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.
J. Cirici, D. Egas Santander, M. Livernet and S. Whitehouse, Derived A-infinity algebras and their homotopies. Topology and its Applications (special issue) to appear (also available at http://arxiv.org/abs/1609.08077).
D.Chataur, J.Cirici, Rational homotopy of complex projective varieties with normal isolated singularities. Forum Mathematicum 29 (2017), no.1, 41--57
J. Cirici, F. Guillén, Homotopy theory of mixed Hodge complexes.Tohoku Mathematical Journal 68 (2016), no.3, 349--375.
J. Cirici, Cofibrant models of diagrams: mixed Hodge structures in rational homotopy. Transactions of the American Mathematical Society 367 (2015), no.8, 5935--5970.
U. Buijs and F. Cantero and J. Cirici, Weight decompositions of Thom spaces of vector bundles in rational homotopy theory. arXiv:1610.02917 [math.AT] 2017
Cirici and G. Horel, Mixed Hodge structures and formality of symmetric monoidal functors. arXiv:1703.06816 [math.AT] 2017
J. Cirici and A. Roig, Sullivan minimal models of operad algebras. arXiv:1612.03862 [math.AT] 2016
Chataur and J. Cirici, Mixed Hodge structures on the intersection homotopy type of complex varieties with isolated singularities. arXiv:1603.09125 [math.AT] 2016