Derived Algebraic Geometry, CoHAs and Operads

Angers, 15-19 Juin 2026

How to reach the lab.

We want to emphasize the use of derived algebraic geometry and operads as tools to make significant progress in two directions:

• geometric representation theory, and specifically with the aim of constructing and studying cohomological Hall algebras ;
• topological field theories, via the use of mapping stacks and Simpson shapes.

These two axes are related, at least via (shifted) symplectic geometry, and the crucial use of lagrangian structures. More specifically, in some situations may naturally appear moduli of curves, that can often be dealt with using operadic methods. The first axis is extremely active at present, and tackled through various closely related angles by several teams, see eg [DHM, KPS, DPSSV]. The second axis morally relies on the fully extended AKSZ construction performed in [CHS] associated to the Betti shape, as well as on the recent proof of the Moore-Tachikawa conjecture in [CM].

• [CHS] D. Calaque, R. Haugseng & C. Scheimbauer. The AKSZ construction in derived algebraic geometry as an extended topological field theory, Mem. Amer. Math. Soc. 308 (2025), no. 1555, v+173 pp, arXiv:2108.02473.
• [CM] P. Crooks & M. Mayrand. The Moore-Tachikawa conjecture via shifted symplectic geometry, arXiv:2409.03532.
• [DHM] B. Davison, L. Hennecart & S. S. Mejia. BPS algebras and generalised Kac-Moody algebras from 2-Calabi-Yau categories, arXiv:2303.12592.
• [DPSSV] D-E. Diaconescu, M. Porta, F. Sala, O. Schiffmann & E. Vasserot. Cohomological Hall algebras of one-dimensional sheaves on surfaces and Yangians, arXiv:2502.19445.
• [KPS] T. Kinjo, H. Park & P. Safronov. Cohomological Hall algebras for 3-Calabi-Yau categories, arXiv:2406.12838.

Organisers

• Tristan Bozec - Université Angers
• Damien Calaque - Université Montpellier
• Julien Grivaux - Sorbonne Université
• Hugo Pourcelot - Université Angers