for this workshop

## Combinatorics and complexity of Kronecker coefficients

at the

American Institute of Mathematics, Palo Alto, California

organized by

Igor Pak, Greta Panova, and Ernesto Vallejo

This workshop, sponsored by AIM and the NSF, 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.

The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.

The deadline to apply for support to participate in this workshop has passed.

For more information email *workshops@aimath.org*