UBC Harmonic Analysis and Fractal Geometry: Shukun Wu

The SL_2 Kakeya problem is a special case of the three-dimensional Kakeya conjecture, and it is surprisingly connected to the restricted projection problem in geometric measure theory. In this talk, I will first discuss a proof of SL_2 Kakeya problem using regulus strips. Then I will discuss the connection between SL_2 Kakeya and the restricted projection theorem, and why regulus strip is the correct object to study. Finally, I will discuss a related problem that helps to rule out the SL_2 enemy scenario in Katz-Zahl's improvement in three-dimensional Kakeya conjecture. This talk is based on joint work with Nets Katz and Joshua Zahl.