Projects per year

## Personal profile

### Research interests

**Pure Mathematics:** Higher Category Theory, Homotopy Theory, Algebraic Topology, Bicategories and 2-Categories, Quasi-categories and Complicial Sets, Applications to Mathematical Physics and Computer Science.

**Computer Science: **Programming Languages, Type Systems, Dependent Type Theory, Homotopy Type Theory, Formal Verification of Software Systems.

### Biography

Dominic Verity started his computational career in the early 1980s as a software developer for the influential British personal computing pioneer Acorn Computers; the company which created the BBC Microcomputer and ultimately invented the ubiquitous ARM microprocessor. He went on from there to work for the BBC World Service, where he was involved in designing and developing microcomputer technologies for application in radio production departments.

He studied as both an undergraduate and postgraduate at the University of Cambridge (UK) and emerged from that institution in 1992 with a PhD in Mathematics. From 1994-2000 he worked in the investment banking industry, as a mathematical consultant in derivative securities valuation and hedging, as a quantitative analyst in equity derivatives for Deutsche Bank Australia and as the Head of Equity Derivatives Trading for HSBC Australia.

He returned to academe in late 2000, and since then he has worked as a mathematician and computer scientist at Macquarie University. His research interests lie in the mathematical fields of Homotopy Theory, sometimes known as “rubber sheet geometry”, Algebraic Topology and Category Theory, a kind of “theory of everything” for pure mathematics. He is also active in exploring applications of this work to the Computer Science of Programming Languages. His most cited paper introduced “Traced Monoidal Categories”, structures that have become a key component in modern accounts of iterative processes in traditional and quantum computation. In recent years, he has held visiting Professorship positions at Harvard University, John’s Hopkins University, the Max Planck Institute for Mathematics, and the University of Cambridge.

Professor Verity is a passionate and engaging teacher of Computer Science and in 2008 his contributions in this area were recognised by the award of a Macquarie University Vice-Chancellor's Award for Teaching Excellence. In 2011 he gained national recognition for his work as an educator with the award of an Australian Learning and Teaching Council Citation for Outstanding Contribution to Student Learning “For a decade of inspirational and innovative educational leadership in the field of information technology”.

Over the past decade, Professor Verity has been highly active in academic leadership roles at the Department, Faculty and University levels. Most recently he led Macquarie’s academic governance as Chair of it’s Academic Senate, the “principal academic body in the University”.

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## Projects

## Working synthetically in higher categorical structures

Lack, S., Verity, D., Garner, R. & Street, R.

19/06/19 → 18/06/22

Project: Other

## Monoidal categories and beyond: new contexts and new applications

Street, R., Verity, D., Lack, S., Garner, R. & MQRES Inter Tuition Fee only, M. I. T. F. O.

30/06/16 → …

Project: Research

## Transforming exams across Australia: processes and platform for e-exams in high stakes, supervised environments

Bower, M., Hillier, M., Fluck, A., Cowling, M., Howah, K., Blackmore, K., Newhouse, P., Verity, D., Baird, M., Grant, S., Leitch, S., Geer, R. & White, B.

1/01/16 → …

Project: Research

## Centre of Australian Category Theory (CoACT)

Lack, S., Verity, D., Street, R., Chikhladze, D., Cohen, J., Corbett, J., Davydov, A., Flax, L., Kennett, C., Paoli, S., Palm, T., Pastro, C., Weber, M., Valckenborgh, F., Batanin, M. & Johnson, M.

1/01/09 → …

Project: Research

## Structural homotopy theory: a category-theoretic study

Street, R., Lack, S., Verity, D., Garner, R., MQRES, M., MQRES 3 (International), M. 3., MQRES 4 (International), M. & MQRES (International), M. (.

1/01/13 → 31/12/16

Project: Research

## Research Outputs

## Fibrations and Yoneda's lemma in an ∞-cosmos

Riehl, E. & Verity, D., 1 Mar 2017, In : Journal of Pure and Applied Algebra. 221, 3, p. 499-564 66 p.Research output: Contribution to journal › Article

## Kan extensions and the calculus of modules for ∞–categories

Riehl, E. & Verity, D., 2017, In : Algebraic and geometric topology. 17, 1, p. 189-271 83 p.Research output: Contribution to journal › Article

## Homotopy coherent adjunctions and the formal theory of monads

Riehl, E. & Verity, D., 2 Jan 2016, In : Advances in Mathematics. 286, p. 802-888 87 p.Research output: Contribution to journal › Article

## Infinity category theory from scratch

Riehl, E. & Verity, D., 19 Aug 2016, (Unpublished) 53 p.Research output: Other contribution

## Completeness results for quasi-categories of algebras, homotopy limits, and related general constructions

Riehl, E. & Verity, D., 2015, In : Homology, Homotopy and Applications. 17, 1, p. 1-33 33 p.Research output: Contribution to journal › Article