Survey on incidence estimates for tubes

To be held at ESB 2012 and on Zoom: https://ubc.zoom.us/j/68285564037?pwd=R2ZpLy9uc2pUYldHT3laK3orakg0dz09
Meeting ID: 682 8556 4037
Passcode: 636252

Reception and refreshments at 14:30 in the PIMS lounge, ESB 4th floor.

Given a set T of distinct \delta-tubes and a set P of disjoint \delta-balls in R^n, the set of incidences between T and P is defined as  $I (P, T) = \{ (p, l)\in P\times T: p\cap l \neq \emptyset \}$.  The well-known Szemeredi-Trotter theorem in combinatorics studies a discrete analogue, the number of incidences between points and lines in the plane.  On the other hand, the incidence for tube problems are  natural generalizations of projection theorems in geometric measure theory. 

In this talk, we will survey recent progress on incidence bounds for tubes including the Furstenberg sets estimate in the plane, restricted projections, Kakeya problem and discuss their connections and future problems.  A lot of progress is made by members of the analysis group at UBC.