February 12
3:00pm, BRH 105
Joshua Wiscons
(Sacramento State)

Title:
Investigating groups via the geometry of their involutions

Abstract:
The set of involutions (elements of order two) of a group is often highly structured,
and investigating this set can be an effective way to better understand the group.
This talk will explore the involutions of two familiar groups: $\operatorname{SO}_3(\mathbb{R})$
(the group of rotations the sphere), and $\operatorname{PSL}_2(\mathbb{C})$ (the group of Möbius transformations of $\mathbb{C}\cup\{\infty\}$).
In the former case, the group structure endows the set of involutions with the structure of a projective plane. In the latter case, the involutions form a projective plane with a missing quadric. The talk will conclude by indicating how the tension between these two examples (genuine plane vs. almost plane) is driving progress on a 15 yearold problem related to the classification of the (modeltheoretically important) simple groups of finite Morley rank. Familiarity with basic group theory and linear algebra will be assumedgroup actions will also appear. But sadly, no model theory will be needed.