Mathematics Colloquia and Seminars

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One way to measure the geometry of a Riemannian manifold M is the systole: the minimal length of a non-contractible closed geodesic on M. On the other hand, a way to measure the topology of M is the systolic genus: the minimal genus such that a surface group of genus g is a subgroup of the fundamental group of M. There is a known relationship between these values for hyperbolic manifolds, which is no longer true for higher rank lattices. I will present recent work showing there exist infinitely many non-uniform lattices in SL(8,R) each with a sequence of commensurable lattices whose systole is going to infinity, yet they all contain the same 3-manifold group. This is a notable characteristic of these lattices being higher rank.