Research

Research Interests

Our research activity focuses on design theory, graph decompositions and their symmetries, incidence geometry and embeddings, linear codes, Clifford parallelisms.

Keywords

  • Design theory

  • Graph decompositions and their symmetries

  • Incidence geometries and their embeddings

  • Error correcting codes

  • Clifford parallelisms

Major Research Topics

  • Design theory, graph decompositions and their symmetries. The research activity focuses on Design Theory and Graph Decompositions with potential applications to the design of statistical experiments, and in areas such as Coding Theory, Communications Systems and Software Testing. One of the primary objectives is constructing designs which have desirable properties with respect to concepts such as symmetries, colorings, resolutions, and studying generalizations such as packing and covering designs.

  • Incidence Geometry and correcting codes. This research activity is concerned with the study of Grassmannians of polar spaces and, more in general, incidence geometries in determining the possible ranks and dimensions and in describing their structure. This has applications both to the theory of Lie groups and to the study and construction on novel error correcting codes.

  • Clifford parallelisms. The research is aimed at studying parallelisms in 3-dimensional projective spaces. In particular the target of the investigation are the Clifford parallelism arising in projective spaces associated to quaternion algebras. We focus on the study of Clifford-like parallelism, namely parallelisms whose parallel classes are either left or right Clifford parallel classes, and of their groups of automorphisms.

Strategic collaborations

  • Angela Aguglia, Polytechnic of Bari, Italy

  • Rosemary Bayley, School of Mathematical Sciences, Queen Mary, University of London, London, UK

  • Simona Bonvicini, Department of Physics, Informatics and Mathematics, University of Modena and Reggio Emilia, Italy

  • Marta Bortoletto, IRCCS Istituto Centro San Giovanni di Dio Fatebenefratelli, Cognitive Neuroscience Section, Brescia, Italy

  • Marco Buratti, Department of Mathematics and Computer Science, University of Perugia, Italy

  • Andrea Burgess, Department of Mathematics and Statistics, University of New Brunswick, Saint John, NB, Canada

  • Haitao Cao, Nanjing Normal University, Nanjing, China

  • Stefano Capparelli, Department of Basic and Applied Sciences for Engineering, Sapienza University of Rome, Italy

  • Ilaria Cardinali, University of Siena, Italy

  • Yanxun Chang, Department of Mathematics, Beijing Jiaotong University, Beijing, China

  • Marco Dalai, DII, University of Brescia, Italy.

  • Peter Danziger, Department of Mathematics, Ryerson University, Toronto, ON, Canada

  • Stefano della Fiore, DII, University of Brescia, Italy

  • Tao Feng, Department of Mathematics, Beijing Jiaotong University, Beijing, China

  • Martino Garonzi, Departamento de Matemática, Campus Universitário Darcy Ribeiro, Brasil

  • Masaaki Homma, Kanagawa University, Japan

  • Graham J. Lovegrove, Department of Mathematics and Statistics, The Open University, UK

  • Guglielmo Lunardon, University of Naples, Italy

  • Eric Mendelsohn, Department of 6Mathematics, University of Toronto, Toronto, ON, Canada

  • Francesca Merola, Department of Mathematics and Physics, Roma Tre University, Italy

  • Carlo Miniussi, University of Trento, Center for Mind/Brain Sciences – CIMeC, Rovereto, Italy.

  • Koji Momihara, Faculty of Advanced Science and Technology, Kumamoto University, Japan

  • Fiorenza Morini, Department of Mathematical, Physical and and Computer Sciences, University of Parma, Italy

  • Matt Ollis, Marlboro Institute for Liberal Arts and Interdisciplinary Studies, Emerson College, Boston, USA

  • Antonio Pasini, University of Siena, Italy

  • ‪Adrián Pastine‬, Departamento de Matemática, Universidad Nacional de San Luis, Argentina

  • Marco A. Pellegrini, Department of Mathematics and Physics, Università Cattolica, Brescia, Italy

  • Gloria Rinaldi, Department of Sciences and Methods for Engineering, University of Modena and Reggio Emilia, Italy

  • John R. Schmitt, Mathematics Department, Middlebury College, Middlebury, USA

  • Brett Stevens, School of Mathematics and Statistics, Carleton University, Ottawa, ON, Canada

  • Xiaomiao Wang, Department of Mathematics, Ningbo University, Ningbo, China

  • Dianhua Wu, Guangxi Normal University, Guilin, China

  • Agnese Zazio, IRCCS Istituto Centro San Giovanni di Dio Fatebenefratelli, Cognitive Neuroscience Section, Brescia, Italy