On May 20th 2010, the Department hosted a One-Day Colloquium in Combinatorics. As is becoming traditional, the meeting was organised jointly with Queen Mary, who held a linked event on the previous day.
The LSE event consisted of six talks on combinatorics delivered by speakers from the UK and elsewhere. Andrew Thomason (Cambridge) started the day with an entertaining talk about hereditary properties of coloured and weighted graphs. Peter Allen, who has a PhD from LSE and is now a postdoc at Warwick, spoke on the extent to which various theorems from extremal combinatorics could be transferred to random settings. Both Oleg Pikhurko (Carenagie Mellon) and Daniela Kuhn (Birmingham) gave talks explaining recent proofs of long-standing conjectures involving trees.
In Pikhurko's case, this was a conjecture of Entringer on labellings of trees, while Kuhn's talk concerned the proof of a conjecture of Sumner stating that all tournaments on 2n-2 vertices contain a copy of every directed tree on n vertices. Mathew Penrose (Bath) discussed some models and results on percolation problems in the plane. The final talk of the day was the Norman Biggs lecture, delivered by Tomasz Luczak (Poznan): the theme of the talk was the use of VC-dimension (a topic Norman Biggs is very familiar with) in extremal graph theory.
Overall, there were a variety of different topics covered in the entertaining and instructive talks.
More details can be found here.