We explain how an extension of Haefliger's approach to transverse measures for foliations allows us to define and study measures and geometric measures (densities) on differentiable stacks. The abstract theory works for any differentiable stack, but it becomes very concrete for proper stacks - for example, when computing the volume associated with a density, we recover the explicit formulas that are taken as definition by Weinstein. This talk is based on joint work with Marius Crainic.
Measures and densities on differentiable stacks Sponsored by the Meyer Fund
Mar. 09, 2016 4:15pm (MATH 3…
Grad Student Seminar
Natalie Coston
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The fifteen puzzle consists of a 4x4 puzzle board grid on which there are 15 tiles and one blank. The goal of the puzzle it to slide the tiles around until the numbers appearing on the board are ordered 1 to 15. If we started with an ordered board and were mixing the tiles back up to give to a friend, as curious mathematicians we might wonder "How do I know if my board is really mixed?" or, "How long should I mix these tiles?" In this talk, which is based off the paper "The Mixing Time of the Fifteen Puzzle" by Morris and Raymer, I will introduce Markov Chains and demonstrate how they can be used to bound the time it takes to mix the 15 puzzle.
Measures and densities on differentiable stacks