Hidetoshi Masai

I will talk about the program called HIKMOT which rigorously proves hyperbolicity of a given triangulated 3-manifold. To prove hyperbolicity of a given triangulated 3-manifold, it suffices to get a solution of Thurston's gluing equation. Since symbolic calculation is very slow, it is convenient if we use floating point arithmetic. We use the notion called interval arithmetic to overcome two types errors from floating point arithmetic; round-off errors, and truncated errors. I will also talk about an application of HIKMOT to exceptional surgeries along alternating knots. This talk is based on joint work with N. Hoffman, K. Ichihara, M. Kashiwagi, S. Oishi, and A. Takayasu.