Hochschild (co)homology and Geometric Regularity - Andrea Solotar

Explore Hochschild (co)homology and its applications in geometric regularity in this comprehensive lecture by Andrea Solotar from Universidad de Buenos Aires. Delve into the fundamental concepts of Hochschild (co)homology as homological invariants of associative algebras and their role in describing various algebraic properties. Examine how these spaces can be utilized to determine the regularity of algebraic varieties in the context of commutative and finitely generated algebras. Gain insights into the challenges and complexities that arise when extending these concepts to non-commutative settings. Begin with an introduction to Hochschild (co)homology, progress through established results in the commutative case, and conclude with a discussion on the implications and open questions in non-commutative scenarios.