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Factorization homology and applications (introductory lecture)

Banff International Research Station for Mathematical Innovation and Discovery

Factorization algebras, and factorization homology, began in the work of Beilinson-Drinfeld, as an algebro-geometric/coordinate-free approach to vertex algebras and conformal blocks, respectively. They were re-interpreted by Costello-Gwilliam as a framework for algebras of observables in quantum field theory. A special class, the so-called "locally constant" factorization algebras received special attention from Lurie, Ayala-Francis, and Scheimbauer in the context of fully extended topological field theories. In the first lecture I shall recall this history, define factorization homology in the mold of Ayala-Francis, and recall the key property of excision, which both uniquely determines factorization homology as a functor, and gives an effective mechanism for its computation. In the second lecture, I will turn to examples in geometry and representation theory, following Ben-Zvi-Francis-Nadler, and our works with Ben-Zvi-Brochier and Brochier-Snyder. Specializing the "coefficients" to lie in presentable k-linear categories (the natural home of algebraic geometry and representation theory), one recovers character varieties, and their canonical quantizations, as a computation in factorization homology.

Mathematics; Algebraic geometry; Quantum theory; Mathematical physics

video/mp4

Author affiliation: University of Edinburgh

2019-03-24

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/69131

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/