Expository Talks by Dr. Dolors Herbera

Expository Talk by Prof. Dolors​ Herbera  (Universitat Autònoma de Barcelona, Spain), as part of the Thematic Program TDA PARTI: Topological Data Analysis, Persistence And Representation Theory Intertwined.

Title:  Parametrizing large projective modules

Time: 10:30-11:30, August 7, 2025

Abstract:  A theorem of Kaplansky states that, over any ring, projective module decompose as a direct sum of countably generated (projective) modules.

There has been a lot of effort in describing finitely generated projective modules over suitable classes of rings, while the infinitely generated ones have remained relatively forgotten. Recently, this situation has changed drastically.

In the talk I will explain a particular type of countably generated projectives modules that we call "relatively big projectives". This is an interesting class of modules as, for example, any countably generated projective module over a module finite algebra over a commutative noetherian ring is relatively big.

To us parametrize such class of modules over a ring means to study its associated monoid, that is, the set of isomorphism classes with the addition induced by the direct sum. I will explain how this works over suitable algebras over commutative domains, and over group algebras RG with G a finite group and R a (suitable) Dedekind domain.

Location: OIST, Lab 5, Floor D, Room L5D23

Zoom Link: Zoom link
Meeting ID: 947 8296 0593
Passcode: 584111