Dylan G. L. Allegretti

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20182025

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math.RT2025

Monoidal categorification of genus zero skein algebras

Dylan G. L. Allegretti, Hyun Kyu Kim, Peng Shan

We prove a conjecture of the first and third named authors relating the Kauffman bracket skein algebra of a genus zero surface with boundary to a quantized $K$ -theoretic Coulomb br…

math.RT2024

Dualities of $K$ -theoretic Coulomb branches from a once-punctured torus

Dylan G. L. Allegretti, Peng Shan

We consider the quantized $SL_{2}$ -character variety of a once-punctured torus. We show that this quantized algebra has three $Z_{2}$ -invariant subalgebras that are i…

math.RT2024

Skein algebras and quantized Coulomb branches

Dylan G. L. Allegretti, Peng Shan

To a compact oriented surface of genus at most one with boundary, we associate a quantized $K$ -theoretic Coulomb branch in the sense of Braverman, Finkelberg, and Nakajima. In the…

Monoidal categorification of genus zero skein algebras

Dualities of K-theoretic Coulomb branches from a once-punctured torus

Skein algebras and quantized Coulomb branches

Dualities of $K$ -theoretic Coulomb branches from a once-punctured torus