Francesco Matucci 

Centro de Álgebra da Universidade de Lisboa
Instituto para a Investigação Interdisciplinar da Universidade de Lisboa
Avenida Professor Gama Pinto 2
1649-003 Lisbon, Portugal
Phone: +351 21 79 04 713

E-mail: francesco.matucci (at)

I am a Fundação para a Ciência e a Tecnologia postdoctoral research fellow at the Centro de Álgebra of the Universidade de Lisboa. Before arriving here, I was at Cornell, CRM Barcelona, Virginia and Paris Sud 11.

I am interested in questions of asymptotic, combinatorial and geometric group theory: decision problems, finiteness properties, subgroup classification, growth and dynamics in groups, and dynamics in groups, such as piecewise-linear homeomorphism groups, Thompson groups, groups of diagrams, free groups, Baumslag-Solitar groups, surface groups, lamplighter groups, nilpotent groups and finite groups.


Research papers

  1. Intersection growth in metabelian groups,
    with I.Biringer, K.Bou-Rabee, M.Kassabov, in progress
  2. Dynamics and centralizers in the higher dimensional Thompson's group 2V,
    with J. Belk, C.Martinez-Perez, B.Nucinkis, in progress
  3. Intersection growth in nilpotent groups,
    with I.Biringer, K.Bou-Rabee, M.Kassabov, in preparation
  4. Rover's Simple Group is of Type F_\infty,
    with J.Belk, preprint (abstract, arXiv)
  5. Embeddings into Thompson's group V and coCF groups,
    with C.Bleak, M.Neunhoffer, submitted (abstract, arXiv)
  6. Cohomological finiteness conditions and centralisers in generalisations of Thompson's group,
    with C.Martinez-Perez, B.Nucinkis, submitted (abstract, arXiv)
  7. On groups with slow intersection growth,
    with M.Kassabov, to appear in Proceedings of the Edinburgh Mathematical Society (abstract, arXiv)
  8. Intersection growth in groups,
    with I.Biringer, K.Bou-Rabee, M.Kassabov, to appear in Transactions of the American Mathematical Society (abstract, arXiv)
  9. The Conjugacy Problem in Extensions of Thompson's group F,
    with J.Burillo, E.Ventura, to appear in Israel Journal of Mathematics (abstract, arXiv)
  10. Conjugacy and Dynamics in Thompson's groups,
    with J.Belk, Geometriae Dedicata 169, No. 1 (2014) 239-261 (abstract, arXiv)
  11. Deciding Conjugacy in Thompson's Group F in Linear Time,
    with J. Belk, N. Hossain, R. McGrail, 2013 15th International Symposium on International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, 89-96 (abstract, paper, slides, proceedings website)
  12. Centralizers in R.Thompson’s group V_n,
    with C.Bleak, H.Bowman, A.Gordon, G.Graham, J.Hughes, J.Sapir, Groups, Geometry and Dynamics 7, No. 4 (2013), 821-865 (abstract, arXiv)
  13. Presentations for the Higher Dimensional Thompson's groups nV,
    with J.Hennig, Pacific Journal of Mathematics 257, No. 1 (2012) 53--74 (abstract, arXiv)
  14. The Simultaneous Conjugacy Problem in Groups of Piecewise Linear Functions,
    with M.Kassabov, Groups, Geometry and Dynamics 6, No. 2 (2012) 279--315 (abstract, arXiv)
  15. Structure Theorems for Subgroups of Homeomorphisms Groups,
    with C.Bleak, M.Kassabov, International Journal of Algebra and Computation 21, no. 6 (2011), 1007--1036, (abstract, arXiv)
  16. Bounding the residual finiteness of free groups,
    with M.Kassabov, Proceedings of the American Mathematical Society 139 (2011), no. 7, 2281--2286 (abstract, arXiv)
  17. Mather invariant in groups of piecewise-linear homeomorphisms,
    Trends in Mathematics, Combinatorial and Geometric Group Theory (2010) 251--260 (abstract, arXiv)
  18. Finite solvable groups whose Quillen complex is Cohen-Macaulay,
    Journal of Algebra 322 (2009) 969--982 (abstract, arXiv)
  19. Cryptanalysis of the Shpilrain-Ushakov Protocol in Thompson's Group,
    Journal of Cryptology, 21(3) (2008) 458--468 (abstract, arXiv)

PhD thesis

  1. Algorithms and Classification in Groups of Piecewise-Linear Homeomorphisms,
    PhD Thesis, Cornell University, 2008, Advisors: Ken Brown and Martin Kassabov (abstract, arXiv)

Selected Talks