topological recursion from an algebraic perspective
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Topological recursion from an algebraic perspective Gatan Borot HU - PowerPoint PPT Presentation

Jan 20, 2023 •5 likes •365 views

Algebraic and combinatorial perspectives in mathematical sciences May Angeli Topological recursion from an algebraic perspective Gatan Borot HU Berlin Oct. 2, 2020 I. Bottom-up : how 2d topology arises from algebra II. Two examples : 2d

  1. Algebraic and combinatorial perspectives in mathematical sciences May Angeli Topological recursion from an algebraic perspective Gaëtan Borot HU Berlin Oct. 2, 2020

  2. I. Bottom-up : how 2d topology arises from algebra II. Two examples : 2d TQFT and Virasoro constraints III. Topological expansions in hermitian matrix models IV. Top-down: from geometric to topological recursion

  3. I How 2d topology arises from algebra

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How 2d topology arises from algebra — Airy structures Let be a vector space over V C Choose a basis of linear coordinates ( x i ) i ∈ I The Weyl algebra is the graded algebra of differential operators on V W ~ deg x i = deg ~ ∂ x i = 1 deg ~ = 2 V = C [ ~ ] h x i , ~ ∂ x i i 2 I i An Airy structure is a linear map such that L : V → W ~ V deg 1 condition : L i = ~ ∂ x i + O (2) ideal condition : [ L ( V ) , L ( V )] ⊂ ~ W ~ V · L ( V )

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