An Arithmetic Count of Rational Plane Curves -
There is a unique line through 2 points in the plane, and a unique conic through 5. These counts generalize to a count of degree d rational curves in the plane passing through 3d-1 points. Surprisingly, the problem of determining these numbers turns out to be deep and connected to string theory, and it was not until the 1990's that Kontsevich determined them with a recursive formula. Such formulas are valid when you allow your curves to be defined with complex coefficients. For more general fields, we show there is a bilinear form giving an arithmetic count of rational plane curves using A1-homotopy theory. This is joint work with Jesse Kass, Marc Levine, and Jake Solomon.
Thursday, November 19, 2020 at 4:45pm to 5:30pmVirtual Event
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