#
Combinatorics and complexity of Kronecker coefficients

November 3 to November 7, 2014
at the

American Institute of Mathematics,
Palo Alto, California

organized by

Igor Pak,
Greta Panova,
and Ernesto Vallejo

## Original Announcement

This workshop will be devoted to the study of Kronecker coefficients which describe the
decomposition of tensor products of irreducible representations of a
symmetric group into irreducible representations. We concentrate on
their combinatorial interpretation, computational aspects and
applications to other fields.
The workshop will focus on:

- Finding combinatorial interpretation for the Kronecker
coefficients. In terms of complexity theory this amounts to working on
resolving whether the problem $KRON$ is in $\#P$. The aim will be to use
complexity theory to find evidence for or against that.
- Determining the complexity of deciding the problem $KP$ of
positivity of the Kronecker coefficients. Mulmuley's conjecture
states that $KP$ is in $P$. The goal will be to either prove this
conjecture or else show that, for example, $KP$ is $NP$--hard.
- Resolving combinatorial special cases. Among them are
proving the Saxl conjecture that for every large enough symmetric
group has an irreducible representation whose tensor square contains
every irreducible representation as a constituent. Other interesting
combinatorial aspects include the application of Kronecker
coefficients to solving combinatorial problems of different origins,
specifically proving unimodality results.

## Material from the workshop

A list of participants.
The workshop schedule.

A report on the workshop activities.

Papers arising from the workshop: