# Counting Representations of Arithmetic Lattices

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Nir Avni, Harvard University
Fine Hall 322

I will talk about the the number of representations of dimension $d$ of an arithmetic lattice when $d$ tends to $\infty$. For higher rank lattices, this sequence grows polynomially, with some mysterious exponent. I will talk about some known values of this exponent, and the conjectural relations between the representation growths of different lattices.