( Photo by Jacopo )                                                 

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Publications 

My Springer LNPM: An Introduction to Noncommutative Spaces and their Geometries, Springer 1997;  Online Second Edition 2002
(send me an e-mail for a free electronic copy)

My arXived papers at arXiv

A sub-collection of my papers as listed at inSPIRE

My coworkers

Current research activity

( noncommutative ) differential topology and geometry ... and ... their uses in mathematical physics

Main lines of research:
noncommutative manifolds (construction of metric and spin structures, vector and principal bundles),
harmonic analysis on noncommutative manifolds (Dirac and Laplace operators, index theorems),
noncommutative gauge theories (duality equations, constructions of solutions, study of moduli spaces),
Hopf algebras and quantum groups (as noncommutative manifolds, their use as generalized symmetries),

...  ...


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PhD Students

Jacopo Zanchettin : Algebraic Structures in Noncommutative Geometry
(SISSA-Trieste, January 2024)

Daan van de Weem : Noncommutative geometry, symmetry and real division algebras
(SISSA-Trieste, May 2022)

Xiao Han : Quantum principal bundles, gauge groupoids and coherent Hopf 2-algebras
(SISSA-Trieste, September 2020)

Francesca Arici : Principal circle bundles, Pimsner algebras and Gysin sequences
(SISSA-Trieste, September 2015)

Lucio Cirio : Symmetries of noncommutative spaces and equivariant cohomology
(SISSA-Trieste, October 2008)

Francesco D'Andrea : Noncommutative geometry and quantum group symmetries
(SISSA-Trieste, October 2007)

Chiara Pagani : Quantum principal bundles and instantons
(SISSA-Trieste, November 2005)

Walter D. van Suijlekom : The geometry of noncommutative spheres and their symmetries
(SISSA-Trieste, October 2005)

Pasquale Siniscalco : A finite quantum symmetry from A(SLq(2)) at a cubic root of unity
(SISSA-Trieste, November 1997)


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Current Editorial Work

Journal of Geometry and Physics ( Editor in Chief )

Journal of Noncommutative Geometry ( Founding Editor )

Letters in Mathematical Physics ( Editor )

Symmetry, Integrability and Geometry: Methods and Applicazions ( Member of the Editorial Board )

Rendiconti dell'Istituto di Matematica dell'Universita` di Trieste ( Member of the Editorial Board )



Quondam Editorial Work

Journal of Geometry and Physics (Editor; January 2010 - December 2017)

International Journal of Geometric Methods in Modern Physics (Founding Editor, Member of the Editorial Board; September 2003 - September 2013)

Advances in Mathematical Physics (Founding Editor, Member of the Editorial Board; June 2008 - December 2013)



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Teaching/Didattica
 

A Springer ULNP: Linear Algebra and Analytic Geometry for Physical Sciences, Springer 2018


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Ricevimento studenti: sempre (per appuntamento)   e-mail


Corsi:

a.a. 2024-2025:
 
Meccanica Analitica (secondo semestre LT matematica): tutte le informazioni sono qui 

Advanced Mathematical Physics 1 - mod B (second semester LM matematica): all the info are here



a.a. 2015/16 ---- a.a. 2023/24:

Meccanica Analitica (secondo semestre LT matematica)
Fisica Matematica 1 (secondo semestre LM matematica)

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