# Isabelle Shankar: Symmetry Adapted Gram Spectrahedra

**Time: **
Tue 2021-09-07 10.15

**Location: **
KTH, 3418 and Zoom, meeting ID: 659 3743 5667

**Lecturer: **
Isabelle Shankar (MPI Leipzig)

### Abstract

Sum of squares (SOS) relaxations are often used to certify nonnegativity of polynomials and are equivalent to solving a semidefinite program (SDP). The feasible region of the SDP for a given polynomial is the Gram Spectrahedron. For symmetric polynomials, there are reductions to the problem size that can be done using tools from representation theory. In joint work with Serkan Hosten and Alexander Heaton, we investigate the geometric structure of the spectrahedra that arise in the study of symmetric SOS polynomials, the Symmetry Adapted PSD cone, and the Symmetry Adapted Gram Spectrahedron.