Louis Theran, Unlabelled distance geometry

In the 1930s, Schönberg and Young--Householder classified when n(n−1)/2 numbers m_ij are the pairwise distances among n points p₁, …, p_n in a Euclidean space and showed how to find the points from the distances. This question of finding the points becomes more difficult when you take away the association between the m_ij and the points p_i, but it was solved by Boutin and Kemper in the mid 2000s. I'll talk about some generalisations of Boutin and Kemper's results obtained jointly with Shlomo Gortler and Dylan Thurston and Ioannis Gkioulekas, Shlomo Gortler, and Todd Zickler.