The 12 lectures from the 10-day workshop of mini-courses are presented here as an introduction to research into the three overlapping areas in an expository manner accessible to graduate students and researchers in mathematics. They address ideas and problems that have been generated by the confluence of different areas of mathematics over the past 30 years. Among them are quantum field theory and the volume conjecture, knots and tropical curves, from angled triangulations to hyperbolic structures, fully augmented links, and fields of definition of canonical curves. There is no index. Annotation ©2011 Book News, Inc., Portland, OR (booknews.com)
