Event Details

Speaker 1: Jan Grabowski (Lecturer) A variety of flags Speaker 2: Patrick Ramsey (PhD student) Modelling many moving objects using configuration spaces

Speaker 1: Jan Grabowski (Lecturer)

A variety of flags

Some mathematical ideas are both simple and pervasive but obliquely named, and flags are a good example of this. To a mathematician, a flag is a collection of subspaces of a vector space, each contained in the next and having dimension less than its predecessor. So in three dimensions, we could picture a plane containing a line, both containing the origin. The collection of all flags has a fascinating geometrical and algebraic structure and we will explore some small examples and some related topics.

Speaker 2: Patrick Ramsey (PhD student)

Modelling many moving objects using configuration spaces

Traditionally, it has been common to model physical situations by replacing objects by points. When we have many objects which can move freely, this gives us a configuration space of points. However, there are various situations when a point-shaped model contains insufficient information, in particular when the objects are constrained by some boundary which significantly limits their space to move. In this situation, we may replace the points by objects with volume. We will discuss some of the techniques we use for understanding configuration spaces, and what changes when going from the configuration space of points in a plane to the configuration space of hard discs inside a circle.