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        "event_title":"Colloquium: Anthony Licata- Geometric Group Theory and Triangulated Categories",
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        "event_title":"Emerging Democracies Roundtable | A New Era of War and Dictators?",
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        "combined_title":"Emerging Democracies Roundtable | A New Era of War and Dictators?: Bruce Bueno de Mesquita, NYU Christian Davenport, U-M Megan Stewart, U-M Dan Slater, U-M (moderator)",
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        "event_title":"Fried Apples and Apple Fritters: Print Your Own 19th Century Recipe Cards",
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        "event_title":"Get to Know Boosterthon: A School Fundraising Company",
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        "description":"Measured foliations and train tracks are fundamental tools for understanding the geometry of hyperbolic surfaces and 3\u2013manifolds. In particular, a hyperbolic 3\u2013manifold with finitely generated fundamental group is uniquely determined by its topological type and its end invariants\u2014geometric data encoded by the ending laminations on its boundary [1]. Both compressible and incompressible boundaries can occur. However, in the compressible case\u2014when a surface bounds a handlebody\u2014not every lamination can arise as an ending lamination; only those that are incompressible can.\r\n\r\nThis phenomenon was studied by Masur and Kerckhoff in the 1980s, who showed that the mapping class group of a handlebody acts properly discontinuously on an open subset of the space of projective measured laminations [2]. This open set, known as the Masur domain, has full measure with respect to the Thurston measure and consists entirely of incompressible laminations [3]. In this talk, we follow Masur and Kerckhoff\u2019s approach to reproduce this result. Also, we will see that it contains a beautiful application of train track theory.\r\n\r\nReference:\r\n[1] J. F. Brock, R. D. Canary, and Y. N. Minsky, The classification of Kleinian surface groups II: The Ending Lamination Conjecture, Annals of Mathematics (2) 176 (2012), no. 1, 1\u2013149.\r\n[2] H. Masur, Measured foliations and handlebodies, Ergodic Theory and Dynamical Systems 6 (1986), no. 1, 99\u2013116.\r\n[3] S. P. Kerckhoff, The measure of the limit set of the handlebody group, Topology 26 (1987), no. 3, 353\u2013362.",
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