Derived Algebraic Geometry, CoHAs and Operads

Angers, 16-19 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

Speakers

• Ben Davison - University Edinburgh
• Lucien Hennecart - Université Picardie Jules Verne
• Šarūnas Kaubrys - Kavli IPMU
• David Kern
• Alyosha Latyntsev - Beijing Institute of Mathematical Sciences and Applications
• Joost Nuiten - Université Toulouse
• Emanuele Pavia - Université Luxembourg
  Categorified Representations Of Topological Groups

  In his celebrated 2014 ICM address, Costantin Teleman suggested that one first step towards a theory of G-gauged TQFTs, where G is a compact Lie group, is provided by studying categorified representation theory of Lie groups. Building on the work of Jacob Lurie and showing evidence provided by concrete, computable examples, he hinted at some of the desirable properties that such categorical representations should enjoy.

  In this talk, we will see how the powerful formalism of higher category theory allows us to pursue these insights of Teleman: we provide rigorous proofs of some of his claims and deduce analogs of fundamental statements in classical representation theory. In particular, we are able to formulate a categorified Koszul duality statement in the topological setting.

  This is based on joint work with James Pascaleff and Nicolò Sibilla.

• Renata Picciotto - Cambridge University
• Hugo Pourcelot - Université Angers
• Nikola Tomić - Université Montpellier

Schedule

Tuesday 16	Wednesday 17	Thursday 18	Friday 19
9h30 - 10h45 Nuiten	9h30 - 10h45 Latyntsev	9h30 - 10h45 Hennecart	9h30 - 10h45 Pourcelot
10h45 - 11h15 coffee break	10h45 - 11h15 coffee break	10h45 - 11h15 coffee break	10h45 - 11h00 coffee break
11h15 - 12h30 Pavia	11h15 - 12h30 Kaubrys	11h15 - 12h30 Davison	11h00 - 12h00 Picciotto
Lunch // discussions	Lunch // discussions	Lunch // discussions
15h30 - 16h45 Kern		16h00 - 17h15 Tomic
	19h - Dinner La Réserve