Institute of Mathematics for Industry

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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

Place Lecture Room L-3, Faculty of Mathematics building, Ito Campus

Object person  

Speaker Mikhail Kapranov (Kavli Institute for the Physics and Mathematics of the Univserse)

Date: Thursday, October 2, 2014
         15:40〜16:00 (teatime in the lounge)
         16:00〜17:00 (lectures in Lecture Room L-3)

Speaker:Mikhail Kapranov (Kavli Institute for the Physics and Mathematics of the Univserse)

Title:Relations between discriminants and resultants, their generalizations and categorification.

Abstract:
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.




*This seminar collaborates with Algebra Seminar.