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Will Troiani

"As humans we could never be content with knowing all, yet we can't be content with the fact that our brains will never know." ~ Tommy Rogers

Mathematics

Projects

2020: Gentzen-Mints-Zucker Duality

2019: (Finite) simplicial sets are algorithms and an update Describing finite colimits using the internal language of a topos

2017: A proof tree constructor for the Linear Lambda Calculus

Notes

Algebra

Commutative algebra collection

Completion (Hensel's Lemma)

Introduction to homological algebra

Algebraic Geometry

Varieties

Selected Hartshorne Solutions

Logic

Proof-nets

Cut-elimination for intuitionistic, linear sequent calculus

First order, intuitionistic sequent calculus

Seminars

Coordinated:

Computation, Geometry, Logic (2021)

Will Troiani: "Proof-nets" 6/5

Will Troiani: "The Sequentialisation Theorem" 6/6

Will Troiani: "Geometry of Interaction Zero, proofs as permutations" 17/6

Daniel Murfet: "Cut operations on matrix factorisations" 1/7

Daniel Murfet: ?? 15/7

James Clift: "Smooth relaxation of Turing Machines" 29/7

Will Troiani: "Geometry of Interaction I: proofs as operators" 12/8

Participated in:

Melbourne Haskell Group (2020)

"Gentzen-Mints-Zucker Duality", video 

Topological Quantum Computing (2019)

"Reversible Turing Machines", Notes

"A crash course in simplicial cohomology with coefficients in Z mod 2", Notes

Graduate Topology Seminar

"Arithmetisation and localisation", Notes

Deep Learning

"Approximation of Continuous Functions by ReLU Nets", Notes

Topos Theory and Categorical Logic (2018)

"Monads and programs", Notes, Video

"Higher-order Logic and Topoi", Notes, Video

"The Classifying Space of Rings", Notes

DST Seminar (2017)

"Monads and Programs", Slides

Curry-Howard Correspondence (2016)

"The Church-Rosser Theorem", Notes, Improved notes

"Introduction to Lambda-Calculus", Notes

"System F in the real world: Haskell and functional programming", Notes, the referenced talk by Rich Hickey is Simple made easy

Music

2021: Obdurate

2021: Magneck (coming soon)

Art

2021 Collaborated with Nobby Seymour, "Usurping the authority of the Frame, which examines limits, both initial and terminal. Also, influenced by Godel's Theory of Incompleteness, the artist is investigating applying anomalous aspects of number theory to Design Theory". Algorithm

2016: Provided mathematical help for Nobby Seymour whilst he worked on Etherium