Besicovitch 1/2 Conjecture and Linear Programming
Event details
| Date | 15.03.2024 |
| Hour | 14:15 |
| Speaker | Dr. Federico Glaudo (IAS-Princeton) |
| Location | |
| Category | Conferences - Seminars |
| Event Language | English |
Abstract:
In 1928 Besicovitch formulated the following conjecture: if E is a Borel subset of the plane with finite length and its length is more than 1/2 of its diameter in all sufficiently small disks centered at its points, then E is rectifiable.
The value 1/2 cannot be lowered and Besicovitch himself showed that the statement holds if 1/2 is replaced by 3/4. His bound was improved by Preiss and Tiser in the nineties to ~0.732.
In this talk, I will report on further progress stemming from a joint work with Camillo De Lellis, Annalisa Massaccesi, and Davide Vittone. Besides improving substantially the bound of Preiss and Tiser, our work uncovers a connection with a class of linear programming problems.
Practical information
- General public
- Free
Organizer
- Prof. Maria Colombo
Contact
- Prof. Maria Colombo