中科院数学与系统科学研究院
数学研究所
调和分析及其应用研究中心
学术报告
调和分析和偏微分方程研讨班
报告人：王虹（纽约大学）
题 目：Furstenberg sets estimate in the plane（Ⅰ）
时 间：2024.07.29（星期一）11:00-12:00
地 点：南楼N913
摘 要：Furstenberg set conjecture states that a set containing an s-dim subset of a line in every direction should have dimension at least (3s+1)/2 when s>0. It can be viewed as an incidence problem for tubes and a continuous version of the Szemeredi-Trotter theorem.
We will survey a sequence of results by Orponen, Shmerkin and a recent joint work with Ren that leads to the solution of this conjecture.
The first lecture will be a research talk, starting from the second lecture, we will discuss a short proof of Bourgain's discretized sum-product theorem, followed by proofs of recent results by Orponen, Shmerkin, Ren and myself. No prior knowledge on geometric measure theory is required.
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