## PhD research topic - Marco Manetti

#### Research area

Lie and homotopy methods in deformation theory

#### Keywords

Differential graded Lie algebras, L-infinity algebras, obstruction theory, model categories.

#### Research topic

Deformation theory is the study of small variations of algebro-geometric structures. It is a classical subject whose origin dates back to the works of Kodaira and Grothendieck [1]. It is an intrisically difficult subject since it involves nonadditive structures and it can be reduced to an additive framework only in the infinitesimal setting.

Il the last 30 years a new powerful approach to deformation theory ofer a field of characteristic 0 has been proposed by Deligne, Drinfeld, Kontsevich and other by using methods and ideas from rational homotopy theory [2], homotopical algebra [3], differential graded Lie algebras [4,5] and L-infinity algebras [6].

#### Bibliography

[1] C.S. Seshadri: Theory of moduli. Proceeding symposia in pure Mathematics, Vol 29, 1975.

[2] M. Schlessinger, J. Stasheff: Deformation theory and rational homotopy type, arXiv 1211.1647.

[3] M. Manetti, F. Meazzini: Formal deformation theory in left-proper model categories, arXiv 1802.06707.

[4] M.Manetti: Differential graded Lie algebras and formal deformation theory. In Algebraic Geometry: Seattle 2005. Proc. Sympos. Pure Math. 80 (2009)

[5] D. Iacono, M. Manetti: An algebraic proof of Bogomolov-Tian-Todorov theorem. In Deformation Spaces. vol. 39, p. 113-133, Vieweg Verlag, (2010).

[6] D. Fiorenza, M. Manetti: Formality of Koszul brackets and deformations of holomorphic Poisson manifolds. Homology, Homotopy and Applications, Vol. 14 (2012).