News · The Rising Sea

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.