TOMASSINI Adriano
 Curriculum Vitae
 Teaching
 Appointments
 Research
General news
 Born: 01/28/1969, Rome.
 bachelor degree in Mathematics, italian Dottore in Matematica, received on 06/19/1992 by Università di Firenze.
 PhD in Mathematics received by Università di Firenze, July 1997, under the advice of Prof. Paolo de Bartolomeis.
 12/30/1996 – 10/31/2002: Assistant Professor, italian Ricercatore universitario SSD GEOMETRIA, Università di Palermo and Parma.
 November 2002 – June 2011: Associate Professor, italian Professore Associato, Facoltà di Scienze Università di Parma, SSD MAT03/GEOMETRIA.
 Current position: Full Professor, italian Professore Ordinario SSD MAT03/GEOMETRIA, Università di Parma (since 06/30/2014).
 He spent research periods and has been visiting professor at University of Michigan, University of Minnesota, University of Notre Dame, Florida International University, Université de Bourgogne, Ruhr Universität, University of Edinburgh, University of Pais Vasco, Stanford, University of Zaragoza, Centre International de Rencontres Mathématiques, Luminy, where he gave talks.
 He attended and was invited to give talks at international scientific meetings held in: Pisa at Centro de Giorgi, Firenze, Perugia, Trento, Kuehlungsborn, Tenerife, Les Rasses Sainte Croix, Bordeaux, Castro Urdiales, Torino, Benasque, Fribourg, Bucharest, Trieste, Bedlewo, Trondheim, Parigi.
 He gave talks at Universities of Milano Bicocca, Piemonte Orientale, Bologna, Firenze, Roma II, Perugia, Potenza, Palermo.
 Local coordinator of the Research Unit in Parma, Project PRIN: "Varieta' reali e complesse: geometria, topologia e analisi armonica", Scientific coordinator Prof. Fulvio Ricci.
 Member of Collegio dei Docenti of PhD Program in Mathematics at the Universities of Pavia, MilanoBicocca and INdAM.
 He has been Presidente del Corso di Laurea triennale in Matematica, starting from December 2012 to December 2013.
 He has been chairman of the Dipartimento di Matematica e Informatica dell'Università di Parma, starting from December 2013 to December 2016.
 He takes part of the Committee of Abilitazione Scientifica Nazionale, Settore Concorsuale 01/A2 Geometria e Algebra.
 He is the editorinchief of Rivista di Matematica della Università di Parma, since January 2009.
 He is the chairman of Scuola Matematica Interuniversitaria, since January 2018.
 He has been referee for Duke Math. J., Intern. Math. Res. Notices, J. Geom. and Phys., Adv. In Geom., Ann. Mat. Pura Appl., Ann. SNS, J. Geom Anal., Proc. AMS., Inventiones Math., Ann. Inst. Fourier., Math. Z., Quarterly J. Math, Comm. Anal. Geom., Math. Annalen, Compositio Mathematica, Math. Z..
 Advisor of the PhD theses of:
Daniele Angella, Universita' di Pisa.
Giulio Catellani, Universita' di Firenze.
Federico Alberto Rossi, Universita' di MilanoBicocca.
Michele Maschio, Universita' di Parma.
Nicoletta Tardini, Universita' di Pisa.
Research activity
A.T.’s research activity focuses mainly on two topics, both related to analytic and geometric properties of manifolds endowed with special structures.
The first one deals with the existence problem for special structures on (almost) complex and symplectic manifolds. In particular, he investigates on compact 2ndimensional symplectic manifolds, endowed with a tamed almost complex structure and a dbar closed nowhere vanishing (n,0)form of constant length. These manifolds provide a possible generalization to the non holomorphic case of the notion of CalabiYau manifolds. In (de Bartolomeis, T., Ann. Inst. Fourier (Grenoble) 2006, de Bartolomeis, T., Internat. J. Math. 2006, Conti, A.T., Q. J. Math 2007), the geometry of such manifolds is studied, when the almost compex structure is compatible with the symplectic form: then the notion of special Lagrangian submanifold is introduced, showing that the Maslov class of a special Lagrangian submanifold vanishes and several examples of these structures on non Kähler solvmanifolds are given.
The TianTodorov Theorem states that the moduli space of CalabiYau is totally unobstructed: in (de Bartolomeis, T., Ann. Inst. Fourier (Grenoble) 2013), an appropriated moduli space of almost complex deformations of a CalabiYau manifold is defined and it is proved that, under a suitable cohomological assumption, it is totally unobstructed too.
Generalized geometries have been introduced by (Hitchin, Q. J. Math 2003) and then studied by (Gualtieri, Ann. Math. 2011) in the case of generalized complex and Kähler structures and by (Witt, Comm. Math. Phys. 2006) in the case of generalized G_2 structures on 7dimensional manifolds. In (Fino, T., J. Symplectic Geom. 2009) we construct a family of non Kähler solvmanifolds carrying a generalized Kähler structure, in (Fino, T., Internat. J. Math. 2008) we study the connection between SU(3)structures on 6dimensional manifolds M and generalized G_2 structures on the product M times S^1 and we construct a family of generalized G_2 manifolds.
In (Fino, A.T., Adv. Math. 2009, Fino, T., J. London Math. Soc. (2) 2011) we study Hermitian metrics (on ndimensional complex manifolds and, more generally, on complex orbifolds) whose fundamental form (its (n2)power respectively) is ddbar closed. Such metrics have been studied by many authors, e.g., (Bismut, Math. Ann. 1989), (Gauduchon, C. R. Acad. Sci. Paris Sér. AB 1977), (Jost, Yau, Acta Math. 1993). By blowup procedures we obtain new examples of such structures on simplyconnected manifolds.
The second research theme deals with the study of cohomological properties of almost complex manifolds. The study of such a topic is motivated, from one hand, by the aim of generalizing cohomological decomposition in the non Kähler context, and, on the other hand, by the study of the connections between the tamed symplectic cone and the compatible symplectic cone
In this direction Donaldson conjectures that on a compact almost complex 4manifold the tamed symplectic cone is empty if and only if the compatible symplectic cone is empty.
Furthermore (Draghici, Li, Zhang, Internat. Math. Res. Notices, 2010) prove that on any compact almost complex 4manifold the second de Rham cohomology group decomposes as the direct sum of the subgroups formed by cohomology classes admitting invariant and antiinvariant representatives respectively, with respect to the natural action of the almost complex structure on the space of 2forms. This fact does not hold true in higher dimension as showed in (Fino, T., J. Geom. Anal. 2010), where the case of Lefschetz manifolds is treated.
In (Angella,T., J. Symplectic Geom. 2011) we show that, on a given complex manifold, the existence of such a cohomological decomposition is not stable under the deformation of the complex structure. In (Angella, A.T., Internat. J. Math. 2012) we extend the result by (Li, Zhang, Comm. Anal. Geom. 2009) in the context of the balanced and strongly Gauduchon metrics cones.
In [Angella, A.T., Zhang, Proc. AMS (2014)], the almostKähler case is considered. Analogue notions in the symplectic settings are studied in [Angella, T., J. Symplectic Geom. (2014)].
In (Hind, Medori, A.T., Proc. Amer. Math. Soc. 2014), on a compact almost complex manifold of dimension greater than four, under suitable topological assumptions, we show that, for a special 2cohomology class, there exists an almost complex structure with respect to which the 2class admits both invariant and antiinvariant representatives.
For further results on antiinvariant cohomology and L2cohomology see [Hind, Medori, T., J. Geom. Anal. 2015] and [Hind, T., 2017 arXiv:1708.06316].
Towards the aim to better understand complex nonKähler manifolds, we investigated BottChern and Aeppli cohomologies. The research in this direction has been developed, (and is still developing,) under several aspects. The relation between BottChern and Aeppli cohomologies and de Rham and Dolbeault cohomologies is investigated in [Angella, T., Invent. Math (2013)]. There, we proved an inequality à la Frölicher involving the dimensions of the BottChern cohomology and the Betti
numbers: the equality characterizes the validity of the $\partial\overline\partial$Lemma, a central property in Kähler geometry. A generalization in the generalizedcomplex setting, here included the symplectic case, is studied in [Angella, T., J. Noncommut. Geom. (2015)]. The results are applied and refined for compact complex surfaces in [Angella, Dloussky, T., Ann. Mat. Pura Appl. 2016]. In [Angella, Suwa, Tardini, T. arXiv:1712.08889] the behaviour of $\partial\overline\partial$Lemma under modifications of compact complex manifolds is investigated.
As an attempt to understand the algebraic structure of BottChern cohomology, we introduced a notion of geometric formality with respect to the BottChern cohomology. A first attempt is done in [Angella, T., J. Geom. Phys. (2015)], and continued in [Tardini, T., Internat. J. Math. (2014)], where the behaviour under small deformations of the complex structure is investigated. Furthermore, in [A.T., Torelli, Internat. J. Math. (2014)] we show the Dolbeault formality is not stable under small deformations of the complex structure and in [A. Cattaneo, T., J. Geom. Phys. (2015)] we study Dolbeault Massey products on complex manifolds. In the almostcomplex setting, subgroups of the de Rham cohomology are constructed in [Li, Zhang, Comm. Anal. Geom. (2009)], with the aim to provide a counterpart of Dolbeault cohomoloy. Such subgroups are investigated in [Angella, T. J. Symplectic Geom. (2011)], [Angella, T., Internat. J. Math. (2012)], also in connections with cones of special Hermitian metrics. In [Angella, T., Zhang, Proc. AMS (2014)], the almostKähler case is considered. Analogue notions in the symplectic settings are studied in [Angella, T., J. Symplectic Geom. (2014)]. In [Anthes, Cattaneo, Rollenske, T.] arXiv:1711.05107 [math.DG], to appear in Ann. Glob. Anal. Geom., deformations of complex symplectic manifolds, introduced in [Cattaneo, T., Ann. Mat. Pura ed Appl., 2017], have been studied.
MR Author ID: 362161
Earliest Indexed Publication: 1994
Total Publications: 63
Total Citations: 329
hindex: 11:
hindex SCOPUS: 12
Total citations: 434
hindex WOS: 11
Total citations: 372
Anno accademico di erogazione: 2020/2021
 Course year: 1  Second cycle degree  MATHEMATICS  A.Y.: 2020/2021
 Course year: 2  First cycle degree (DM 270)  MATHEMATICS  A.Y.: 2019/2020
 Course year: 3  First cycle degree (DM 270)  MATHEMATICS  A.Y.: 2018/2019
 Course year: 1  First cycle degree (DM 270)  BIOTECHNOLOGY  A.Y.: 2020/2021
Anno accademico di erogazione: 2019/2020
 Course year: 1  Second cycle degree  MATHEMATICS  A.Y.: 2019/2020
 Course year: 4  Full cicle (6 years)  Medicine and Surgery  A.Y.: 2016/2017
 Course year: 2  First cycle degree (DM 270)  MATHEMATICS  A.Y.: 2018/2019
 Course year: 3  First cycle degree (DM 270)  MATHEMATICS  A.Y.: 2017/2018
 Course year: 1  First cycle degree (DM 270)  BIOTECHNOLOGY  A.Y.: 2019/2020
Anno accademico di erogazione: 2018/2019
 Course year: 1  Second cycle degree  MATHEMATICS  A.Y.: 2018/2019
 Course year: 4  Full cicle (6 years)  Medicine and Surgery  A.Y.: 2015/2016
 Course year: 2  First cycle degree (DM 270)  MATHEMATICS  A.Y.: 2017/2018
 Course year: 3  First cycle degree (DM 270)  MATHEMATICS  A.Y.: 2016/2017
 Course year: 1  First cycle degree (DM 270)  BIOTECHNOLOGY  A.Y.: 2018/2019
Anno accademico di erogazione: 2017/2018
 Course year: 1  Second cycle degree  MATHEMATICS  A.Y.: 2017/2018
 Course year: 2  Full cicle (6 years)  Medicine and Surgery  A.Y.: 2016/2017
 Course year: 4  Full cicle (6 years)  Medicine and Surgery  A.Y.: 2014/2015
 Course year: 2  First cycle degree (DM 270)  MATHEMATICS  A.Y.: 2016/2017
 Course year: 3  First cycle degree (DM 270)  MATHEMATICS  A.Y.: 2015/2016
 Course year: 1  First cycle degree (DM 270)  Biotechnology  A.Y.: 2017/2018
 Course year: 1  Full cicle (6 years)  MEDICINE AND SURGERY  A.Y.: 2017/2018
Anno accademico di erogazione: 2016/2017
 Course year: 1  Full cicle (6 years)  Medicine and Surgery  A.Y.: 2016/2017
 Course year: 2  Full cicle (6 years)  Medicine and Surgery  A.Y.: 2015/2016
 Course year: 4  Full cicle (6 years)  Medicine and Surgery  A.Y.: 2013/2014
 Course year: 2  First cycle degree (DM 270)  MATHEMATICS  A.Y.: 2015/2016
 Course year: 2  First cycle degree (DM 270)  MATHEMATICS  A.Y.: 2015/2016
 Course year: 3  First cycle degree (DM 270)  MATHEMATICS  A.Y.: 2014/2015
 Course year: 1  First cycle degree (DM 270)  Biotechnology  A.Y.: 2016/2017
Anno accademico di erogazione: 2015/2016
 Course year: 1  Second cycle degree  MATHEMATICS  A.Y.: 2015/2016
 Course year: 2  First cycle degree (DM 270)  MATHEMATICS  A.Y.: 2014/2015
 Course year: 3  First cycle degree (DM 270)  MATHEMATICS  A.Y.: 2013/2014
Anno accademico di erogazione: 2014/2015
 Course year: 1  Second cycle degree  MATHEMATICS  A.Y.: 2014/2015
 Course year: 2  First cycle degree (DM 270)  MATHEMATICS  A.Y.: 2013/2014
Anno accademico di erogazione: 2013/2014
 Course year: 1  Second cycle degree  MATHEMATICS  A.Y.: 2013/2014

Direttore di Dipartimento (Dipartimento di Scienze Matematiche, Fisiche e Informatiche) from 01/01/2020 to 12/31/2023
Professor/Teacher
 Second cycle degree MATHEMATICS A.Y. 2020/2021
 Second cycle degree MATHEMATICS A.Y. 2019/2020
 Second cycle degree MATHEMATICS A.Y. 2018/2019
 Second cycle degree MATHEMATICS A.Y. 2017/2018
 First cycle degree (DM 270) MATHEMATICS A.Y. 2016/2017
 Second cycle degree MATHEMATICS A.Y. 2015/2016
 Second cycle degree MATHEMATICS A.Y. 2014/2015
Teacher tutor
 First cycle degree (DM 270) MATHEMATICS A.Y. 2020/2021
 Second cycle degree MATHEMATICS A.Y. 2020/2021
 First cycle degree (DM 270) MATHEMATICS A.Y. 2019/2020
 Second cycle degree MATHEMATICS A.Y. 2019/2020
 First cycle degree (DM 270) MATHEMATICS A.Y. 2018/2019
 Second cycle degree MATHEMATICS A.Y. 2018/2019
 Second cycle degree MATHEMATICS A.Y. 2017/2018
 First cycle degree (DM 270) MATHEMATICS A.Y. 2017/2018
 Second cycle degree MATHEMATICS A.Y. 2016/2017
 First cycle degree (DM 270) MATHEMATICS A.Y. 2016/2017
 First cycle degree (DM 270) MATHEMATICS A.Y. 2015/2016
 Second cycle degree MATHEMATICS A.Y. 2015/2016
 Second cycle degree MATHEMATICS A.Y. 2014/2015
 First cycle degree (DM 270) MATHEMATICS A.Y. 2014/2015
 First cycle degree (DM 270) MATHEMATICS A.Y. 2013/2014
 Second cycle degree MATHEMATICS A.Y. 2013/2014
Publications

Year: 2019Author/s: Angella, Daniele, Tomassini, Adriano, Verbitsky, Misha

Year: 2019Author/s: Piovani R., Tomassini A.

Year: 2019Author/s: Rollenske S., Tomassini A., Wang X.

Year: 2019Author/s: Tardini N., Tomassini A.

Year: 2018Author/s: PIOVANI, RICCARDO, Tomassini A.
Contacts
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