Michael Walter

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The Kronecker coefficients are among the most fascinating objects in
classical representation theory. While many of their fundamental
properties remain mysterious, the past decade has brought some
significant advances, in part through new and surprising connections
to quantum physics and computational complexity theory. In this talk,
I will give an introduction to this subject and its motivations, and
discuss some recent results.

Specifically, I will explain that the problem of deciding positivity
of Kronecker coefficients is NP-hard in general, while their
asymptotic non-vanishing, as encoded by certain moment polytopes, can
be decided in NP and coNP (arXiv:1410.8144, 1507.02955, 1511.03675).
This is in marked contrast to celebrated results on the
Littlewood-Richardson coefficients and the Horn inequalities, and it
suggests that representation theory can be strictly easier in the
asymptotic regime. Lastly, and somewhat counter-intuitively, our
hardness result can be turned into an efficient algorithm for studying
the failure of the saturation property for Kronecker coefficients,
which is at present only poorly understood.

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Stanford University
Seminarroom 0.02, ETP
Contact: not specified