Adam Sheffer (Theory Seminar)

sheffer.jpg"Few distinct distances implies no heavy lines"
Adam Sheffer
(California Institute of Technology)
Monday, February 22nd, 2016, 2:00 pm
EBU3B, Room 4258
Guth and Katz's almost tight bound for Erdos' distinct distances problem left open the problem of characterizing the structure of point sets that determine a small number of distinct distances (another problem that was posed by Erdos). In this talk I will introduce this problem in detail and discuss what is currently known. We will focus on a specific result, showing that if a set of n points determines o(n) distinct distances then no line contains n^{7/8} points of the set and no circle contains n^{5/6} such points. This result combines tools from incidence geometry and additive combinatorics.

Joint work with Joshua Zahl and Frank de Zeeuw.