Lie Groups and Representation Theory

Seminar information archive ~12/12Next seminarFuture seminars 12/13~

Date, time & place Tuesday 16:30 - 18:00 Room #126 (Graduate School of Math. Sci. Bldg.)

2018/03/12

15:00-16:30   Room #126 (Graduate School of Math. Sci. Bldg.)
Christian Ikenmeyer (Max-Planck-Institut fur Informatik)
Plethysms and Kronecker coefficients in geometric complexity theory
[ Abstract ]
Research on Kronecker coefficients and plethysms gained significant momentum when the topics were connected with geometric complexity theory, an approach towards computational complexity lower bounds via algebraic geometry and representation theory. This talk is about several recent results that were obtained with geometric complexity theory as motivation, namely the NP-hardness of deciding the positivity of Kronecker coefficients and an inequality between rectangular Kronecker coefficients and plethysm coefficients. While the proof of the former statement is mainly combinatorial, the proof of the latter statement interestingly uses insights from algebraic complexity theory. As far as we know algebraic complexity theory has never been used before to prove an inequality between representation theoretic multiplicities.