On Wednesday 13th June 2018, Dr Simon Smith gave his prestigious “morning lecture” at the British Mathematical Colloquium 2018, held this year at the University of St Andrews. The BMC is the largest pure mathematics conference to be held annually in the UK, and it has been held every year since 1949. An archive of historical “Morning Speakers” is maintained by the University of St Andrews here: http://www-history.mcs.st-and.ac.uk/BMC/morning.html.
There were 12 Morning Speakers this year, including Clifford Cocks (one of the inventors of the RSA encryption algorithm), David Conlon (a professor of mathematics at the University of Oxford who was awarded the European Prize in Combinatorics in 2011 for his work on Ramsey Theory), and Jonathan Bennett (a professor of mathematics at the University of Birmingham who was awarded the Whitehead Prize in 2011 for his contributions to harmonic analysis).
Simon talked about his recent work on permutation groups that are subdegree-finite (meaning that all orbits of point stabilisers are finite – any automorphism group of a connected, locally finite graph is an example). In particular, Simon has developed a structure theory for such groups when they are infinite and primitive. His results show that the group structure in the infinite case mirrors the finite case (which is covered by the famous O’Nan—Scott Theorem) but with one important difference: groups can be “built” from smaller groups using the box product construction that Simon developed in his 2017 paper in Duke Math. J.
Peter Cameron has written more about Simon’s talk on his blog: https://cameroncounts.wordpress.com/2018/06/14/british-mathematical-colloquium-days-3-and-4/