

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Approximate incidence geometry in the plane.

These are lecture notes for a mini-course given in Banff in June 2024. They discuss the problem of bounding the number of $δ$ -incidences $I_{δ} (P, L) : = {(p, ℓ) \in P \times L : p \in {[ℓ]}_{δ}}$ under various hypotheses on $P \subset R^{2}$ and $L \subset A (2, 1)$ . The main focus will be on hypotheses relevant for the Furstenberg set problem.

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来源期刊

Research in the Mathematical Sciences Mathematics-Computational Mathematics

CiteScore

2.00

自引率

8.30%

发文量

期刊介绍： Research in the Mathematical Sciences is an international, peer-reviewed hybrid journal covering the full scope of Theoretical Mathematics, Applied Mathematics, and Theoretical Computer Science. The Mission of the Journal is to publish high-quality original articles that make a significant contribution to the research areas of both theoretical and applied mathematics and theoretical computer science. This journal is an efficient enterprise where the editors play a central role in soliciting the best research papers, and where editorial decisions are reached in a timely fashion. Research in the Mathematical Sciences does not have a length restriction and encourages the submission of longer articles in which more complex and detailed analysis and proofing of theorems is required. It also publishes shorter research communications (Letters) covering nascent research in some of the hottest areas of mathematical research. This journal will publish the highest quality papers in all of the traditional areas of applied and theoretical areas of mathematics and computer science, and it will actively seek to publish seminal papers in the most emerging and interdisciplinary areas in all of the mathematical sciences. Research in the Mathematical Sciences wishes to lead the way by promoting the highest quality research of this type.