Research

Published papers

• Computing Higher Leray–Serre Spectral Sequences of Towers of Fibrations
  A. Guidolin, A. Romero
  To appear in Foundations of Computational Mathematics.
• Effective homological computations on finite topological spaces
  J. Cuevas-Rozo, L. Lambán, A. Romero, H. Sarria
  To appear in Applicable Algebra in Engineering, Communications and Computing.
• Computing invariants for multipersistence via spectral systems and effective homology
  A. Guidolin, J. Divasón, A. Romero, F. Vaccarino
  To appear in Journal of Symbolic Computation 104 (2021) 724–753.
• A new Kenzo module for computing the Eilenberg-Moore spectral sequence
  A. Romero, J. Rubio, F. Sergeraert, M. Szymik
  ACM Communications in Computer Algebra 54(2) (2020) 57–60.
• Computing multipersistence by means of spectral systems
  A. Guidolin, A. Romero, J. Divasón, F. Vaccarino
  Proceedings of ISSAC 2019, ACM (2019) 195–202.
• A Kenzo interface for algebraic topology computations in Sagemath
  J. Cuevas-Rozo, J. Divasón, M. Marco-Buzunáriz, A. Romero
  ACM Communications in Computer Algebra 53(2) (2019) 61–64.
• Using Krakatoa for Teaching Formal Verification of Java Programs
  J. Divasón, A. Romero
  Lecture Notes in Computer Science 11758 (2019) 37–51.
• An implementation of effective homotopy of fibrations
  A. Romero, J. Rubio, F. Sergeraert
  Journal of Symbolic Computation 94 (2019) 149–172.
• Effective computation of generalized spectral sequences
  A. Guidolin, A. Romero
  Proceedings of ISSAC 2018, ACM (2018) 183-190.
• A Bousfield–Kan Algorithm for Computing the Effective Homotopy of a Space
  A. Romero, F. Sergeraert
  Foundations of Computational Mathematics 17 (2017) 1335-1366.
• Effective homology of filtered digital images
  A. Romero, J. Rubio, F. Sergeraert.
  Pattern Recognition Letters 83 (2016) 23-31.
• SynapCountJ: A Tool for Analyzing Synaptic Densities in Neurons
  G. Mata, J. Heras, M. Morales, A. Romero, J. Rubio
  BIOIMAGING 2016: 25-31
• A Combinatorial Tool for Computing the Effective Homotopy of Iterated Loop Spaces
  A. Romero, F. Sergeraert
  Discrete and Computational Geometry 53 (2015) 1-15.
• Zigzag persistent homology for processing neuronal images
  G. Mata, M. Morales, A. Romero, J. Rubio
  Pattern Recognition Letters 62 (2015) 55-60.
• Verifying a platform for digital imaging: a multi-tool strategy
  J. Heras, G. Mata, A. Romero, J. Rubio, R. Sáenz
  Lecture Notes in Computer Science 7961 (2013) 66-81.
• Homotopy groups of suspended classifying spaces: an experimental approach
  A. Romero, J. Rubio
  Mathematics of computation 82 (2013) 2237-2244.
• Effective homotopy of fibrations
  A. Romero, F. Sergeraert
  Applicable Algebra in Engineering, Communication and Computing 23 (2012) 85-100.
• Computing the homology of groups: The geometric way
  A. Romero, J. Rubio
  Journal of Symbolic Computation 47 (2012) 752-770.
• Programming before Theorizing, a case study
  A. Romero, F. Sergeraert
  Proceedings of ISSAC 2012, ACM (2012) 289-296.
• Integrating multiple sources to answer questions in Algebraic Topology
  J. Heras, V. Pascual, A. Romero, J. Rubio
  Lecture Notes in Artificial Inteligence 6167 (2010) 331-335.
• Computing the first Stages of the Bousfield-Kan Spectral Sequence
  A. Romero
  Applicable Algebra in Engineering, Communication and Computing 21 nº 3 (2010) 227-248.
• Interoperating between Computer Algebra systems: computing homology of groups with Kenzo and GAP
  A. Romero, G. Ellis, J. Rubio
  Proceedings of ISSAC 2009, ACM (2009) 303-310.
• Computing Spectral Sequences
  A. Romero, J. Rubio, F. Sergeraert
  Journal of Symbolic Computation 41 nº 10 (2006) 1059-1079.
• Remote access to a Symbolic Computation system for Algebraic Topology: a client-server approach
  M. Andrés, V. Pascual, A. Romero, J. Rubio
  Lecture Notes in Computer Science 3516 (2005) 635-642.

Preprints

• Defining and computing persistent Z-homology in the general case
  A. Romero, J. Heras, J. Rubio, F. Sergeraert
  http://arxiv.org/abs/1403.7086
• Discrete Vector Fields and Fundamental Algebraic Topology
  A. Romero, F. Sergeraert
  http://arxiv.org/abs/1005.5685
• Effective homotopy in a Kan fibration
  A. Romero, F. Sergeraert
  Preprint.
• Effective homotopy of the fiber of a Kan fibration
  A. Romero, F. Sergeraert
  Preprint.