Pedro Marcias Marques: Families of local Artinian Gorenstein algebras, Jordan type, and related invariants

Abstract.

In a joint work with Tony Iarrobino, we construct examples of families \(\mathrm{Gor}(T)\) of local AG algebras with given Hilbert function T, and use obstructions that the symmetric decomposition of the associated graded algebra of an AG algebra A imposes on the Jordan type of A to study their irreducible components. Together with Johanna Steinmeyer, we explore possible generalisations of Jordan type and try to understand how they might apply to these topological questions.