## University of Sydney Algebra Seminar

# Matthew Dyer (University of Notre Dame)

## Friday 11 November, 12:05-12:55pm, Carslaw 175

### Groupoids, root systems and weak order

Several (largely equivalent) points of view for notions of groupoid with root system will be described. They are obtained by abstracting basic properties of Coxeter groups, such as the symmetric groups, with their root systems and weak orders. This talk will focus on examples and on aspects of the theory which generalize defining properties of Coxeter groups, such as the exchange condition and their presentations by braid relations.