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Presented By: Department of Mathematics

RTG Seminar on Geometry, Dynamics and Topology Seminar

On closed orbits of the diagonal subgroup on the space of unimodular lattices

The action of diagonalizable subgroups on homogeneous spaces has a different flavor than the action of unipotent subgroups. For instance, the modular surface has closed divergent orbits of the diagonal subgroup. In this talk, we will look at closed orbits of the diagonal subgroup A on the space of unimodular lattices SL_d(R)/SL_d(Z). We will discuss an explicit construction of periodic A-orbits in the case d=2 using binary quadratic forms (following Einsiedler-Lindenstrauss-Michel-Venkatesh). Using the language of algebraic number theory, we will then generalize this construction to any dimension d.
This se dinar will be on zoom: https://umich.zoom.us/j/92258297975
No password Speaker(s): Mitul Islam (U Michigan)

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