Explore a lecture on the Wall finiteness obstruction theorem for DG categories, delivered by Alexander Efimov from the Steklov Mathematical Institute of Russian Academy of Sciences. Delve into the analogue of this classical theorem for DG categories over a field, examining the criteria for when a homotopically finitely presented DG category is Morita equivalent to a finite cell DG category. Discover the implications of this result, including applications to smooth and proper phantom DG categories and the derived category of the Barlow surface. Learn how these findings disprove two conjectures by Orlov and their significance for smooth proper algebraic varieties with stratifications by affine spaces. Gain insights into a similar Wall finiteness obstruction result for algebras over DG operads, understanding the role of the cotangent complex in this context. Cover key topics such as de deformed tensor algebra, DG quotients, topological results, stable authentic categories, commodity equalizers, and complexifications of DG algebras. Read more