Marco Macchia

My research is currently developing in two directions:

• I am interested in the study of bounding techniques for the non-negative rank of matrices, in particular those coming from Information Theory and Discrete Mathematics.
• Moreover, along with S. Fiorini, I am studying the extension complexity of 2-level polytopes, also known in literature as compressed polytopes. We also developed an algorithm for the enumeration of their combinatorial types (available at github.com/ulb/tl).

In 2013-2014, in my Master's thesis I studied discrete and computational topology: I dealt with the problem of deciding whether it is always possible to reach an optimal discrete Morse vector executing elementary collapses in a greedy fashion over a finite simplicial complex (algorithm due to B. Benedetti and F. Lutz).

• Recognizing Cartesian products of matrices and polytopes,
  with Manuel Aprile, Michele Conforti, Yuri Faenza, Samuel Fiorini, Tony Huynh.
  to appear, 18^th Cologne-Twente Workshop on Graphs and Combinatorial Optimization (2020).
  Preprint available at [arxiv:2002.02264].
• Bounds on the number of 2-level polytopes, cones and configurations,
  with Samuel Fiorini, Kanstantsin Pashkovich.
  to appear, Discrete & Computational Geometry (2020)
  Preprint available at [arxiv:1806.06011].
• Lower Bound Computations for the Nonnegative Rank,
  with Krystal Guo, Samuel Fiorini, Matthias Walter.
  17^th Cologne-Twente Workshop on Graphs and Combinatorial Optimization, extended abstract (2019).
• Enumeration of 2-level polytopes, [new data]
  with Adam Bohn, Yuri Faenza, Samuel Fiorini, Vissarion Fisikopoulos, Kanstantsin Pashkovich.
  Journal version, Mathematical Programming Computations, preprint (2019) available at [arxiv:1703.01943].
• Extension complexity of the correlation polytope,
  with Pierre Aboulker, Samuel Fiorini, Tony Huynh, Johanna Seif.
  Operations Research Letters, preprint (2019) available at [arxiv:1806.00541].
• The biclique covering number of grids,
  with Krystal Guo, Tony Huynh.
  Electronic Journal of Combinatorics (2019)
  Preprint available at [arxiv:1811.03396].
• Extension complexity of stable set polytopes of bipartite graphs,
  with Manuel Aprile, Yuri Faenza, Samuel Fiorini, Tony Huynh.
  Proceedings of 43^rd International Workshop on Graph-Theoretic Concepts in CS (2017), available at [arxiv:1702.08741].
• Two-level Polytopes with a Prescribed Facet, [data]
  with Samuel Fiorini, Vissarion Fisikopoulos.
  Proceedings of the 4^th International Symposium on Combinatorial Optimization, ISCO 2016, Vietri sul Mare, Italy.
• Enumeration of 2-level polytopes
  with Adam Bohn, Yuri Faenza, Samuel Fiorini, Vissarion Fisikopoulos, Kanstantsin Pashkovich.
  Proceedings of the European Symposium on Algorithms, ESA 2015, Patras, Greece.

• Two level polytopes: geometry and optimization [pdf],
  Advisor: Prof. Samuel Fiorini (Université libre de Bruxelles)

• Teoria di Morse discreta (Discrete Morse Theory),
  Advisors: Prof. Bruno Benedetti (University of Miami), Prof. Giulia Dileo (Università degli Studi di Bari).

• Proprietà omotopiche dei fibrati vettoriali reali e complessi (Homotopic properties of real and complex vector bundles),
  Advisor: Prof. Dr. Anna Maria Pastore (Università degli Studi di Bari).