Tracking the symmetries of Z3-orbifold K3s within the Mathieu groups

Abstract: This seminar starts EARLIER than the usual schedule.

We shall open the seminar room + ZOOM meeting at 12.00 for (virtual) coffee and close ZOOM at 13.30

The goal of this talk is to determine the group of holomorphic symplectic automorphisms of Z3-orbifold limits of K3 surfaces, and to track this group within two of the sporadic groups Mathieu 12 and Mathieu 24. To do so, I will provide a counterpart to the extensive studies by Nikulin and others of the geometry and symmetries of classical Kummer surfaces, which involves a variation of Kondo's lattice techniques that Taormina and Wendland introduced earlier in the genesis of their symmetry surfing programme. I will realise the finite group of symplectic automorphisms of this class of K3 surfaces as a subgroup of Mathieu 12 and Mathieu 24 in terms of permutations of respectively 12 and 24 elements. The talk is based on a joint work with Kasia Budzik, Anne Taormina, Mara Ungureanu and Katrin Wendland.

mathematical physicsalgebraic topologydifferential geometryrepresentation theorystatistics theory

Audience: researchers in the topic

( slides )

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Prague-Hradec Kralove seminar Cohomology in algebra, geometry, physics and statistics

Series comments: Virtual coffee starts on Zoom already 15 minutes before the seminar.

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