Dylan G. L. Allegretti

activity

20182025

collaborators

4 papers

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.CA2018

Voros symbols as cluster coordinates

Dylan G. L. Allegretti

We show that the Borel sums of the Voros symbols considered in the theory of exact WKB analysis arise naturally as Fock-Goncharov coordinates of framed $P G L_{2} (C)$ -local sy…

math.GT2018

The monodromy of meromorphic projective structures

Dylan G. L. Allegretti, Tom Bridgeland

We study projective structures on a surface having poles of prescribed orders. We obtain a monodromy map from a complex manifold parameterising such structures to the stack of fram…

Monoidal categorification of genus zero skein algebras

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

Voros symbols as cluster coordinates

The monodromy of meromorphic projective structures

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