A first research interest regards the topology and geometry of
3-manifolds, together with the study of the associated groups and
polynomials, such as the Kazhdan-Luzstig polynomials. The study is
developed through the analysis of different representation methods,
such as the Heegaard diagrams, the polyhedral schemes and the cyclic
branched coverings on knots or links.

In the last years my research focused on Mathematics Education,
especially about the integration of technology in teaching Mathematics
at university level. The main topics of research are the
individualization of teaching and learning at tertiary level of
instruction, the scaffolding strategies in digital environments and
the handling of multiple representation of mathematical objects,
together with the connection between semiotic representations and
meanings.

Another research topic regards Epistemology of Mathematics and the
mathematical contaminations in literature and art.

A. I. Telloni, On the groups of some fibered spaces, J. Group Theory 12 (6) (2009), 883-894.

A. Cavicchioli, F. Spaggiari, A. I. Telloni, Topology of compact space forms from Platonic solids. I, Topology and its Applications 156 (2009), 812-822.

A. I. Telloni, G. Williams, Smith forms of circulant polynomial matrices, Linear Algebra and its Applications, 458 (2014), 559-572.

A. I. Telloni, Special matchings calculate parabolic Kazhdan-Luzstig polynomials for the Universal Coxeter groups, Journ. of Algebra, 465 (2016), 21-40.

A. Cusi, A. I. Telloni, The role of formative assessment to fostering individualized teaching at university level, in corso di pubblicazione.