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Pages

Posts

portfolio

publications

An opensource tool for filtered two-fluid simulations of fluidized gas-particle flows

Joint with Federico Municchi and Jan Cloete. Published in APS-DFD 2020, Chicago, 2020

We present a numerical solver based on the opensource finite volume library OpenFOAM that solves the filtered two-fluid equations for fluidized gas-particle flows using a wide range of diverse models developed in recent literature. We illustrate the phase coupling algorithm and discuss the implementation of the model of Sarkar et al. (2016). Finally, we compare the predictions from different constitutive models against experimental results using very coarse grids.

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A Laurent phenomenon for the Cayley plane

Joint with Tom Ducat. Published in SIGMA 20 (2024), 2024

We describe a Laurent phenomenon for the Cayley plane, which is the homogeneous variety associated to the cominuscule representation of \(E_6\). The corresponding Laurent phenomenon algebra has finite type and appears in a natural sequence of LPAs indexed by the \(E_n\) Dynkin diagrams for \(n\leq 6\). We conjecture the existence of a further finite type LPA, associated to the Freudenthal variety of type \(E_7\).

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A Framework for Generalized Tropical Homotopy Continuation

Joint with Yue Ren. Published in Lecture Notes in Computer Science, Springer, 2024

We present a framework for generalizing tropical homotopy continuation for computing stable intersections of tropical hypersurfaces, tropical linear spaces, and tropical inverted linear spaces. We also report on beginning implementations in OSCAR.

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talks

Interdisciplinary applications of cluster algebras

Published:

A 5-day conference at the INI focused on drawing out deep connections between cluster algebras and representation theory, combinatorics, algebraic, hyperbolic and symplectic geometry, amongst many others.

ICMS and MAC-MIGS Modelling Camp 2022

Published:

A short modelling camp where participants split into groups and solve problems with industry partners. Our team came first place for designing and implementing preprocessing pipelines for underwater ROV imaging.

ISM Discovery School on Mutations

Published:

An exploration of the connections between representation theory and cluster algebras, with emphasis on combinatorial problems in tau-tilting theory.

Computational Geometry Workshop

Published:

Updates on computational geometry, including recent trends in open source computer algebra software, lattice polytopes, and Fano varieties.

Newton-Okounkov Bodies & Tropical Geometry

Published:

A meeting of many different topics (not all related to tropical geometry!) including things like Hilbert schemes, Khovanskii-finiteness for rational curves of genus two and low degree hypersurfaces, and degenerations of polarized projective varieties to complexity-one varieties.

Quivers, Clusters, Moduli and Stability

Published:

A meeting between geometers and algebraists, to share problems and methods in their respective fields. Topics include quiver moduli, counting sheaves and represenations of CY4 quivers, the Grassmannian cluster category and mirror symmetry, and the birational geometry of quiver varieties.

Cluster Structures in the North

Published:

A short meeting gathering the experts in cluster theory in the North of England. Topics included maximal green sequences, growth of frieze patterns, and expansion formulae for loop graphs.

teaching

Linear Algebra 1

Undergraduate course, Durham University, 2022

I was a TA for Durham’s Linear Algebra course, running regular tutorials and marking assignments.