*Species of structure: a Bridge between Differential Lambda Calculus and Combinatorics*

Species of structure lie at the intersection of combinatorics and denotational semantics. They were first introduced by Joyal as a unified framework for the theory of generating series in enumerative combinatorics and multiple tools were developed for the resolution of differential equations of species in this setting. Later, Fiore presented a generalized definition that both encompasses Joyal's species and constitutes a model of linear logic.

We will first introduce and connect the different viewpoints of species of structure and their series counterpart (analytic and normal functors) presented by Joyal, Girard and Hasegawa. Next, we will examine how the bicategory of generalized species of structure forms a model of differential linear logic.

As our end goal is to develop methods of resolution of differential equations for λ-terms, we will investigate the possible directions to tackle this problem.

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*Verifying Database Histories*

Popular databases offer control over the isolation level to which the operations in one transaction are visible to the operations in other concurrent transactions. Lower levels allow weaker consistency. So, we have to ensure that the histories of a database are consistent with their isolation levels.

Unfortunately, these isolation levels are mostly defined as low-level operations which makes it complicated to reason about the behavior of the system running under those isolations.

In this talk, we will present some popular isolation levels and consistency criteria for databases. We will introduce a framework, in which it becomes easier to formally reason about the behavior of a system. Then we will explore the complexities of deciding some consistency criteria using that framework.