*Abstract*:

In representation theory, an algebra A is studied via its representations, that is, via the category of A-modules. In order to describe this category one often uses reduction techniques. One can use the notion of a torsion pair to decompose the category in a pair of smaller subcategories which are still big enough to reconstruct the whole category. Or one can decompose the objects: under suitable finiteness conditions every module is a direct sum of indecomposable modules, and therefore we can often reduce our investigations to the indecomposables.

The representation type of A is a measure for the complexity of the category of indecomposable A-modules. We will review some classic results on representation type obtained over the last fifty years, including the celebrated dichotomy between tame and wild representation type. Then we will present a new approach that measures the complexity of the lattice formed by all torsion pairs. This gives rise to a class of algebras which is transversal with respect to the classical tame-wild dichotomy and will lead us to a number of interesting open problems.

*Short Bio*:

Prof. Lidia Angeleri Hügel completed her Studies in Mathematics at Ludwig-Maximilians-Universität München, she was a ``Ramon y Cajal'' fellow at the Universitat Autònoma de Barcelona and she served as an Associate Professor at Università degli Studi dell'Insubria, Varese and later joined Università degli Studi di Verona, where she became a Full Professor in November 2016. She is also a member of the PhD School Dottorato Interateneo in Matematica Trento - Verona.

Her research focuses on the representation theory of algebras, with connections to geometry, topology, data science, and theoretical physics. She has authored approximately sixty publications in international journals and serves on the Editorial Boards of several prominent journals. She previously served as Vice-Rector for International Relations at the University of Verona, and she is currently involved in coordinating scientific projects. Prof. Lidia Angeleri Hügel is currently the PI of a FIS project supported by the Italian Ministry for Universities and Research.

• THE REPRESENTATION TYPE OF AN ALGEBRA - Prof. Lidia Angeleri Hügel ( Download)
• Mutation, t-structures, and torsion pairs - Jan Šťovíček (Charles University, Prague) ( Download)