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 …
Abstract: Our research in this topic can be divided in two related lines. First, the right-angled Artin groups, which are defined by means of a graph, offer a natural bridge between Graph Theory and Algebra. Usually, the graph-theoretic properties are easy to translate in terms of group-theoretic features, but it is very difficult to walk …
Graphs, right-angled Artin groups and cryptography Leer más »
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 …
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 …
Khovanov spectrum of periodic links admits a homology group action Leer más »
Abstract: Given a link diagram, we construct a graph in such a way that the cohomology of its independence simplicial complex equals the extreme Khovanov homology of the link. As stressed by M. Khovanov, this is the first known relation between the cohomology of independence complexes and Khovanov homology. Researchers: J. González-Meneses, Marithania Silvero, P.M. …
Abstract: In 1983 Louis Kauffman conjectured that the classes of alternative and pseudoalternating links are identical. We proved that Kauffman Conjecture holds for those links whose first Betti number is at most 2. However, it is not true in general when this value increases, as we also proved by finding two counterexamples: a link and …
Abstract: The (Diophantine) Frobenius problem is a well-known NP-hard problem (also called the stamp problem or the chicken nugget problem) whose origins lie in the realm of combinatorial number theory. In the first paper we present an algorithm which solves it, via a translation into a QUBO problem of the so-called Apéry set of a numerical …
Quantum vs Classical Complexity in Numerical Semigroups Leer más »
Abstract: In a series of papers, joint with Nicholas M. Katz (Princeton U.) and Pham H. Tiep (Rutgers U.) we realize some of the sporadic simple groups as monodromy groups of parametric families of exponential sums: that is, these sums follow the same distributions as the traces of the elements of these sporadic groups on …
Realization of sporadic finite simple groups via families of exponential sums Leer más »
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
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, …
