Joshua Zahl & 王虹 - 三维挂谷集猜想
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https://www.slmath.org/workshops/1089/schedules/37025
The Kakeya set conjecture in three dimensions
March 3rd, 2025 (03:30 pm) - March 3rd, 2025 (04:30 pm)
Speakers: Joshua Zahl, University of British Columbia
Abstract:
A Besicovitch set is a compact subset of R^n that contains a unit line segment pointing in every direction. The Kakeya set conjecture asserts that every Besicovitch set in R^n has Minkowski and Hausdorff dimension n. I will discuss some recent progress on this conjecture, leading to the resolution of the Kakeya set conjecture in three dimensions. This is joint work with Hong Wang.
https://www.slmath.org/workshops/1089/schedules/37196
The Kakeya set conjecture in three dimensions II
March 6th, 2025 (02:00 pm) - March 6th, 2025 (03:00 pm)
Speakers: Hong Wang, New York University, Courant Institute
Abstract:
Given any set of delta-tubes in R^3, we can factor tubes into clusters, such that within each cluster, the tubes are dense and fill out a convex set, and these convex sets are essentially disjoint. We discuss some new aspects of the argument, putting into a broader context of projection theory. This is joint work with Josh Zahl.
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