Algebra seminar

10:00 (ZOOM) - Nicola Di Vittorio (Macquarie University, Sydney): Towards 2-derivators for formal ∞-category theory
3:40 (room K2) - Bárbara Muniz (Univ. Krakow): Symplectic branching through crystals

Abstract (Nicola Di Vittorio): Derivators provide a categorical framework for studying homotopy theory. They are based on the idea that, while homotopy categories retain only limited information, the collection of homotopy categories of diagram categories often suffices for many homotopical constructions. As a particular example, one may think of derived categories viewed as homotopy categories, where the model structure is placed on a suitable category of (co)chain complexes and the weak equivalences are the quasi-isomorphisms. In this sense, derivators (in particular the stable ones) provide an enhancement of the triangulated structure on derived categories. In this talk, I will introduce a set of axioms for a 2-dimensional analogue of derivators. In this setting, the homotopy 2-categories of enriched model categories – specifically those intended to model (∞, 2)-categories – play the role that homotopy categories of model categories play for ordinary derivators. This inaugurates a program aimed at the axiomatic study of phenomena that appear in the theory of ∞-categories from an (∞, 2)-categorical perspective.
Abstract (Bárbara Muniz): The decomposition of gl-representations when restricted to sp is a classic problem in representation theory, commonly referred to as symplectic branching. The multiplicities that describe this decomposition have a known combinatorial description in terms of certain Littlewood-Richardson tableaux. In this talk, we use tableau combinatorics to present an alternative approach. We argue that the branching can be seen at the quantum level through the highest weight vectors of the crystals. By describing the highest weight tableaux, we establish their correspondence with the one in the classical branching rules.