Speaker: Colva Roney-Dougal Affiliation: University of St Andrews, UK Time: 4:00 pm Thursday, 1 March, 2018 Location: Mathematics & Physics Building MLT2/303-102 |
How can we study infinite groups using only a finite amount of data? One solution, which dates back to Hamilton in the 1850s, is to work with them via presentations: the elements of the group are strings of letters, called words, and we’re given some rules about how to multiply the words together. Unfortunately, it was shown by Novikov and Boone in the 1950s that the word problem is undecidable: there exists no algorithm to determine whether two words describing elements of a group given via a presentation in fact represent the same group element. This is something of a drawback. In this talk I’ll show how we can associate geometries to finitely-presented groups, and use geometric ideas to answer a range of decision problems. |