Nicolas Banks, Department of Pure Mathematics, University of Waterloo
"Intersection theory, Chow groups, and a generalized Bezout's Theorem"
Bezout's Theorem is a classical result which states that two plane curves intersect in a number of points equal to the product of their degrees. This theorem has an interesting history: it was essentially known to Newton in the 17th century, while the first proof was attempted a century later by Bezout. The first rigorous, algebro-geometric proof was finally given by Serre in 1958.
Such a rigorous treatment of Bezout's Theorem requires algebraic definitions of intersection multiplicities, degrees, and homology rings - the Chow ring provides the answer to all three. This talk will explore these ideas, drawing motivations from differential geometry along the way. We will end the talk by using this machinery to generalize Bezout's Theorem.
This seminar will be held both online and in person:
- Room: MC 4060
- Zoom link: https://uwaterloo.zoom.us/j/98347327227?pwd=anFGNjRsd0ZPUk10SW9vQVNqL3Z0UT09