Categorical Noncommutative Geometry

Explore the categorical approach to algebraic geometry in this colloquium talk by Alexander Efimov titled "Categorical Noncommutative Geometry." Delve into the study of algebraic varieties and schemes through their derived categories of coherent sheaves, viewed as differential graded (dg) categories. Discover how this perspective allows for the consideration of more general dg categories as noncommutative algebraic varieties or schemes. Learn about the application of concepts such as smoothness and properness in this context, as well as the adaptation of classical invariants like de Rham cohomology and K-theory. Gain insights into recent developments and results in this field of mathematics during this hour-long presentation from the University of Chicago Department of Mathematics colloquium series.