**Talk 1:**

**Speaker:**Matthew Burke

**Title**: Sites of Smooth Affine Schemes

**Abstract**:

In this talk we will sketch the construction of a few well-adapted models of synthetic differential geometry. Then we will recall the definition of an intuitionistic order relation and show how to define one in the Dubuc topos. Finally we will formulate Lie’s third theorem in a manner appropriate to this setup.

**Talk 2:**

**Speaker**: Ben MacAdam

**Title**: Linear/Non-Linear models in a 2-category: Part 1

**Abstract**:

A linear/non-linear model is a monoidal adjunction between a cartesian category and symmetric monoidal category. Such an adjunction gives rise to a coalgebraic modality which in turn a model of MELL. Birkedal showed that these results translate easily to fibred monoidal categories — here one obtains a model in each fiber category. We show that many of these results can be further generalized to pseudomonoids in 2-categories with suitable universal properties.