arXiv subjects

Ángel González-Prieto

Publications and source records attributed to Ángel González-Prieto.

41 records · Page 3Linked to original sources

arXiv2020

DeepFair: Deep Learning for Improving Fairness in Recommender Systems

The lack of bias management in Recommender Systems leads to minority groups receiving unfair recommendations. Moreover, the trade-off between equity and precision makes it difficult to obtain recommendations that meet both criteria. Here we propose a Deep Learning based Collaborative Filtering algorithm that provides recommendations with an optimum balance between fairness and accuracy without knowing demographic information about the users. Experimental results show that it is possible to make fair recommendations without losing a significant proportion of accuracy.

cs.LG↗

arXiv2020

Virtual classes of parabolic $\mathrm{SL}_2(\mathbb{C})$-character varieties

In this paper, we compute the virtual classes in the Grothendieck ring of algebraic varieties of $\mathrm{SL}_2(\mathbb{C})$-character varieties over compact orientable surfaces with parabolic points of semi-simple type. When the parabolic punctures are chosen to be semi-simple non-generic, we show that a new interaction phenomenon appears generating a recursive pattern.

math.AG↗

arXiv2019

Motivic theory of representation varieties via Topological Quantum Field Theories

In this paper, we use lax monoidal TQFTs as an effective computational method for motivic classes of representation varieties. In particular, we perform the calculation for parabolic $\mathrm{SL}_2(\mathbb{C})$-representation varieties over a closed orientable surface of arbitrary genus and any number of marked points with holonomies of Jordan type. This technique is based on a building method of lax monoidal TQFTs of physical inspiration that generalizes the construction of González-Prieto, Logares and Muñoz.

math.AG↗

arXiv2018

Topological Quantum Field Theories for character varieties

This PhD Thesis is devoted to the study of Hodge structures on a special type of complex algebraic varieties, the so-called character varieties. For this purpose, we propose to use a powerful algebro-geometric tool coming from theoretical physics, known as Topological Quantum Field Theory (TQFT). With this idea in mind, in the present Thesis we develop a formalism that allows us to construct TQFTs from two simpler pieces of data: a field theory (geometric data) and a quantisation (algebraic data). As an application, we construct a TQFT computing Hodge structures on representation varieties and we use it for computing explicity the Deligne-Hodge polynomials of parabolic $\mathrm{SL}_2(\mathbb{C})$-character varieties.

math.AG↗

arXiv2018

A lax monoidal Topological Quantum Field Theory for representation varieties

We construct a lax monoidal Topological Quantum Field Theory that computes Deligne-Hodge polynomials of representation varieties of the fundamental group of any closed manifold into any complex algebraic group $G$. As byproduct, we obtain formulas for these polynomials in terms of homomorphisms between the space of mixed Hodge modules on $G$. The construction is developed in a categorical-theoretic framework allowing its application to other situations.

math.AG↗