Joint IAS/PU Groups and Dynamics Seminar

In this talk, we show that the pair correlation of the Laplacian eigenvalues on 3-dimensional rectangular flat tori follows Poissonian statistics. Similar to the earlier work of Eskin, Margulis, and Mozes on 2D flat tori, these eigenvalues are...

The normal rank (or weight) of a group G is the smallest number of elements that normally generate G. This plays an important role in 3-manifold topology, but it is poorly understood. It is extremely difficult to give lower bounds apart from looking...

The generalized Markoff equation gives rise to a dynamical system via the Markoff group acting on the solution set. This talk considers the resulting dynamics over finite fields, which has strong connections with combinatorial group theory and...