Hall algebras and Donaldson-Thomas invariants

TL;DR

This survey explores the role of Hall algebras in understanding motivic invariants of moduli spaces of coherent sheaves on Calabi-Yau threefolds, highlighting key developments by leading researchers.

Contribution

It provides a comprehensive overview of how Hall algebras are applied to study motivic invariants in the context of Calabi-Yau threefolds, summarizing recent advances and ideas.

Findings

Summarizes key concepts and results in Hall algebras and motivic invariants.

Highlights the contributions of Joyce, Kontsevich, Reineke, Soibelman, and Toda.

Connects Hall algebra structures to enumerative geometry of Calabi-Yau threefolds.

Abstract

This is a survey article on Hall algebras and their applications to the study of motivic invariants of moduli spaces of coherent sheaves on Calabi-Yau threefolds. It is a write-up of my talks at the 2015 Salt Lake City AMS Summer Research Institute and will appear in the Proceedings. The ideas presented here are mostly due to Joyce, Kontsevich, Reineke, Soibelman and Toda.