Triangulations and combinatorial differential geometry
Student No.:50
Time:Mon/Wed 15:10-17:00, 2014-07-07 ~ 2014-07-16
Instructor:Stephan Tillmann  [The University of Sydney]
Place:Conference Room 4, Floor 2, Jin Chun Yuan West Building
Starting Date:2014-7-7
Ending Date:2014-7-16





The theme of this course is connections between combinatorics and geometry in the study of triangulated manifolds. I will describe various geometric properties that can be computed from triangulations, and connections (or obstructions) between them and the combinatorics of a triangulation. The starting point will be triangulations and ideal triangulations of 3-dimensional manifolds, such as knot complements. I will describe how various geometric structures (e.g. hyperbolic, Cauchy-Riemann and Anti-de-Sitter) can be computed from triangulations, and how normal surface theory leads to natural obstructions. Moreover, moduli spaces of such structures will be studied viainteresting functions on them.In arbitrary dimensions, I will focus onCAT(0) structures and discrete notions of spin structures computed from triangulations.





The students should know some basic algebraic topology (fundamental groups, covering spaces, homology theory) and differential geometry.




Lecture notes and additional materials will be made available during the course.