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Relations between discriminants and resultants, their generalizations and categorification.

Hold Date
2014-10-02 16:00〜2014-10-02 17:00
Lecture Room L-3, Faculty of Mathematics building, Ito Campus
Object person
Mikhail Kapranov (Kavli Institute for the Physics and Mathematics of the Univserse)

The classical resultant $R(f,g)$ of two polynomials $f,g$ in one variable has many analogs in other areas of mathematics: the integral of product of first Chern classes, Legendre symbols, linking numbers and others. On the other hand, the classical discriminant $D(f)$  of a polynomial $f$ satisfies the "coboundary" condition $R(f,g)^2 = D(fg)/(D(f) D(g))$. The talk will explain known and conjectural analogs of the discriminant and of the coboundary condition in other contexts where the analogs of the resultant make sense.