Sullivan’s work on Lipschitz structures

Speaker: Mike Freedman

Title: Sullivan’s work on Lipschitz structures

Abstract: I’ll begin with an elementary, but now little known, piece of PL topology: engulfing. John stalling used it to give an alternative proof of the high dimensional Poincare conjecture. Then I’ll explain Dennis Sullivan’s enhancement of Kirby’s torus trick (which relies on engulfing.) I’ll note an open question regarding Lipschitz structures on 4-manifolds.

2nd speaker: Bowen Yang

Title: Quantum Cellular Automata and Algebraic L-Theory

Abstract: Quantum cellular automata (QCAs) are models of reversible quantum dynamics that preserve locality; they can be thought of as quantum analogues of classical cellular automata, but with much richer structure. I will describe a classification of the Clifford subclass of QCAs using methods from algebraic L-theory. The main result identifies the group of Clifford QCAs, up to natural equivalences, with L-theory homology of the underlying space. This gives a conceptual explanation of previously observed periodic patterns in lattice models and extends the picture to more general spaces. I will outline the ideas behind the construction and indicate how the framework connects topology, operator algebras, and quantum information. If time permits, I will also comment on what is known — and unknown — about the general (non-Clifford) case.

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