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This lecture by Leonardo Cavenaghi from IMECC, University of Michigan explores new Z-values G-birational invariants in dimensions 2 and 3, where G represents a p-cyclic group acting through regular automorphisms on smooth projective varieties X. Discover how these invariants are derived from the modular symbol construction developed by Kontsevich-Pestun-Tschinkel and the theory of atoms by Katzarkov-Kontsevich-Pantev-Yu, now extended to the G-equivariant setting. The presentation also introduces a conjectural statement in 4 dimensions that goes beyond current technological capabilities, along with its application. The work presented is based on joint research with L. Grama, L. Katzarkov, and M. Kontsevich.
