Speaker:  Amina Abdurrahman (IHES)

Abstract: When does a sequence of hyperbolic 3-manifolds with volume going to infinity have exponentially growing torsion homology? For arithmetic towers, the work of Bergeron-Sengun-Venkatesh suggests a set of conditions that conjecturally imply exponential growth of torsion homology. Their work relies on Cheeger-Mueller's theorem, linking torsion homology and analytic torsion. For nice sequences of hyperbolic 3-manifolds we use a different approach to find a condition implying exponential torsion homology growth: we give a condition on the spectrum of the Laplacian. I will give several motivations for this condition and show how to construct concrete examples of sequences satisfying it. This is based on joint work with Anshul Adve, Vikram Giri, Ben Lowe and Jonathan Zung.