Residual Intersections in Geometry and Algebra by David Eisenbud
Explore the fascinating world of residual intersections in geometry and algebra through this distinguished lecture by David Eisenbud, Director of the Mathematical Sciences Research Institute and Professor of Mathematics at UC Berkeley. Delve into the 19th-century geometric questions that sparked the development of residual intersection theory, from intriguing problems like determining the number of conics tangent to five given conics in a plane to fundamental concepts such as the Riemann-Roch theorem and space curve classification. Gain insights into the refinement of this theory in algebra and discover open problems in the field. Aimed at non-specialists, this talk covers topics including algebraic geometry, real algebra, twisted cubics, circles, conics, intersections, and historical context, providing a comprehensive overview of this important mathematical subject.