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Prof.

Professore di I fascia
• 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, Milano-Bicocca 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 editor-in-chief 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 Milano-Bicocca.
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 2n-dimensional symplectic manifolds, endowed with a tamed almost complex structure and a d-bar closed nowhere vanishing (n,0)-form of constant length. These manifolds provide a possible generalization to the non holomorphic case of the notion of Calabi-Yau 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 Tian-Todorov Theorem states that the moduli space of Calabi-Yau is totally unobstructed: in (de Bartolomeis, T., Ann. Inst. Fourier (Grenoble) 2013), an appropriated moduli space of almost complex deformations of a Calabi-Yau 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 7-dimensional 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 6-dimensional 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 n-dimensional complex manifolds and, more generally, on complex orbifolds) whose fundamental form (its (n-2)-power respectively) is dd-bar closed. Such metrics have been studied by many authors, e.g., (Bismut, Math. Ann. 1989), (Gauduchon, C. R. Acad. Sci. Paris Sér. A-B 1977), (Jost, Yau, Acta Math. 1993). By blow-up procedures we obtain new examples of such structures on simply-connected 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 4-manifold 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 4-manifold the second de Rham cohomology group decomposes as the direct sum of the subgroups formed by cohomology classes admitting invariant and anti-invariant representatives respectively, with respect to the natural action of the almost complex structure on the space of 2-forms. 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 almost-Kähler 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 2-cohomology class, there exists an almost complex structure with respect to which the 2-class admits both invariant and anti-invariant representatives.
For further results on anti-invariant cohomology and L2-cohomology see [Hind, Medori, T., J. Geom. Anal. 2015] and [Hind, T., 2017 arXiv:1708.06316].
Towards the aim to better understand complex non-Kähler manifolds, we investigated Bott-Chern and Aeppli cohomologies. The research in this direction has been developed, (and is still developing,) under several aspects. The relation between Bott-Chern 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 Bott-Chern 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 generalized-complex 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 Bott-Chern cohomology, we introduced a notion of geometric formality with respect to the Bott-Chern 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 almost-complex 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 almost-Kähler 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
h-index: 11:

h-index SCOPUS: 12
Total citations: 434
h-index WOS: 11
Total citations: 372

### Anno accademico di erogazione: 2020/2021

• Course year: 1 - Second cycle degree - - A.Y.: 2020/2021
• Course year: 2 - First cycle degree (DM 270) - - A.Y.: 2019/2020
• Course year: 3 - First cycle degree (DM 270) - - A.Y.: 2018/2019
• Course year: 1 - First cycle degree (DM 270) - - A.Y.: 2020/2021

### Anno accademico di erogazione: 2019/2020

• Course year: 1 - Second cycle degree - - A.Y.: 2019/2020
• Course year: 4 - Full cicle (6 years) - - A.Y.: 2016/2017
• Course year: 2 - First cycle degree (DM 270) - - A.Y.: 2018/2019
• Course year: 3 - First cycle degree (DM 270) - - A.Y.: 2017/2018
• Course year: 1 - First cycle degree (DM 270) - - A.Y.: 2019/2020

### Anno accademico di erogazione: 2018/2019

• Course year: 1 - Second cycle degree - - A.Y.: 2018/2019
• Course year: 4 - Full cicle (6 years) - - A.Y.: 2015/2016
• Course year: 2 - First cycle degree (DM 270) - - A.Y.: 2017/2018
• Course year: 3 - First cycle degree (DM 270) - - A.Y.: 2016/2017
• Course year: 1 - First cycle degree (DM 270) - - A.Y.: 2018/2019

### Anno accademico di erogazione: 2017/2018

• Course year: 1 - Second cycle degree - - A.Y.: 2017/2018
• Course year: 2 - Full cicle (6 years) - - A.Y.: 2016/2017
• Course year: 4 - Full cicle (6 years) - - A.Y.: 2014/2015
• Course year: 2 - First cycle degree (DM 270) - - A.Y.: 2016/2017
• Course year: 3 - First cycle degree (DM 270) - - A.Y.: 2015/2016
• Course year: 1 - First cycle degree (DM 270) - - A.Y.: 2017/2018
• Course year: 1 - Full cicle (6 years) - - A.Y.: 2017/2018

### Anno accademico di erogazione: 2016/2017

• Course year: 1 - Full cicle (6 years) - - A.Y.: 2016/2017
• Course year: 2 - Full cicle (6 years) - - A.Y.: 2015/2016
• Course year: 4 - Full cicle (6 years) - - A.Y.: 2013/2014
• Course year: 2 - First cycle degree (DM 270) - - A.Y.: 2015/2016
• Course year: 2 - First cycle degree (DM 270) - - A.Y.: 2015/2016
• Course year: 3 - First cycle degree (DM 270) - - A.Y.: 2014/2015
• Course year: 1 - First cycle degree (DM 270) - - A.Y.: 2016/2017

### Anno accademico di erogazione: 2015/2016

• Course year: 1 - Second cycle degree - - A.Y.: 2015/2016
• Course year: 2 - First cycle degree (DM 270) - - A.Y.: 2014/2015
• Course year: 3 - First cycle degree (DM 270) - - A.Y.: 2013/2014

### Anno accademico di erogazione: 2014/2015

• Course year: 1 - Second cycle degree - - A.Y.: 2014/2015
• Course year: 2 - First cycle degree (DM 270) - - A.Y.: 2013/2014

### Anno accademico di erogazione: 2013/2014

• Course year: 1 - Second cycle degree - - A.Y.: 2013/2014

### Teacher tutor

• First cycle degree (DM 270) A.Y. 2020/2021
• Second cycle degree A.Y. 2020/2021
• Second cycle degree A.Y. 2019/2020
• First cycle degree (DM 270) A.Y. 2019/2020
• First cycle degree (DM 270) A.Y. 2018/2019
• Second cycle degree A.Y. 2018/2019
• First cycle degree (DM 270) A.Y. 2017/2018
• Second cycle degree A.Y. 2017/2018
• First cycle degree (DM 270) A.Y. 2016/2017
• Second cycle degree A.Y. 2016/2017
• First cycle degree (DM 270) A.Y. 2015/2016
• Second cycle degree A.Y. 2015/2016
• Second cycle degree A.Y. 2014/2015
• First cycle degree (DM 270) A.Y. 2014/2015
• First cycle degree (DM 270) A.Y. 2013/2014
• Second cycle degree A.Y. 2013/2014

### Professor/Teacher

• Second cycle degree A.Y. 2020/2021
• Second cycle degree A.Y. 2019/2020
• Second cycle degree A.Y. 2018/2019
• Second cycle degree A.Y. 2017/2018
• First cycle degree (DM 270) A.Y. 2016/2017
• Second cycle degree A.Y. 2015/2016
• Second cycle degree A.Y. 2014/2015

Phone number
906970
Fax number

906950