A personal survey on recent and less recent results on tilting theory

TL;DR

This paper presents a personal survey discussing recent and older developments in tilting theory, highlighting its history, key ideas, surprising facts, and open problems through informal conversations.

Contribution

It offers a personal, informal overview of tilting theory's evolution, emphasizing lesser-known results and open questions not typically covered in formal literature.

Findings

Highlights unexpected facts in tilting theory

Identifies open problems for future research

Provides historical context and general ideas

Abstract

This note is the written version of conversations with young colleagues on unofficial history, general ideas, unexpected facts and open problems concerning tilting theory.