On the decidability of noncommutative sums of squares, with applications to Connes' embedding problem and quantum logic

Datum

07.12.2017

Zeit

13:15 - 14:15

Sprecher

Tobias Fritz

Zugehörigkeit

MPI-MIS, Leipzig

Sprache

en

Hauptthema

Mathematik

Andere Themen

Mathematik

Host

Prof. Dr. A. Thom

Beschreibung

Due to Positivstellensätze, sums of squares play a fundamental role in real algebraic geometry. While this remains true in the noncommutative case, the noncommutativity makes the problem generally undecidable: there is no algorithm to decide whether a given noncommutative polynomial can be approximated by sums of squares. I will explain why this is the case, how it implies the undecidability of quantum logic, and how it relates to Connes' embedding problem. Based on arXiv:1207.0975 and arXiv:1607.05870.

Links

• Seminar Algebra, Geometrie und Kombinatorik

Letztmalig verändert: 29.11.2017, 15:49:52