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（III）

时  间：2024.08.06（星期二）11:00-12:00

地  点：思源楼S803

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 third 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.