Ravi Vakil's excellent book The Rising Sea opens with the following quote from David Mumford: "[Algebraic geometry] seems to have acquired the reputation of being esoteric, exclusive, and very abstract, with adherents who are secretly plotting to take over all the rest of mathematics! In one respect the last point is accurate..." In this talk we will look at some of the fundamentals of algebraic geometry from the more concrete perspective of polynomials and we will let this guide us to the land of abstraction. If time permits, there may be secret plotting.
From Affine to Zariski: Demystifying Algebraic Geometry
Sep. 18, 2019 5pm (Math 350)
MathClub
Yuhao Hu (CU Boulder postdoc)
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Imagine a convex curve in the plane. Fitting the curve tightly between two parallel lines, the distance between those lines tells us the width of the curve in a particular direction. If such width does not depend on the angle in which you direct the parallel lines, the curve is said to have constant width. Analogously, we have the notion of bodies of constant width. Rolling a flat board over bodies of the same constant width creates an illusion of rolling over round balls of the same radius. Beyond such counter-intuitiveness, there are more interesting mathematical aspects related to/inspired by shapes of constant width.