Bézout’s theorem and the birth of algebraic topology
OTHER MATHEMATICS DEPARTMENT EVENTS: MATH TABLE, SEMINARS: OPEN NEIGHBORHOOD
When: September 3, 2025
4:30 pm - 5:30 pm
Where: Science Center Hall A
Address:
1 Oxford Street, Cambridge, MA 02138, United States
Speaker: Joe Harris - Harvard University
Bézout’s theorem is a direct generalization of the Fundamental Theorem of Algebra to polynomials in multiple variables: it predicts the number of solutions of a system of n polynomials in n variables. It was originally proved by algebraic methods, using resultants to reduce the problem to the FTA; but Poincaré saw in it the germ of an idea that he would ultimately develop into what we now recognize as homology, cohomology, cup product and Poincaré duality. In this talk, I’ll try to sketch how this came about, and why Bézout’s theorem is ultimately an elementary theorem in algebraic topology.
For more information, visit the Harvard Math Table website.