My name is Rohan Hitchcock and I am currently a PhD Candidate at CSRIO and the University of Melbourne. I am looking at simulations of physical systems using neural networks.

I am currently running a seminar on statistical mechanics.

Masters thesis

I have recently completed a Master of Science in Mathematics and Statistics at the University of Melbourne. I completed a thesis under the supervision of Dr Daniel Murfet which studied the bicategory of Landau-Ginzburg models, which you can read here.

This bicategory can be thought of as a bicategory in which the objects are polynomials with isolated singularities and the 1-morphisms between polynomials \(U(x_1, \cdots, x_n)\) and \(V(y_1, \cdots, y_m)\) are algebraic subsets of the zero set of \(U - V\).

Talks in the Metauni Landau-Ginzburg Seminar (seminar webpage)

• An introduction to bicategories (notes, video).
• Matrix factorisations and geometry (notes, video).
• The Perturbation Lemma (notes, video1, video2).
• Composition in the bicategory of Landau-Ginzburg models (notes, video).
• The cut operation (notes, video1, video2).
• Differentiation and division (notes, video1, video2).
• The cut operation revisited (notes, video).

Other notes

• Introduction to idempotent completion in preadditive categories (notes).
• Another introduction to matrix factorisations (notes). This is an edited version of an assessment for a subject called Communication for Research Scientists, where the task was to write a short journal-style article.

Deep learning and singular learning theory

I began my Master’s thesis looking at deep learning, algebraic geometry and singular learning theory, along the lines of the book Algebraic Geometry and Statistical Learning Theory (2009) by Sumio Watanabe.

• A short review of literature on singular learning theory (notes).
• A non-technical blog-style article on deep learning and singular learning theory (notes). This was an assessment piece for a subject called Communication for Research Scientists.
• Notes from a talk on blow-ups and singular learning theory (notes).
• A ‘Stone-Weierstrass’ Theorem for neural networks (notes).

In the January 2021 I completed the course The Mathematical Engineering of Deep Learning as part of the Australian Mathematical Sciences Institute Summer School.

• Final project (notes, video, code). This project was a review and demonstration of results in the paper “Wasserstein GAN” (2017) by M. Arjovsky, S. Chintala, and L. Bottou arXiv: 1701.07875 [stat.ML].

Miscellaneous

• Paper: “Display of Native Antigen on cDC1 That Have Spatial Access to Both T and B Cells Underlies Efficient Humoral Vaccination” (2020) by Kato et. al. doi:10.4049/jimmunol.2000549. My contribution to this paper consisted of writing simulations of biological processes to support experimental data, and rewriting legacy image processing code. This work was undertaken while I was a research assistant at the Peter Doherty Institute for Infection and Immunity.
• From June 2018 to August 2020 I worked on a cross-disciplinary research project at The Peter Doherty Institute for Infection and Immunity and The University of Melbourne (code). The aim of this project wa to determine a stochastic model the motion for a certain population of immune cells residing in the liver. I worked with and was supervised by Dr Lynette Beattie (Dept. Microbiology and Immunology), Professor Jonathan Manton (Dept. Electrical and Electronic Engineering) and Professor William Heath (Dept. Microbiology and Immunology), all at The University of Melbourne.
• AMSI Vacation Research Scholarship (report). In the summer of 2019/2020 I completed a six week research project at the University of Western Australia under the supervision of Dr John Bamberg and Professor Michael Guidici. My project was centred around understanding the paper “Octonions, Albert Vectors and the group \(E_6(F)\)” (2019) by J. N. Bray, Y. Stepanov and R. A. Wilson arXiv:1906.08846.