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Solving a problem open for 20 years: Intersection of parabolic subgroups in spherical Artin groups.

Abstract: We solved an important problem from the area of Artin groups and create a new simplicial complex that has been very celebrated and studied.  Thanks to this result, published in Adv. Math., the solution to the problem has been generalized to other Artin groups using our case as a base case. For this result …

Solving a problem open for 20 years: Intersection of parabolic subgroups in spherical Artin groups. Leer más »

Homotopy theory of classifying spaces

Abstract: Our research interest has been the homotopy theory of classifying spaces. In the compact case, we described the BZ/p-nullifications of classifying spaces of compact Lie groups (joint with N. Castellana). Moreover, in joint work with R. Foote and J. Scherer, we completely characterized the BZ/p-cellular approximations of classifying spaces, in a program that also …

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Khovanov spectrum of periodic links admits a homology group action

Abstract: We prove that, given an $m$-periodic link, the Khovanov spectrum constructed by Lipshitz and Sarkar admits a homology group action. The action of Steenrod algebra on the cohomology of the spectrum gives an extra structure of the link. Another consequence of our construction is an alternative proof of the localization formula for Khovanov homology …

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Gauss-Manin system of the Dwork familiy

Abstract: We compute algebraically the invariant part of the Gauss–Manin cohomology of a generealized Dwork family under the action of certain subgroup of automorphisms. To achieve that goal we use the algebraic theory of D-modules, especially one-dimensional hypergeometric ones.  Researchers: Alberto Castaño Related publications: https://doi.org/10.4171/rmi/1088 iMAT research line:   ⊕ RL11. Algebra, Geometry and Topology

Hodge ideals of free divisors

Abstract: We describe explicitly the Hodge filtration and the Hodge ideals associated with divisors for which the logarithmic comparison theorem hold, we conjecture a bound for the generating level of the Hodge filtration, and we develop an algorithm to compute Hodge ideals of such divisors and we apply it to some examples.  Researchers: Alberto Castaño, …

Hodge ideals of free divisors Leer más »