You are here: Home » PEOPLE » Paola Cristofori

Paola Cristofori

Associate Professor in Geometry
Department of Physics, Computer Science and Mathematics
University of Modena and Reggio Emilia
Via Campi 213/b I-41125 Modena - Italy
Phone: +39-0592055189
E-mail: paola.cristofori (at)

Geometric topology of low dimensional manifolds, representations of PL-manifolds by edge-colored graphs (Graph Encoding Manifolds), applications of GEMs to the theory of random tensor models, knot theory.

August 5, 1994.   PhD in Mathematics, dissertation: “Rappresentazioni di varieta` ed insiemi universali di ramificazione” (Representations of manifolds and universal branching sets) , supervisor: Prof. L. Grasselli.
October 1991-December 1992.   Visiting PhD student at the Universidad Complutense and UNED of Madrid (Spain).
March 1990-October 1993.   PhD student at the University of Florence.
November 1989-February 1990.   Istituto Nazionale di Alta Matematica (INDAM) scholarship.
November 15, 1988.   Degree in Mathematics cum laude from the University of Ferrara; dissertation: “Algoritmi di semplificazione per triangolazioni di varieta` lineari a tratti“ (Simplification algorithms for triangulations of PL manifolds), supervised by Prof. C. Gagliardi.

You can download a detailed CV here

Conferences and talks since 2000:

  • 6/07/2023: 2023 International Conference on Topology and its Applications - Nafpaktos  (Greece), Gem-induced trisections of PL 4-manifolds.
  • 3/06/2022: Combinatorics 2022 - Mantova, From Kirby diagrams to edge-colored graphs representing PL 4-manifolds.
  • 20-26/06/2021: 8th European Congress of Mathematics - Minisymposium “Applied Combinatorial and Geometric Topology”, Crystallizations of compact 4-manifolds minimizing combinatorially defined PL-invariants (see slides here).
  • 3/06/2020: Séminaire Tensor Journal Club (online), Crystallizations of compact 4-manifolds minimizing combinatorially defined PL-invariants.
  • 5-9/11/2018: Nagoya workshop on Physics and Mathematics of Discrete Geometries, Nagoya University. Topological aspects of colored tensor models (see slides here)
  • 17-20/09/2018: Joint Meeting UMI-SIMAI-PTM, Wroclaw, special session: Computational Aspects of Applied Topology. Talk (invited): Topological aspects of Colored Tensor Models in Quantum Gravity.
  • 30/01-03/02/2017: Congreso Bienal de la Real Sociedad Matemática Española, Sesión Especial: Topología Geométrica, Saragozza, Topology in colored tensor models via crystallization theory.
  • 17-21/10/2016: 2nd French-Russian Conference “Random Geometry and Physics”, Paris, Institut Henri Poincarè, Representing PL-manifolds by edge-colored graphs: basic concepts and recent results  (see slides here).
  • 14-15/01/2016: Workshop “Colored Graphs and Random Tensors” - LPT Orsay; Complexity notions on colored graphs and Crystallization theory: extensions to the singular and boundary case
  • 7-12/09/2015: XX Convegno U.M.I. - Siena, Classificazione di 4-varietà PL tramite genere regolare e gem-complessità.
  • 9-15/09/2012: Combinatorics 2012 - Perugia, Colored graphs representing PL 4-manifolds.
  • 12-17/09/2011: XIX Convegno U.M.I. - Bologna, Stime della complessità di Matveev di una 3-varietà: diagrammi di Heegaard generalizzati e grafi colorati.
  • 8-13/09/2003: XVII Convegno U.M.I. - Milano, Una generalizzazione delle varietà di Dunwoody.
  • 28/11/2001: Department of Mathematics Ecole Polytechnique Fédérale de Lausanne, Representing manifolds by crystallization theory.


  • 2020-present: Algebraic Topology (Bachelor degree in Mathematics), Geometric Topology of Manifolds (Master degree in Mathematics)
  • 2007-present: Geometry and Linear Algebra (Bachelor degree in Civil and Environmental Engineering)
  • 2017-2018: Geometry (Bachelor degree in Physics)
  • 2000-2013: Geometry A, Geometry B (Bachelor degree in Mathematics)

Most recent publications and preprints

  • P. Cristofori – E. Fominykh – M. Mulazzani – V. Tarkaev, 4-colored graphs and knot/link complements, Results in Math. 72 (2017), 471-490.
  • A.F. Costa, - P. Cristofori – A.M. Porto, The double of the doubles of Klein surfaces, Rev. Mat. Iberoamericana 33 (2017), 183-194.
  • P. Cristofori – E. Fominykh – M. Mulazzani – V. Tarkaev, Minimal 4-colored graphs representing an infinite family of hyperbolic 3-manifolds, RACSAM 112 (2018) 781-792. 
  • M.R. Casali – P. Cristofori – L. Grasselli, G-degree for singular manifolds, RACSAM 112(3) (2018), 693-704.   
  • M.R. Casali - P. Cristofori - S. Dartois - L. Grasselli, Topology in colored tensor models  via crystallization theory, J. Geom. Phys., 129 (2018), 142-167. 
  • M.R. Casali – P. Cristofori – C. Gagliardi, Crystallizations of compact 4-manifolds minimizing combinatorially defined PL-invariants, Rend. Istit. Mat. Univ. Trieste 52 (2020), 431-458.
  • M.R. Casali – P. Cristofori, Compact 4-manifolds admitting special handle-decompositions, RACSAM 115, 118 (2021).  
  • M.R. Casali – P. Cristofori, Classifying compact 4-manifolds via generalized regular genus and G-degree, Ann. Inst. Henri Poincarè D - Combinatorics, Physics and their interactions, vol. 10  (2023), p. 121-158.
  • M.R. Casali – P. Cristofori, Kirby diagrams and 5-colored graphs representing compact 4-manifolds, Revista Matemática Complutense, vol. 36 (2023), p. 899-931.
  • M.R. Casali – P. Cristofori, Gem-induced trisections of compact PL 4-manifolds, to appear in Forum Math., arXiv:1910.08777.