Simons fellowship 2019-2020

I plan to spend the sabbatical at the Weizmann Institute of Science in Rehovot, Israel. I plan to work on the following projects: 1. Words in finite and arithmetic groups: study word maps in finite and arithmetic groups and their applications in model theory and low-dimensional topology. 2. Higher counting: study sequences of homotopy $n$-types of the form $k --> |X(Z / k)|$, where $X$ is a higher stack and $| A |$ denotes the geometric realization of the higher groupoid $A$. 3. Study Schrodinger operators on trees that are invariant under lattices in the automorphisms groups of the trees.