Research seminar on higher structures



The topic of this seminar will be derived deformation theory. Preliminary schedule.



Familiarity with basic ∞-category theory as developed in Chapters 1-4 of the book Higher Topos Theory.

Talk 1 (Oct 14)Introduction and organization(Severin)notes
Talk 2 (Oct 21)Examples of deformations I: associative algebras and modules(Xinyang)notes
Talk 3 (Oct 28)Examples of deformations II: complex manifolds and vector bundles(Walker)
Talk 4 (Nov 04)Formalisation of deformation problems: Schlessinger's deformation functors(Malte)notes
Talk 5 (Nov 11) Differential graded Lie algebras and Mauer-Cartan theory(Arndt)notes
Talk 6 (Nov 18) Deformations of singularities(Jonte)
Talk 7 (Nov 25) The idea of derived deformation theory and the motivation for Lurie's theorem(Tobias)
Talk 8 (Dec 02) Deformation contexts and formal moduli problems(Angus)
Talk 9 (Dec 09) Tangent complex and deformation theories(Merlin)
Talk 10 (Dec 16)∞-topoi and hypercoverings(Severin)notes
Talk 11 (Jan 06)Deformation theories classify formal moduli problems(Walker)
Talk 12 (Jan 13)Homology and cohomology of Lie algebras(Fernando)
Talk 13 (Jan 20)Koszul duality and the proof of the Lurie-Pridham Theorem(Julian)
Talk 14 (Jan 27)Moduli problems for E_n-algebras(Tobias)