Speaker: Lucas Seco.
Schedule: The link is here.
Abstract: We describe the inverse image of the Riemannian exponential map a compact symmetric space as the disjoint union of so called focal orbits through a maximal torus: these are orbits of a subgroup of the isotropy group. We show how the dimensions (infinitesimal data) and connected components (topological data) of these orbits are encoded in the diagram, Weyl group and lattice of the symmetric space. Obtaining this data is precisely what we mean by counting geodesics. This extends previous results on compact Lie groups [SS18]. We apply our results to give short independent proofs of known results on the cut and conjugate loci of compact symmetric spaces [Tak78].
References
[SS18] L. Seco, L.A.B. San Martin: Counting geodesics on compact Lie groups, Diff. Geom. Appl. 56 (2018) 1-19.
[Tak78] M. Takeuchi: On conjugate loci and cut loci of compact symmetric spaces I, Tsukuba J. Math. 2 (1978), 35-68.
André M. Sá Gomes - Universidade Estadual de Campinas (Brazil)
Brian David Grajales Triana - (Colombia)
Bruno Alexandre Rodrigues - Universidade Estadual de Maringá (Brazil)
Eduardo Celso Viscovini - Univesidade Estadual de Maringá (Brazil)
Geovane Cardoso de Brito - Universidade de São Paulo (Brazil)
João Victor Uzita - Universidade Estadual de Campinas (Brazil)
Josiney Alves de Souza - Universidade Estadual de Maringá (Brazil)
Kennerson Nascimento de Sousa Lima - Universidade Estadual de Campinas (Brazil)
Luan Carlos Rigoleto Fernandes - Universidade Estadual de Maringá (Brazil)
Thiago Matheus Cavalheiro - Universidade Estadual de Maringá (Brazil)
The template of the poster can be found here.