Project descriptionThis research project focuses on the study of homotopical structures of algebraic varieties, with a special emphasis on their motivic formulation, using techniques of algebraic geometry and homotopy theory. In particular, we aim to develop suitable algebraic frameworks for motivic rational homotopy theory. Also, we plan to study the existence and properties of mixed Hodge structures on homotopy theoretic invariants arising from rational homotopy, intersection cohomology and deformation theory.
D.Chataur, J.Cirici, Rational homotopy of complex projective varieties with normal isolated singularities. arXiv:1503.05347 [math.AT]
J. Cirici, F. Guillén, Homotopy theory of mixed Hodge complexes. Tohoku Mathematical Journal (to appear).
J. Cirici, Cofibrant models of diagrams: mixed Hodge structures in rational homotopy. Transactions of the American Mathematical Society 367 (2015), no.8, 5935--5970.