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April 2018

School of Mathematical Sciences Colloquium

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Complexity of 3-Manifolds
15:10 Fri 23 Mar, 2018 :: Horace Lamb 1022 :: A/Prof Stephan Tillmann :: University of Sydney

In this talk, I will give a general introduction to complexity of 3-manifolds and explain the connections between combinatorics, algebra, geometry, and topology that arise in its study. The complexity of a 3-manifold is the minimum number of tetrahedra in a triangulation of the manifold. It was defined and first studied by Matveev in 1990. The complexity is generally difficult to compute, and various upper and lower bounds have been derived during the last decades using fundamental group, homology or hyperbolic volume. Effective bounds have only been found in joint work with Jaco, Rubinstein and, more recently, Spreer. Our bounds not only allowed us to determine the first infinite classes of minimal triangulations of closed 3-manifolds, but they also lead to a structure theory of minimal triangulations of 3-manifolds.
15:10 Fri 4 May, 2018 :: Horace Lamb 1022 :: Dr Anthony Licata :: Australian National University

15:10 Fri 18 May, 2018 :: Horace Lamb 1022 :: Dr Robby Marangell :: University of Sydney

15:10 Fri 25 May, 2018 :: Horace Lamb 1022 :: Dr Ngamta (Natalie) Thamwattana :: University of Wollongong

15:10 Fri 1 Jun, 2018 :: Horace Lamb 1022 :: A/Prof Eduardo Altmann :: University of Sydney