Representation theory and geometry – Geordie Williamson (ICM2018) [video]

Here is a link to the corresponding SIGMA 2018 paper and a link to the video shown at the end of the talk, which shows an animation illustrating the conjectures in the paper.

An animation illustrating the conjectures [video] https://www.youtube.com/watch?v=Ru0Zys1Vvq4

The Intro begins...

  These conjectures resulted from our attempts to
  understand data obtained following a 9 month
  calculation in magma on a supercomputer at the MPIM
  in Bonn. These results go far beyond existing 
  calculations and are obtained using a new algorithm.
  The algorithm relies in an essential way on ideas of 
  Libedinsky, Riche and the second author. The behaviour 
  we observe appears highly non-trivial, which suggests 
  that proving anything might be difficult.

Billiards and Tilting Characters for SL3 [pdf]

http://emis.ams.org/journals/SIGMA/2018/015/sigma18-015.pdf