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Yuki Maehara(前原 悠究)

日本語版はこちらからどうぞ

email: y-maehara@imi.kyushu-u.ac.jp

I am a postdoctoral researcher at Institute of Mathematics for Industry, Kyushu University, Fukuoka, Japan.
Before that, I was a PhD student of Dominic Verity and Ross Street at Macquarie University, Sydney, Australia.

I am interested in category theory in general, and so far my research has focused on (∞,n)-categories and the Gray tensor product.

Here (no. 8) is my 5 minute self-introduction from the Higher Categories and Categorificaction program at the MSRI in spring 2020.

Publications

(∞,n)-categories

  1. (with Brandon Doherty and Chris Kapulkin) Equivalence of cubical and simplicial approaches to (∞,n)-categories, submitted.
  2. Orientals as free weak ω-categories, submitted.
  3. (with Tim Campion and Chris Kapulkin) A cubical model for (∞,n)-categories, submitted.
  4. The Gray tensor product for 2-quasi-categories, Advances in Mathematics, vol.377, 107461, 2021.
  5. Inner horns for 2-quasi-categories, Advances in Mathematics, vol.363, 107003, 2020.

Mahavier limits/generalised inverse limits

What are these limits?

This is a generalisation of the notion of inverse limit (of topological spaces) where one allows the diagram to involve continuous-ish multi-valued maps. Continuum theorists were particularly interested in complicated spaces that can be built as inverse limits of very simple spaces such as the unit interval, and introduced this generalisation as a tool for constructing/analysing even more complicated spaces.
For my honours project (supervised by Sina Greenwood, Auckland University), I characterised these "limits" by a certain universal property.

Other material

Category theory

First-order characterisations of groups

About the project

This is a summer project I did between the second and third years of my undergraduate (supervised by André Nies, Auckland University).
The last section ("Polylogarithmic compressibility") of my report below is original, and some of the material there appeared in Section 2 of this paper of Nies and Tent.

Talks

Research talks

Expository talks

I (re)started the Junior Category Theory Seminar (to which no "grown-ups" beyond postdocs are invited) at Macquarie University and spoke about the following topics in 2018-2019:

Other expository talks I have given include:

Other places you might have met me

If I look familiar to you but none of the talks above rings a bell, you might have met me in one (or more) of the following events.