Analysis Seminar

Title: Sharp Furstenberg Sets Estimate in the Plane
Speaker: Kevin Ren
Speaker Info: Princeton
Brief Description:
Special Note:

Fix a real number 0 < s <= 1. A set E in the plane is a s-Furstenberg set if there exists a line in every direction that intersects E in a set with Hausdorff dimension s. For example, a planar Kakeya set is a special case of a 1-Furstenberg set, and indeed we know that 1-Furstenberg sets have Hausdorff dimension 2. However, obtaining a sharp lower bound for the Hausdorff dimension of s-Furstenberg sets for any 0 < s < 1 has been a challenging open problem for half a century. In this talk, I will explain the recent resolution of the Furstenberg set conjecture using tools from Fourier analysis and additive combinatorics. Joint works with Yuqiu Fu and Hong Wang.
Date: Monday, April 22, 2024
Time: 4:10pm
Where: Lunt 105
Contact Person: Xiumin Du
Contact email: xdu@northwestern.edu
Contact Phone:
Copyright © 1997-2024 Department of Mathematics, Northwestern University.