Phone
E-mail para@mat.uab.cat
Position Professor
Research interests Algebraic Geometry
Area Algebra, Geometry, Number Theory and Topology
Ara, Pere
Biosketch

I have developed my scientific career at the Department of Mathematics of the Universitat Autònoma de Barcelona. I have enjoyed several research stays, including a 3-months stay at the Pure Mathematics Research Centre of Queen’s University Belfast (2008), and a 3-months stay at the Department of Mathematics of the University of California at Santa Barbara (2009). I have worked on several problems in the theory of non-commutative rings and in operator algebras. I have written two research books (one jointly with Martin Mathieu, and the other jointly with Gene Abrams and Mercedes Siles Molina), and more than 100 research papers.

Projects

Anillos, módulos, C*-álgebras, y dinámica: clasificación, estructura fina y regularidad, 
Ara Bertran, P., Bosa Puigredon, J., Cantier, L. N., Claramunt Carós, J., Antoine Riolobos, R., Cedo Gine, F., Herbera Espinal, M. D., Pardo Espino, E.  Perera Domenech, Ministerio de Economia y Competitividad (MINECO)

Estructura y clasificación de anillos, módulos y c*-algebras: interacciones con dinámica, combinatoria y topología
Ara Bertran, P., Bosa Puigredon, J., Cantier, L. N., Claramunt Carós, J., Dicks Mclay, W., Jespers, E. F., Okninski, J., Sánchez Serdà, J., Antoine Riolobos, R., Cedo Gine, F., Herbera Espinal, M. D., Pardo Espino, E. & Perera Domenech, F. Ministerio de Economia y Competitividad (MINECO)

Selected publications
  • Pere Ara, Joan Bosa, Enrique Pardo, Aidan Sims, The groupoids of adaptable separated graphs and their type semigroups, International Mathematics Research Notices IMRN 2021, no. 20, 15444–15496
  • Pere Ara, Matias Lolk, Convex subshifts, separated Bratteli diagrams, and ideal structure of tame separated graph algebras, Advances in Mathematics, 328 (2018), 367-435.
  • P. Ara, K. R. Goodearl, The realization problem for von Neumann regular rings and the Atiyah problem, Transactions of the American Mathematical Society, 369 (2017), 5665-5710.
  • Ara, R. Exel, Dynamical systems associated to separated graphs, graph algebras, and paradoxical decompositions, Advances in Mathematics 252 (2014), 748-804.
  • Ara, K. R. Goodearl, Leavitt path algebras of separated graphs, Journal für die reine und angewandte Mathematik, 669 (2012), 165-224.
  • Ara, K. R. Goodearl, C*-algebras of separated graphs, Journal of Functional Analysis, 261 (2011), 2540-2568.
  • Ara and M. Mathieu, A not so simple local multiplier algebra, Journal of Functional Analysis, 237 (2006), 721-737.
  • Ara, K. C. O’Meara and F. Perera, Stable finiteness of group rings in arbitrary characteristic, Advances in Mathematics, 170 (2002), 224-238