TOMASSINI Adriano
 Curriculum Vitae
 Teaching
 Appointments
 Research
General news
 Born: 01/28/1969, Rome.
 Bachelor degree in Mathematics, received on 06/19/1992 by Università di Firenze.
 PhD in Mathematics, Università di Firenze, 07/1997, advisor Paolo de Bartolomeis.
 12/30/1996 – 10/31/2002: Assistant Professor, SSD GEOMETRIA, Università di Palermo and Parma.
 11/200206/2011: Associate Professor, Università di Parma, SSD MAT03/GEOMETRIA.
 Current position: Full Professor, SSD MAT03/GEOMETRIA, Università di Parma (since 06/30/2014).
 He spent research periods and has been visiting professor at Universities of Michigan, Minnesota, Stanford, Notre Dame, Florida International University, Bourgogne, Ruhr, Edinburgh, Pais Vasco, Zaragoza, Centre International de Rencontres Mathématiques, Luminy, Grenoble, Trondheim, 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, Paris, Oberwolfach, Niigata, Pisa Scuola Normale Superiore, Grenoble.
 Local coordinator of the Research Unit in Parma, Project PRIN 2010, 2011 2015: "Varieta' reali e complesse: geometria, topologia e analisi armonica", Scientific coordinator Fulvio Ricci.
 Local coordinator of the Research Unit in Parma, Project PRIN 2017: "Real and Complex Manifolds: Topology, Geometry and holomorphic dynamics", Scientific coordinator Filippo Bracci.
 Member of Collegio dei Docenti of PhD Program in Mathematics at the Universities of Pavia, MilanoBicocca and INdAM.
 Presidente del Corso di Laurea triennale in Matematica, starting from December 2012 to December 2013.
 Chairman of the Dipartimento di Matematica e Informatica dell'Università di Parma, starting from December 2013 to December 2016.
 Chairman of the Dipartimento di Scienze Matematiche, Fisiche e Informatiche dell’Università di Parma, since 2020.
 President of “Centro Servizi ELearning e Multimediali di Ateneo” since 2017.
 Chairman of Scuola Matematica Interuniversitaria, SMI, since January 2018.
 Member of the Committee of Abilitazione Scientifica Nazionale, Settore Concorsuale 01/A2 Geometria e Algebra.
 Editorinchief of Rivista di Matematica della Università di Parma, from 2009 to 2020.
 Member of the Governing Board of Annali di Matematica Pura ed Applicata, since January 2022.
 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 Mathematicae, Ann. Inst. Fourier, Math. Z., Quarterly J. Math., Comm. Anal. Geom., Math. Annalen, Compositio Mathematica, Forum Mathematicum, Annals of Global Analysis and Geometry, Manuscripta Mathematica, Journal für die reine und angewandte Mathematik, Nagoya Math. J., Transactions of AMS, Journal of AMS, Selecta Mathematica, international J. of Math., American J. of Math..
Advisor of the PhD theses of:
Catellani, Firenze, 2008.
Angella, Pisa, 2013.
Rossi. MilanoBicocca, 2013.
Tardini, Pisa, 2017.
Maschio, Parma, 2018.
Piovani, Pisa, 2021.
Sferruzza, III year of PhD program Parma
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.
In [Fino, T., J. London Math. Soc. 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].
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
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.
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., Zhang, Proc. AMS (2014)], the almostKähler case is considered. Analogue notions in the symplectic settings are studied in [Angella, T., J. Symplectic Geom. (2014)].
For further results on antiinvariant cohomology and L2cohomology see [Hind, Medori, T., J. Geom. Anal. 2015] and [Hind, T., J. Symplectic Geom. (2019)].
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 ddbarLemma, 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. Complex Manifolds (2020)] the behaviour of $partialoverlinepartial$Lemma under modifications of compact complex manifolds is investigated. For other results on cohomological properties of compact symplectic and complex manifolds we refer to [T., Wang, Internat. J. of Math. (2018)] e [Rollenske, T., Wang, Ann. Mat. Pura Appl. (2020)], [Sferruzza, T., J. of Geom. Physics, (2022)].
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., Ann. Mat. Pura App. (2017)].
For a compact almost complex manifold (M,J), endowed with a JHermitian g, one can define the Dolbeault and BottChern Laplacian, using the natural operators del and delbar an their adjoints. It turns out that such differential operators are elliptic and consequently their kernels are finite dimensional complex vector spaces. Let h^{p,q} be the dimension of the space of Dolbeault harmonic (p,q)forms. In Problem 20, [Hirzebruch, Annals of Math. (1954)]: Kodaira and Spencer asked the following
Question I Let (M,J) be an almostcomplex manifold. Choose a Hermitian metric on (M,J) and consider the numbers h^{p,q}. Is h^{p,q} independent of the choice of the Hermitian metric?
Holt and Zhang in [Harmonic Forms on the KodairaThurston Manifold, (2020)] answered negatively to this question, showing that there exist almostcomplex structures on the KodairaThurston manifold such that the Hodge number h^{0,1} varies with different choices of Hermitian metrics. Furthermore, the authors showed that for a compact 4dimensional almostKaehler manifold h^{1,1} is independent of the metric, and more precisely h^{1,1}=b_+1, where b_ denotes the dimension of the space of the antiselfdual harmonic 2forms. In [HZ] the authors asked the following
Question II Let (M,J) be a compact almostcomplex 4dimensional manifold which admit an almostKaehler structure. Does it have a non almostKaehler Hermitian metric such that
h^{1,1} is different from b_+1 ?
In [Tardini, T., to appear in Math. Res. Lett.] we prove that:
h^{1,1}=b_, respectively h^{1,1}=b_ + 1 if the metric is strictly locally conformally Kaehler respectively globally conformally Kaehler. For further results see [Piovani, T., Math. Zeit. (2022)]. In [Chen, Zhang, Kodaira dimension of almost complex manifolds I, II] the authors introduced the notion of Kodaira dimension of almost complex manifolds. In [Cattaneo, Nannicini, T., Internat. J. Math. (2021)] we provide several computations of Kodaira dimension of almost complex manifolds in dimension 4 and 6.
Total Publications: 79
Total citations: 648
hindex SCOPUS: 15
Total Publications: 72
Total citations: 580
hindex WOS: 14
Anno accademico di erogazione: 2024/2025
 Course year: 1  Second cycle degree  MATHEMATICS  A.Y.: 2024/2025
 Course year: 2  First cycle degree (DM 270)  MATHEMATICS  A.Y.: 2023/2024
 Course year: 3  First cycle degree (DM 270)  MATHEMATICS  A.Y.: 2022/2023
 Course year: 1  First cycle degree (DM 270)  BIOTECHNOLOGY  A.Y.: 2024/2025
Anno accademico di erogazione: 2023/2024
 Course year: 1  Second cycle degree  MATHEMATICS  A.Y.: 2023/2024
 Course year: 2  First cycle degree (DM 270)  MATHEMATICS  A.Y.: 2022/2023
 Course year: 3  First cycle degree (DM 270)  MATHEMATICS  A.Y.: 2021/2022
 Course year: 1  First cycle degree (DM 270)  BIOTECHNOLOGY  A.Y.: 2023/2024
Anno accademico di erogazione: 2022/2023
 Course year: 1  Second cycle degree  MATHEMATICS  A.Y.: 2022/2023
 Course year: 2  First cycle degree (DM 270)  MATHEMATICS  A.Y.: 2021/2022
 Course year: 3  First cycle degree (DM 270)  MATHEMATICS  A.Y.: 2020/2021
 Course year: 1  First cycle degree (DM 270)  BIOTECHNOLOGY  A.Y.: 2022/2023
Anno accademico di erogazione: 2021/2022
 Course year: 1  Second cycle degree  MATHEMATICS  A.Y.: 2021/2022
 Course year: 2  First cycle degree (DM 270)  MATHEMATICS  A.Y.: 2020/2021
 Course year: 3  First cycle degree (DM 270)  MATHEMATICS  A.Y.: 2019/2020
 Course year: 1  First cycle degree (DM 270)  BIOTECHNOLOGY  A.Y.: 2021/2022
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 01/01/2024 to 12/31/2027
Professor/Teacher
 Second cycle degree MATHEMATICS A.Y. 2024/2025
 Second cycle degree MATHEMATICS A.Y. 2023/2024
 Second cycle degree MATHEMATICS A.Y. 2022/2023
 Second cycle degree MATHEMATICS A.Y. 2021/2022
 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. 2024/2025
 Second cycle degree MATHEMATICS A.Y. 2024/2025
 First cycle degree (DM 270) MATHEMATICS A.Y. 2023/2024
 Second cycle degree MATHEMATICS A.Y. 2023/2024
 First cycle degree (DM 270) MATHEMATICS A.Y. 2022/2023
 Second cycle degree MATHEMATICS A.Y. 2022/2023
 First cycle degree (DM 270) MATHEMATICS A.Y. 2021/2022
 Second cycle degree MATHEMATICS A.Y. 2021/2022
 Second cycle degree MATHEMATICS A.Y. 2020/2021
 First cycle degree (DM 270) 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
 First cycle degree (DM 270) MATHEMATICS A.Y. 2017/2018
 Second cycle degree MATHEMATICS A.Y. 2017/2018
 First cycle degree (DM 270) MATHEMATICS A.Y. 2016/2017
 Second cycle degree MATHEMATICS A.Y. 2016/2017
 Second cycle degree MATHEMATICS A.Y. 2015/2016
 First cycle degree (DM 270) 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: 2023Author/s: Cattaneo Andrea, Nannicini Antonella, Tomassini Adriano

Year: 2023Author/s: Fino A., Tardini N., Tomassini A.

Year: 2023Author/s: Hind R, Medori C, Tomassini A

Year: 2023Author/s: Sferruzza T., Tomassini A.

Year: 2022Author/s: Piovani R., Tomassini A.