# Groups, Computation & Geometry at Pingree Park

Last week, I attended an excellent conference “Groups, Computation and Geometry” at the Pingree Park Conference Centre in the Colorado mountains. It was organised magnificently by Peter Brooksbank, Alexander Hulpke, Bill Kantor, Tim Penttila, and James Wilson. Pingree Park is at 9,000 feet (2,700 metres) and I did have headache on the last two days. My trip started badly with a case of gastro, but luckily I had arrived some three days before the conference, so by the second day of talks, I was feeling much better. My 50 minute talk had to be rescheduled to the Friday of the conference, because of this. Apart from your’s truly, the invited talks were given by Colva Roney-Dougal, Şükrü Yalçınkaya, Eric Moorhouse, and Simon Blackburn. Colva spoke about using pregroups to solve problems in combinatorial group theory, mainly word problems, and getting around in a Van Kampen diagram. Şükrü waved the flag for the computational group theorists and spoke on black-box recognition of classical groups. Eric waved the geometry flag and spoke on *p*-ranks of incidence matrices, and in particular, on ways to attack the “prime-order projective plane implies Desarguesian” conjecture. Simon’s talk carried the main theme of different types of discrete logarithm problems and their application to elliptic curve cryptography. All of these talks were amazing, and I followed each one with keen interest.

Bill Kantor was the master of the schedule, and I was one of only a few that enjoyed the format: only Bill knew who was speaking when, and the program for the subsequent day would be posted on a door each evening. No titles or abstracts, just the expectation that you would see the next talk and you would know then and there what it would be about. It’s good reasoning: if you wanted to know the title and abstract before hand, it might be because you were choosing whether to go or not, and with such a cosy conference, that is out of the question! The other argument, might be that you wanted to do some prior reading before the talk, but would you really?

Other talks that need special mention were from young people: John Sheekey gave a nice talk (with excellent jokes!), Phil DeOrsey (hyperovals yes!), Joshua Maglione (a confident presentation), Luke Morgan (but I’d seen it before), and James Wilson (as per usual). There was also a problems session on Wednesday afternoon, and I’ve taken particular interest in the two geometry problems by Tim Penttila and Jason Williford.

On the Wednesday morning, most of us split into teams and went for a hike. I went for a four hour hike with Alexander, Şükrü, Simon, Steve Linton, and Charles Leedham-Green. So I conclude with a few pictures from the top.

Cheers JB! I have to say, though the schedule (or lack thereof) was a bit of a shock to the system at the start, in the end I quite enjoyed it!