Large Structures Seminar: Justin Malestein

I will discuss rigidity of periodic bar-joint frameworks, i.e. structures made of rigid bars and fully rotational joints which are symmetric with respect to some lattice in $\mathbb{R}^n$. In one model, a periodic framework is rigid if all motions through periodic configurations with respect to the lattice are trivial. (The lattice itself may deform continuously.) A periodic framework is ultrarigid if all such motions are trivial even when relaxing the periodicity to arbitrary finite index sublattices. I will present some recent results on this model of rigidity including a finite time algorithm for determining infinitesimal ultrarigidity and a combinatorial characterization of generic ultrarigidity in the case of the minimum number of edge orbits. Joint work with Louis Theran.