Photo taken by Giacomo Tendas

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.

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

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.

- (with Gareth Davies, Sina Greenwood, and Michael Lockyer) Inverse limits of upper semicontinuous functions and indecomposable continua, Topology and its Applications, vol.288, 107471, 2021.
- (with Ittay Weiss) Mahavier completeness and classifying diagrams, Topology and its applications, vol.229, pp.55-69, 2017.
- Categories of inverse systems of compacta with upper semi-continuous bonding functions, Topology and its Applications, vol.204, pp.23-40, 2016.

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.

- Describing groups using first-order language, summer project report.

- Equivalence of cubical and simplicial approaches to weak ω-categories
- Sep. 2021: Seminar on Algebra, Logic and Geometry in Informatics (online; slides)

- Orientals as free weak ω-categories
- Sep. 2021: Category Theory (University of Genoa; online; slides)
- Mar. 2021: Workshop on Computer Science and Category Theory (online)
- Feb. 2021: E8 Sporadic Mathematical Online Lecture Series (online)
- Feb. 2021: Australian Category Seminar (Macquarie University)

- Triangulating weak ω-categories into weak ω-categories
- Oct. 2020: Geometry and topology seminar (University of Western Ontario)

- Augmented simplicial sets as M-sets
- Jul. 2020: Australian Category Seminar (Macquarie University)

- A cubical model for weak ω-categories
- Oct. 2020: Homotopy Type Theory Electronic Seminar Talks (video, slides)
- Jul. 2020: AG-Seminar (Universität Regensburg)
- Jul. 2020: Geometric and Categorical Structures in Computation and Deduction (Satellite Workshop of Formal Structures for Computation and Deduction)
- Jun. 2020: Australian Category Seminar (Macquarie University)
- May 2020: Mathematical Sciences Research Institute, cubical sets seminar (video)

- Towards the formal theory of homotopy coherent monads
- Feb. 2020: Australian Category Seminar (Macquarie University)

- The Gray tensor product for 2-quasi-categories
- Dec. 2020: Annual Meeting of the Australian Mathematical Society (University of New England; slides)
- Feb. 2020: Mathematical Sciences Research Institute, (∞,2)-categories working group
- Nov. 2019: Australian Category Seminar (Macquarie University)
- Jul. 2019: Category Theory (University of Edinburgh)

- Inner horns for 2-quasi-categories
- Mar. 2019: Australian Category Seminar (Macquarie University)
- Dec. 2018: Annual Meeting of the Australian Mathematical Society (University of Adelaide)

- Mahavier limits
- Dec. 2017: Annual Meeting of the Australian Mathematical Society (Macquarie University)

- Indecomposable generalised inverse limits
- Feb. 2014: Devonport Topology Festival; joint talk with Stephen Bell

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:

- Cubical sets
- ω-categories, orientals, and complicial sets
- Monads and theories (this paper by Bourke and Garner)
- Inner horns and spines for ∞-categories
- Martin-Löf type theory
- The formal theory of monads (this paper by Street)
- Quasi-categories
- Model categories

Other expository talks I have given include:

- A friendly introduction to ∞-categories
- Introduction to ∞-categories in general and quasi-categories in particular
- May 2021: Thursday Seminar (Kyoto University; online; slides)

- Associativity without equality
- Jun. 2019: Department Research Congress (Macquarie University)

- Homotopy theory and model categories
- Jan. 2015: Summer Scholar Presentation (Australian National University)

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.

- Higher Categories and Categorification (2020, Mathematical Sciences Research Intitute)
- Summer School on Higher Topos Theory and Univalent Foundations (2019, University of Leeds)
- International Category Theory Conference (2018, University of Azores)