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Some perspectives on the finitistic dimension conjecture
The finitistic dimension conjecture, which serves as a sufficient condition for numerous homological conjectures, has been a central topic of research in homological algebra. Despite over 60 years of study, the conjecture is only solved in special cases under the context of finite dimensional algebras. In this talk, we present three perspectives in studying the finitistic dimension conjecture: 1. the representation theory perspective, 2. the invariant perspective, and 3. the perspective of algebraic operations. These perspectives are closely connected, and their interaction often leads to new ideas for the conjecture. We also mention a potential geometric perspective for future study.