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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