Abstract: In the 1980's (at UWO) I gave a local construction of the Deligne-Langlands epsilon factors attached to representations of Galois groups of local field extensions. The method was to resolve an arbitrary representation by monomial representations, for which the construction was straightforward. At the time my idea was to attack the Langlands programme by making a similar resolution of an arbitrary admissible representation of $GL_{n}K$ where $K$ is a local field.

Returning to this with a bit more knowledge, I now more or less have the correct definition and the outline of the construction to the extent that I can handle $GL_{2}K$!

The entire Langlands programme has many features which were suggested by properties of representations of finite groups such as $GL_{n}{\mathbb F}_{q}$.

So I shall spend a lot of the time illustrating the constructions and properties in the case of finite groups - looking at some or all of: (i) Weil representations, (ii) cuspidality and monomial resolutions, (iii) local L-functions and (iv) Shintani descent.

Abstract: Several models for $(\infty, 1)$-categories have been defined and shown to be equivalent, and they are all being used in different areas of algebra and topology. More recently, there has been interest in more general $(\infty, n)$-categories, especially with Lurie's recent work on the Cobordism Hypothesis. Comparison of different definitions is still work in progress by several authors. In this talk, we will go over some of the models for $(\infty, 1)$-categories and discuss some of the methods for inductively generalizing them to models for $(\infty, n)$-categories.