**abstract:**
In topological data analysis a generalised persistence module is defined to be a functor a pre-ordered set to some abelian target category. Motivated by this, we study functors from posets (or more generally, small categories) to the category of vector spaces over a field $k$. If $\mathcal{P}$ is a poset, we refer to such functors as $k$-linear representations of $\mathcal{P}$, or as $k\mathcal{P}$-modules. Not surprisingly, indecomposable $k\mathcal{P}$-modules, even for a finite poset $\mathcal{P}$, are generally impossible to classify due to $\mathcal{P}$ having what is referred to as a ``wild representation type". Therefore studying such module categories requires employing techniques that allow getting around the classification problem. In this talk I will introduce a new set of ideas for local analysis of modules over posets by methods borrowed from spectral graph theory and multivariable calculus.

Wed 2 Oct, 11:00 - 12:00, Aula Dini

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