Speaker: Larry Guth (MIT)

Title: Perspectives on the unit distance problem

Abstract:

Erdos posed the unit distance problem in the 1940s.  The problem is easy to state but remains far from fully understood.  It was one of the first problems in an area of combinatorics called incidence geometry.  Incidence geometry now has connections to many other areas, including topology, harmonic analysis, and number theory.  This spring, open ai gave a new example for the unit distance problem which gave the first improvement over Erdos's original example from the 1940s.  These new examples are based on high degree number fields, which tie in with Melanie Wood's talk last week (but this talk will be self-contained).

In the first half of the talk, we will give a short survey of incidence geometry.  I will try to describe why I think the unit distance problem is interesting. In the second half of the talk, we will describe the recent new examples.

Reception following the talk in room 2-290.