Ai Guan

Assistant Professor

Colin Maclaurin T.03
a.guan-(at)-hw.ac.uk

I joined Heriot-Watt University as an Assistant Professor in the Department of Mathematics in September 2026. Previously, I held teaching positions at the University of Nottingham and the University of Birmingham and postdoctoral research positions at the University of Seville and Lancaster University. Also at Lancaster I completed my PhD in 2021 under the supervision of Andrey Lazarev. Here is my thesis.

Papers

Operations on the de Rham cohomology of Poisson and Jacobi manifolds (with Fernando Muro)
Selecta Mathematica, 31, Article 94, 2025.
Model category structures on multicomplexes (with Xin Fu, Muriel Livernet and Sarah Whitehouse)
Topology and its Applications, 316, Article 108104, 2022.
Koszul duality for compactly generated derived categories of second kind (with Andrey Lazarev)
Journal of Noncommutative Geometry, 15(4), pp. 1355–1371, 2021.
Gauge equivalence for complete $L_{\infty}$-algebras
Homology, Homotopy and Applications, 23(2), pp. 283–297, 2021.
Review of deformation theory I: concrete formulas for deformations of algebraic structures (with Andrey Lazarev, Yunhe Sheng and Rong Tang)
Advances in Mathematics (China), 49(3), pp. 257–277, 2020.
Review of deformation theory II: a homotopical approach (with Andrey Lazarev, Yunhe Sheng and Rong Tang)
Advances in Mathematics (China), 49(3), pp. 278–298, 2020.

★ denotes events that I have spoken at, or plan to speak at.

Women in (Co)Homology, Loughborough, UK; 2–3 April 2025.
★ Enumerative Algebraic Geometry en Liberté, Birmingham, UK; 17–18 February 2025.
★ British Topology Meeting 36, Sheffield, UK; 5–8 September 2023.
★ Conference on Motivic and Equivariant Topology, Swansea, UK; 15–17 May 2023.
Interactions and Applications of Homotopical Algebra and Geometry, Luxembourg; 14–16 November 2022.
British Mathematical Colloquium, online; 6–9 April 2021.
Additive categories between algebra and functional analysis, online; 1–5 March 2021.
★ Topics in Category Theory: A Spring School, Edinburgh, UK; 11–13 March 2020.
British Topology Meeting 34, Warwick, UK; 16–18 September 2019.
★ Women in Topology III, Hausdorff Institute, Bonn, Germany; 26–30 August 2019.
★ Early Career Topology Researchers, Sheffield, UK; 6–7 June 2019.
Deformation Theory and Homotopy Algebra, Emei, China; 6–11 May 2019.
British Mathematical Colloquium, Lancaster, UK; 8–11 April 2019.
Homotopy algebras, deformation theory and quantization, Będlewo, Poland; 16–22 September 2018.
★ Young Researchers in Mathematics, Southampton, UK; 23–26 July 2018.
★ Young Topologists Meeting, Copenhagen, Denmark; 9–13 July 2018.
Rational Homotopy and its Applications, Lille, France; 18–19 January 2018.
★ British Topology Meeting 32, Leicester, UK; 6–8 September 2017.
School on Deformation Theory, Turin, Italy; 5–8 July 2017.