Expository Talk by Prof. Sergio Estrada (An overview of flat covers and their application to Multiparameter Persistence Theory)

Speaker: Prof. Sergio Estrada (Universidad de Murcia, Spain)

Title: An overview of flat covers and their application to Multiparameter Persistence Theory

Abstract: In a recent paper by Hyry and Puuska, the authors address the interplay between flat covers and injective envelopes via Matlis duality, with a view toward working with persistence modules that are neither tame nor pointwise finite-dimensional. In this expository talk, we will give an overview of their work.

Flat covers originate from Enochs’s pioneering 1981 work ``Injective and Flat Covers, Envelopes and Resolvants", where he conjectured the existence of flat covers over arbitrary rings, a conjecture that became known as the Flat Cover Conjecture. We will provide a brief historical overview of the various kinds of covers and envelopes that are relevant in homological algebra, and we will summarize the main techniques that led to the positive resolution of the flat cover conjecture in 2001.

Since the conjecture was positively settled, many types of extensions—both regarding the existence of flat covers and the techniques used in the original solution—have emerged, with its application to multiparameter persistence theory being one of the most recent contributions to the field. This highlights that the study of flat covers continues to be an active area of research, both at the theoretical and applied levels.

Time: 10:30-11:30, August 4, 2025

This talk will also be broadcast online via Zoom:
Zoom Link
Meeting ID: 947 8296 0593
Passcode: 584111

This talk is part of the Thematic Program TDA PARTI: Topological Data Analysis, Persistence And Representation Theory Intertwined.