Voronoi neighbors of $D_n$ lattices
Voronoi neighbors of $D_n$ lattices
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Mark McConnell, Princeton University
Fine Hall 214
Voronoi defined a tiling of the space of positive definite quadratic forms on $R^n$. Each tile is determined by a perfect lattice. Examples of perfect lattices include the root lattices $A_n$ and $D_n$. We will focus on the tiles that are neighbors of a $D_n$ tile. These are determined by some simple combinatorics, but there are exponentially many different $D_n$ neighbors, and only a few families of them have been understood for all n. I will report on two recent results, one due to myself, and one joint work with Noam Elkies.