CRC Colloquium

16:15 - 17:15 Michael Joswig (TU Berlin): Zeros of $S$-characters - Showcasing the Computer Algebra System OSCAR

The talk will take place in V2-210/216.The concept of $S$-characters of finite groups was introduced by Zhmud' (1995) as a generalization of transitive permutation characters. Any non-trivial $S$-character takes a zero value on some group element. By a deep result depending on the classification of finite simple groups a non-trivial transitive permutation character even vanishes on some element of prime power order. J-P. Serre asked whether this generalizes to $S$-characters. We provide a translation of this question into the language of polyhedral geometry and thereby construct many counterexamples, using the capabilities of the computer algebra system OSCAR. The work on $S$-characters is joint with Thomas Breuer und Gunter Malle. OSCAR is joint work with The OSCAR Development Team, currently lead jointly with Simon Brandhorst, Claus Fieker, Tommy Hofmann and Max Horn.