News:

- Rohan Hitchcock’s masters thesis, October 2022, Differentiation, Division and the Bicategory of Landau-Ginzburg Models.
- Matthew Farrugia-Roberts’ masters thesis, October 2022, Structural Degeneracy in Neural Networks.
- Spencer Wong’s masters thesis, May 2022, From Analytic to Algebraic: The Algebraic Geometry of Two Layer Neural Networks.
- Elimination and cut-elimination in multiplicative linear logic, July 2022, preprint with Will Troiani.
- We taught an introductory algebraic geometry class at metauni (MAG) in June 2022.
- David Li’s summer scholar project, February 2022, AlphaFold.
- Jackson Godfrey’s masters thesis, October 2021, Superbicategories.
- Liam Carroll’s masters thesis, October 2021, Phase transitions in neural networks.
- Tom Waring’s masters thesis, October 2021, Geometric perspectives on program synthesis and semantics.
- The Rising Sea is now on metauni, a network of virtual spaces built on Roblox and Discord. Many of my talks this year will be hosted there.
- Deep Learning is Singular, and That’s Good, October 2020, preprint from MDLG on theory of deep learning.
- Geometry of Program Synthesis, October 2020, preprint with James Clift and James Wallbridge.
- Gentzen-Mints-Zucker duality, August 2020, preprint with William Troiani on sequent calculus, lambda calculus and the Curry-Howard correspondence (video).
- Isaac David Smith’s masters thesis, June 2020, Investigating Defect Topological Quantum Field Theories as Models for Quantum Error-Correction.
- Logic and the 2-Simplicial Transformer published at ICLR 2020 (code and videos | arXiv version).
- Will Troiani’s masters thesis, May 2019, Simplicial sets are algorithms.
- Constructing A-infinity categories of matrix factorisations preprint, March 2019 (my working notes are available).
- The notes and videos for a course on Metric and Hilbert spaces (and video HOWTO).
- Albert Zhang’s masters thesis, October 2018, Vertex algebras, Hopf algebras and lattices (and talk slides).
- Derivatives of Turing machines in Linear Logic preprint with James Clift, May 2018.
- Encodings of Turing machines in Linear Logic preprint with James Clift, May 2018.
- James Clift’s masters thesis, October 2017, Turing machines and differential linear logic.
- Patrick Elliott’s masters thesis, October 2017, A-infinity categories and matrix factorisations over hypersurface singularities.

Some talks:

- Matrix factorisations and Quantum Error Correcting Codes, July 2022 (notes).
- Introduction to singularity theory, March 2021 (notes)
- Theory of Deep Learning, January 2021, a general introduction to the topic in the Rising Sea metauni node (video).
- Introduction to matrix factorisations, April 2020 in University of Melbourne moduli spaces seminar (Part 1 notes | Part 2 notes)
- From critical points to extended TQFTs, April 2020 in Monash topology seminar (notes)
- A-infinity categories of matrix factorisations via A-infinity idempotents, January 2020 at KIAS workshop on Atiyah classes and related topics (notes)
- Mathematics of AlphaGo, November 2019 colloquium at Macquarie (notes | screencast)
- From critical points to A-infinity categories, October 2019 at Macquarie (notes)
- Monoidal bicategories of critical points, July 2019 (notes)
- Constructing A-infinity categories of matrix factorisations, July 2019 at RRAGE (slides)
- Proof synthesis and differential linear logic, June 2019 at CARMA (slides | screencast)
- Derivatives of Turing machines and inductive inference, November 2018 at Peking University (notes)
- The computational content of Landau-Ginzburg models, November 2018 at BICMR, Beijing (notes)
- Derivatives of Turing machines in linear logic, May 2018 in the Melbourne pure math seminar (notes)
- Algebra and Artificial Intelligence, May 2018 in the Melbourne logic seminar (slides | video)
- Bar versus Koszul, April 2018 in the Melbourne topology seminar (notes)
- Mini-course on A-infinity categories and matrix factorisations, September 2017 at the IBS in Korea (lecture 1, lecture 2, lecture 3).
- Turing machines and coalgebras, September 2017 at Neeman’s 60th conference at ANU (notes).
- Clifford algebras and 2D defect topological field theory, June 2017 at Tensor Categories and Field Theory (notes).
- A tour of well-generated triangulated categories, May 2017 at Neeman’s 60th conference (notes).
- Derivatives of proofs in linear logic (joint with James Clift), May 2017 in Melbourne (slides and transcript).
- The cobordism category, October 2016 in the TFT seminar (notes).
- The Curry-Howard principle, October 2016 in the CH seminar (notes).
- The category of simply-typed lambda terms, September 2016 in the CH seminar (lecture 1, lecture 2).
- Sheaves of A-infinity algebras from matrix factorisations, September 2016 at the IPMU (notes).
- Generalised orbifolding, September 2016 minicourse at the IPMU (lecture 1, lecture 2, lecture 3).
- Generalised orbifolding of simple singularities, August 2016 at Geometry at the ANU (notes).
- Two odd things about computation, October 2015 in Vienna and August 2016 in Melbourne (slides and transcript).
- Topological Quantum Field Theory in two dimensions, July 2016 in the TFT seminar (slides).
- Spectral sequences for vertex algebras, July 2016 in Melbourne (notes).
- Linear logic and deep learning (joint with Huiyi Hu), June 2016 at the AAL in Melbourne (slides and transcript).
- A-infinity algebras and matrix factorisations, June 2016 in Banff (notes and video).
- The Landau-Ginzburg/Conformal Field Theory correspondence, May 2016 in Melbourne (notes).
- The super-A-polynomial and knot differentials, May 2016 in Melbourne (notes).
- A-infinity algebras and minimal models [Part 1], May 2016 in Melbourne (notes and screencast).
- Reading group on proof-nets, April 2016 in the Melbourne logic seminar (handout 1, handout 2 and notes).
- Stratifications and complexity in linear logic, March 2016 in the Melbourne logic seminar (slides and screencast).
- An introduction to A-infinity algebras, November 2015 in Melbourne (notes).

I gave a mini-course at the IBS in Korea in January 2016 on topological field theory with defects, specifically the fusion of defects in topological Landau-Ginzburg models. This included several computer demos, the source for which can be found on GitHub.

- Lecture 1: 2D TFT with defects and matrix factorisations (notes and video).
- Lecture 2: The bicategory of Landau-Ginzburg models (notes and video).
- Lecture 3: The cut operation and computing fusions (notes and video).

These lectures were made with the excellent GoodNotes for the iPad Pro.