Zusammenfassungen NTH-Seminar Computeralgebra
Zusammenfassung des Vortrags von Eamonn O'Brien (Auckland, NZL)
An effective model for computation with linear groups
We will discuss the soluble radical model which is used to compute structural information for matrix groups defined over finite fields and illustrate it by example. We will also consider how the components of the model can be constructed.
Zusammenfassung des Vortrags von Gunter Malle (Kaiserslautern)
Problems in the representation theory of certain finite dimensional algebras lead to complicated systems of algebraic equations. We explain how to use various computer algebra tools to solve these equations and therewith prove some instances of conjectures on Hecke algebras. This is joint work with Jean Michel.
Zusammenfassung des Vortrags von Philipp Rostalski (Berkeley, USA)
On semidefinite representations for Grassmann Orbitopes
The Grassmann orbitope is the convex hull over the Grassmann variety of decomposable skew-symmetric tensors of unit length. This variety parametrizes k-dimensional linear subspaces of Rn, and it is the highest weight orbit under the k-th exterior power representation of the group SO(n). In this talk we discuss semidefinite relaxations of the Grassmann orbitope. That convex body can be approximated and represented surprisingly well by projections of spectrahedra (using Lasserre's moment matrices). We show that the first relaxation is exact for k=2, we present numerical evidence that this result extends to higher k, and we discuss relations to a longstanding conjecture on calibrations by Harvey and Lawson. If time permits, three additional classes of orbitopes will be discussed and we explain why the relaxation order is related to a certain polytope. This is an ongoing joint project with Raman Sanyal (FU Berlin).