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Creators/Authors contains: "Lauda, Aaron"

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  1. ; ; (, Quantum Topology)
    We develop the rewriting theory for monoidal supercategories and2-supercategories. This extends the theory of higher-dimensional rewriting established for (linear) 2-categories to the super setting, providing a suite of tools for constructing bases and normal forms for2-supercategories given by generators and relations. We then employ this newly developed theory to prove the non-degeneracy conjecture for the odd categorification of quantum\mathfrak{sl}(2)from A. Ellis and A. Lauda [Quantum Topol. 7 (2016), 329–433] and J. Brundan and A. Ellis [Proc. Lond. Math. Soc. (3) 115 (2017), 925–973] As a corollary, this gives a classification of dg-structures on the odd2-category conjectured by A. Lauda and I. Egilmez [Quantum Topol. 11 (2020), 227–294]. 
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  2. ; ; (, Selecta Mathematica)
    Abstract We relate the Fukaya category of the symmetric power of a genus zero surface to deformed category$$\mathcal {O}$$ O of a cyclic hypertoric variety by establishing an isomorphism between algebras defined by Ozsváth–Szabó in Heegaard–Floer theory and Braden–Licata–Proudfoot–Webster in hypertoric geometry. The proof extends work of Karp–Williams on sign variation and the combinatorics of the$$m=1$$ m = 1 amplituhedron. We then use the algebras associated to cyclic arrangements to construct categorical actions of$$\mathfrak {gl}(1|1)$$ gl ( 1 | 1 ) , and generalize our isomorphism to give a conjectural algebraic description of the Fukaya category of a complexified hyperplane complement. 
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  3. ; ; ; (, arXivorg)
    Accepted Manuscript Full Text Available
  4. ; ; ; (, Pacific Journal of Mathematics)
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  5. ; ; (, Advances in Mathematics)
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  6. ; ; ; (, Letters in Mathematical Physics)
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  7. ; ; ; (, Annals of Physics)
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  8. ; (, Notices of the American Mathematical Society)
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  9. ; ; ; (, Journal of the London Mathematical Society)
    Abstract We develop the categorical context for defining Hermitian non‐semisimple topological quantum field theories (TQFTs). We prove that relative Hermitian modular categories give rise to modified Hermitian Witten–Reshetikhin–Turaev TQFTs and provide numerous examples of these structures coming from the representation theory of quantum groups and quantum superalgebras. The Hermitian theory developed here for the modified Turaev–Viro TQFT is applied to define new pseudo‐Hermitian topological phases that can be considered as non‐semisimple analogs of Levin–Wen models. 
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  10. ; (, Advances in Mathematics)
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