Understanding and Measuring Singularities in Algebraic Geometry

Explore the fundamental concepts of algebraic geometry in this colloquium lecture delivered by Karen E. Smith from the University of Michigan. Delve into topics such as algebraic varieties, smoothness, resolution, and rational singularities. Learn about the coordinate ring of varieties, algebraic correspondence, and the Freshman Dream. Discover the intricacies of F-regularity, the Minimal Model Program, and the process of blowing up. Gain insights into understanding and measuring singularities in algebraic geometry through this comprehensive presentation given at the Virtual 2022 Joint Mathematics Meetings.

Introduction
Algebraic Geometry
Algebraic Varieties
algebraic geometry over any field
smoothness
smooth points
Resolution
Hironaka
Exceptional Sets
RationalSingularities
Varieties
The coordinate ring of the variety
Algebraic correspondence
Coordinate ring
Freshman Dream
Peace Power Map
F regularity
Minimal Model Program
Questions
Blowing up
Conclusion