# Speaker: Steven Gortler

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Title: Springs Springs Springs and Struts

#### Abstract:

Consider replacing each edge of a mesh or a graph with either a spring or a strut. Suppose that we then place the vertices of the graph in space such that this physical system is in equilibrium. What does this imply?

In this talk, I will describe a number of applications of spring and strut systems of graphs. These will include mesh parametrization, sensor network localization (calculating geometry from edge lengths), and rigidity theory (the study of the uniqueness of "fixed-edge-length" graph embeddings in a fixed dimensional space). I will also draw connection to other topics such as non-linear dimensionality reduction, low-rank matrix completion, and semi-definite programming.

#### Short Speaker Bio:

Steven (Shlomo) Gortler is the Robert I. Goldman professor of computer science at Harvard University. His home area of research is computer graphics with a wider interest in geometry.