Guglielmo Nocera

Formal moduli problems

This was a reading seminar based on Derived Algebraic Geometry X by Jacob Lurie, and organised by Federico Conti, Julian Demeio, Michele Pernice, Morena Porzio and myself. It ran from December 2020 to July 2021.
In this course we introduced the necessary background (starting from basics in deformation theory and ∞-category theory) to understand the link between differentially graded Lie algebras and formal moduli problems, as exposed in Lurie's note, Theorem 2.0.2.

Bibliography: [Calaque-Grivaux] Damien Calaque and Julien Grivaux, Formal moduli problems and formal derived stacks, 2019
[DAG X] Jacob Lurie, Derived Algebraic Geometry X , 2011
[Gepner] David Gepner, An introduction to Higher Categorical Algebra, 2019
[HA] Jacob Lurie, Higher Algebra, 2017
[Hovey] Mark Hovey, Model Categories, AMS, Mathematical Monographs and Surveys 63, 1999
[HTT] Jacob Lurie, Higher Topos Theory, Princeton University Press, 2009
[Porta-Vezzosi] Mauro Porta and Gabriele Vezzosi, Infinitesimal and square-zero extensions of simplicial algebras, 2013
[Pridham] J.P. Pridham, Unifying derived deformation theories, Advances in Mathematics, 2010
[Toën] Bertrand Toën, Problèmes de modules formels, Séminaire Bourbaki, 2016