An introduction to the modular representation theory of algebraic groups

In this introductory talk, I will introduce various classes of representations that naturally arise when studying the classical and modular representation theory of algebraic groups. In the classical setting the structure of these modules is understood and governed by combinatorial data (root systems and Weyl groups). In the modular setting, the structure of these modules are poorly understood and many basic questions (dimensions and characters) remain open. I will sketch some of the techniques (including deep connections to the geometry of the affine Grassmannian of the Langlands dual group) used to study these representations and, time permitting, my minuscule contributions to the field.