# Activity

### Introduction:

**Speaker:** Professor Andrew D. Lewis (Queen’s University, Canada) Outline: Distributions, i.e., families of subspaces of tangent spaces, arise naturally in many places, including differential geometry, mechanics, and control theory. These lectures will be a comprehensive treatment of the theory of distributions, with a particular emphasis on the differences in the theory arising in the smooth and real analytic settings. A proper understanding of the real analytic theory requires some nontrivial machinery having a rather algebraic basis, namely tools from sheaf theory. We shall not delve deeply into sheaf theory, but touch upon enough of it so that its relevance is highlighted, and a student needing to use the theory can approach the rather daunting literature with some confidence. A preliminary list of topics is as follows. -Generalised subbundles and distributions: definitions, elementary properties, and applications. -The need for sheaves and an introduction to sheaf theory. -From generalised subbundles to subsheaves of vector sheaves and back to generalised subbundles. -Lie algebraic constructions. -The Orbit Theorem and applications.