My name is Daniel Murfet, I am a mathematician in the School of Mathematics and Statistics at the University of Melbourne. My CV is here and you can contact me by email or on Discord. My papers are on the arXiv with the exception of my PhD thesis which you can find here. I run a seminar, the videos from which may be found on YouTube. The Rising Sea is now available on the Metaverse.
My research interests are in algebraic geometry, mathematical logic and deep learning. You can see some of the things I like to think about in my Spring 2013 article in Emissary on matrix factorisations and my survey of linear logic. I am part of the Melbourne Deep Learning Group. I have various code projects on GitHub including my joint project with Nils Carqueville on computing with matrix factorisations.
The title of this webpage refers to the following quote from Grothendieck, which I learned from Colin McLarty’s article “The Rising Sea: Grothendieck on Simplicity and Generality”
A different image came to me a few weeks ago. The unknown thing to be known appeared to me as some stretch of earth or hard marl, resisting penetration … the sea advances insensibly in silence, nothing seems to happen, nothing moves, the water is so far off you hardly hear it … yet it finally surrounds the resistant substance.
My recent talks:
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.
These lectures were made with the excellent GoodNotes for the iPad Pro.
Mass surveillance is a serious threat to the ideal of free inquiry which makes mathematics (and other beautiful things) possible. Moreover, the technologies which enable it (e.g. machine learning) and the technologies which can be used to protect oneself from it (e.g. encryption) are themselves mathematical. Soon after the Snowden leaks my friend Nils Carqueville and I wrote an essay on this subject, which you might find interesting.
During my PhD under Amnon Neeman at the Australian National University, I took detailed notes. I am making some of these available in the hope that they may be useful. Many notes are heavily cross-referenced with other notes. I use an acronym system, where a reference of the form (MRS, Proposition 6) refers to my “Modules over Ringed Spaces” notes, for example. I have tried to document the relevant acronyms here, but there may be references to notes that I haven’t published online.
It goes without saying that most of the results in my notes are from one book or another. I’ve tried to list some of the main sources below, together with my shorthand for each book.
My handwritten notes for Sections 1 and 2 of Hartshorne (there are some corrections):
These are the notes for the reading group on proof-nets in linear logic, spanning April 8 and 15 of the logic seminar at the University of Melbourne. The aim is to:
The main references are:
Here is a rough plan that makes sense to me, for the first seminar:
The canonical reference for proof-nets and the Sequentialisation Theorem is Girard [G96], but in order to have notational consistency with the second seminar on light linear logic, and to see an overview free of complicating details, I think [BM09] is a better starting point for us. This means we would view [G96], [J91], [PTF09] as augmenting references for the real details (which are completely absent from [BM09]).
A rough plan for the second seminar, which will be taken almost entirely from [BM09].
My interest in the mathematical theory of computation is primarily due to the work of the logician Jean-Yves Girard on linear logic. Below is a list of references for the parts of the theory of computation that I either know a little about, or am interested in.
General “big picture” references on computation and logic:
Some references on lambda-calculus, System F and proof theory:
Some references on computational complexity theory:
Relations between computation and category theory:
Relations between computation and physics:
Some interesting videos: