An Introduction to Modified Traces
Explore the fundamental concepts of modified traces in algebra and topology through this comprehensive lecture. Delve into the importance of trace maps and representation dimensions as key invariants in representation theory, and understand their limitations in non-semi-simple settings. Discover how replacement invariants have emerged over the past decade to address these limitations in modular representation theory, graded representation theory, and quantum group representations at roots of unity. Gain insights into the mysterious nature of these invariants' existence and their applications within representation theory. Learn from Jonathan Kujawa's friendly approach, focusing on examples, basic properties, and practical applications in this first lecture of the series presented by the Hausdorff Center for Mathematics.