Geometria differenziale e complessa

Differential and Complex Geometry

Componenti

Fino Anna Maria (Coordinatore Scientifico)
Vezzoni Luigi (Componente)
Pacini Tommaso (Componente)
Mari Luciano (Componente)
Buzano Reto (Componente)
Garbiero Sergio (Componente)
Gentili Giovanni (Dottorando)
Suarez Ricardo Benjamin (Dottorando)
Paradiso Fabio (Dottorando)
Raffero Alberto (Componente)
Salvatore Francesca (Dottorando)
Lucia Martin-Merchan (Assegnista)
Asia Mainenti (Dottorando)
Fusi Elia (Dottorando)
Brienza Beatrice (Dottorando)

Contatti

Settore ERC

PE1_5 - Lie groups, Lie algebras

PE1_7 - Topology

Attività

L'attività scientifica riguarda principalmente lo studio di strutture speciali in varietà reali e complesse con particolare attenzione a problemi di natura geometrica come equazioni ellittiche (equazione di Monge-Ampere reale e complessa, equazione di Calabi-Yau…) e equazioni di evoluzione (flusso di Ricci, flusso del Laplaciano…).

Settori ERC : PE1_4 Algebraic and complex geometry, PE1_5 Geometry, PE1_7 Lie groups, Lie algebras

Linee di ricerca: Studio di strutture speciali su varietà. Studio di problemi analitici in varietà reali e complesse: PDE su varietà compatte. Gruppi e algebre di Lie: Studio di strutture geometriche su gruppi di Lie nilpotenti e risolubili e loro quozienti compatto; classificazioni di strutture speciali su gruppi e algebre di Lie.

Collaborazioni con altre Università

Università italiane:

Politecnico di Torino,
Università di L'aquila,
Università di Firenze,
Università di Parma,
Scuola Normale Superiore di Pisa,
Università di Palermo,
Università di Lecce,
Università di Cagliari.
Università di Milano.

Università estere:

University of Oregon (USA),
FaMAF (Argentina),
University of Bilbao (Spain),
University of Zaragoza (Spain),
Florida International University Miami (USA),
Universidade de São Paulo (Br),
King's College (London),
Rutgers University (USA),
University College of London.

Progetti di Ricerca

PRIN 2017: "Real and Complex Manifolds: Topology, Geometry and holomorphic dynamics", [link] responsabile dell'unità: Anna Fino
FIRB: "Geometria Differenziale e Teoria Geometrica delle funzioni". [link] Co-PI: Luigi Vezzoni.
Progetto Europeo: FP7-PEOPLE-2012-IEF n. 332209 EDSRGff "Exterior Differential Systems of Riemannian Geometry" (Marie Curie fellowship of Rui Albuquerque, con data d'inizio il 9 Settembre 2013.) PI: Anna Fino.

Organizzazione di workshops

"Workshop Firb", 23-25 October 2013, University of Florence [link]
''Giornata di Geometria Torino-Milano", 7 Giugno 2013
Oberwolfach Mini-Workshop "Quaternion Kähler Structures in Riemannian and Algebraic Geometry", Oberwolfach (Germania), 3-9 Novembre 2013.
Carnival Differential Geometry School, Torino, 24-27 Febbraio 2014.
Workshop Complex Geometry and Lie Groups, Torino, 16-20 Giugno 2014.
Sessione speciale "Symplectic geometry and special metrics" al First Joint International Meeting RSME-SCM-SEMA-SIMAI-UNI, Bilbao, 30 Giugno - 4 Luglio 2014.
Workshop in memory of Sergio Console, Torino, 23-26 Febbraio 2015.
New perspectives in Differential Geometry, INdAM Workshop, Roma, 16-20 November 2015.
The IV Workshop "Complex Geometry and Lie Groups", Nara, Giappone, 22-26 Marzo 2016
A Differential Geometry Day in memory of Sergio Console, 13 Maggio 2016.
Sessione Speciale "Geometric Structures, Lie Theory and Applications " al The first Joint Meeting Brazil - Italy in Mathematics, IMPA, Brasile, 29 Agosto- 2 Settembre 2016.

Differential Geometry Days, Torino, 5- 7 Aprile 2017.
Differential Geometry Days, Torino, 5- 7 Aprile 2017.
Pluripotential Theory, Geometric Analysis and Calibrated Geometry, Torino, 2-4 Maggio 2018.
The 5th Workshop "Complex Geometry and Lie Groups", Firenze, 11-15 Giugno 2018.
Geometries with torsion, Torino, 21 Settembre 2018.
Differential Geometry Day - Workshop and School, Torino, 12 Aprile 2019.
Bridging the Gap between Kaehler and non-Kaehler Complex Geometry, BIRS, 27 Ottobre -1 Novembre 2019.
The 6th Workshop "Complex Geometry and Lie groups", Toki Messe, Niigata, online, 15-20 Febbraio 2021.
A Geometric Analysis Meeting at UniTO, 15-17 Giugno 2022.

Corsi avanzati

Corso di dottorato: S. Console, A. Fino, Flusso di Ricci e strutture Geometriche speciali, 2013.
Corso di dottorato: A. Raffero, Gruppi di olonomia in geometria Riemanniana, 2019
Corso di dottorato: A. Fino, A Raffero,Topological properties of manifolds with exceptional holonomy, 2020.

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Progetti

Geometria Differenziale e Teoria Geometrica delle Funzioni

Prodotti della ricerca

Fernández, Marisa, Fino, Anna, Raffero, Alberto
Exact G2-structures on unimodular Lie algebras.
https://iris.unito.it/handle/2318/1739993

Fino, Anna, Raffero, Alberto
A Class of Eternal Solutions to the G_2-Laplacian Flow.
https://iris.unito.it/handle/2318/1742537

Anna, Fino, Alberto, Raffero (2020)
Closed warped G2-structures evolving under the Laplacian flow.
https://iris.unito.it/handle/2318/1655103

Mari, Luciano, Pessoa, Leandro de Freitas (2020)
Duality between Ahlfors-Liouville and Khas'minskii properties for nonlinear equations.
https://iris.unito.it/handle/2318/1693164

Colombo, Giulio, Mari, Luciano, Rigoli, Marco (2020)
Remarks on mean curvature flow solitons in warped products.
https://iris.unito.it/handle/2318/1721876

Anna, Fino, Gueo, Grantcharov, Luigi, Vezzoni (2019)
Astheno-Kähler and balanced structures on fibrations.
https://iris.unito.it/handle/2318/1655292

Anna Fino, Alberto Raffero (2019)
Closed G_2-structures on non-solvable Lie groups.
https://iris.unito.it/handle/2318/1687784

Fino, Anna, Kath, Ines (2019)
Holonomy groups of G_2^*-manifolds.
https://iris.unito.it/handle/2318/1648971

Ugo Bruzzo, Anna Fino, Pietro Frè, Pietro Antonio Grassi, Dimitri Markushevich (2019)
Crepant resolutions of ℂ^3∕Z_4 and the generalized Kronheimer construction (in view of the gauge/gravity correspondence).
https://iris.unito.it/handle/2318/1735436

Ambrozio, Lucas, Buzano, Reto, Carlotto, Alessandro, Sharp, Ben (2019)
Bubbling analysis and geometric convergence results for free boundary minimal surfaces.
https://iris.unito.it/handle/2318/1721873

Buzano, Reto, Haslhofer, Robert, Hershkovits, Or (2019)
The Moduli Space of Two-Convex Embedded Tori.
https://iris.unito.it/handle/2318/1701051

Buzano, Reto, Nguyen, Huy The (2019)
The Higher-Dimensional Chern–Gauss–Bonnet Formula for Singular Conformally Flat Manifolds.
https://iris.unito.it/handle/2318/1701050

Buzano, R, Nguyen, HT (2019)
The Chern-Gauss-Bonnet formula for singular non-compact four-dimensional manifolds.
https://iris.unito.it/handle/2318/1726079

Pujia, Mattia, Vezzoni, Luigi (2018)
A remark on the Bismut–Ricci form on 2-step nilmanifolds.
https://iris.unito.it/handle/2318/1669073

LEONARDO BAGAGLINI, MARISA FERNANDEZ, ANNA FINO (2018)
Coclosed G_2-structures inducing nilsolitons.
https://iris.unito.it/handle/2318/1650362

Fino Anna Maria, Grantcharov Gueo, Verbitsky Misha (2018)
Algebraic dimension of complex nilmanifolds.
https://iris.unito.it/handle/2318/1648949

Leonardo Bagaglini, Anna Fino (2018)
The Laplacian coflow on almost-abelian Lie groups.
https://iris.unito.it/handle/2318/1671139

Anna Fino, Ines Kath (2018)
Local Type I Metrics with Holonomy in G_2^*.
https://iris.unito.it/handle/2318/1672300

Buzano, Reto, Sharp, Ben (2018)
Qualitative and quantitative estimates for minimal hypersurfaces with bounded index and area.
https://iris.unito.it/handle/2318/1701049

Bedulli, Lucio, He, Weiyong, Vezzoni, Luigi (2018)
Second-Order Geometric Flows on Foliated Manifolds.
https://iris.unito.it/handle/2318/1669075

Ciraolo, Giulio, Vezzoni, Luigi (2018)
A sharp quantitative version of Alexandrov’s theorem via the method of moving planes.
https://iris.unito.it/handle/2318/1619654

Jason D Lotay, Tommaso Pacini
From Lagrangian to totally real geometry: coupled flows and calibrations.
https://iris.unito.it/handle/2318/1742231

Buzano, Reto, Rupflin, Melanie (2017)
Smooth long-time existence of Harmonic Ricci Flow on surfaces.
https://iris.unito.it/handle/2318/1701048

A. Fino, H. Kasuya, Tamed symplectic structures on compact solvmanifolds of completely solvable type, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 16, (2016), 971-979.

S. Console, A. Fino, H. Kasuya, On the de Rham and Dolbeault Cohomology of solvmanifolds, Transform. Groups 21 (2016), no.3, 653-680.

M. Fernández, A. Fino, A. Raffero, Locally conformal calibrated G_2-manifolds, Ann. Mat. Pura Appl. 195 (2016), no. 5, 1721-1736.

M. Fernández, A. Fino, V. Manero Laplacian flow of closed $G_2$-structures inducing nilsolitons, J. Geom. Anal. 26 (2016), no. 3, 1808-1837.

A. Fino, L. Vezzoni, On the existence of balanced and SKT metrics on nilmanifolds , Proc. Amer. Math. Soc. 144 (2016), no. 6, 2455-2459.

Z. Chen, Y. S. Poon, Holomorphic Poisson Structures and its Cohomology on Nilmanifolds, Differential Geom. Appl. 44 (2016), 144-160.

Mantegazza, Carlo, Müller, Reto (2015)
Perelman's entropy functional at Type i singularities of the Ricci flow.
https://iris.unito.it/handle/2318/1701044

Haslhofer, Robert, Müller, Reto (2015)
A note on the compactness theorem for 4d Ricci Shrinkers.
https://iris.unito.it/handle/2318/1701047

A. Corti, M. Haskins, J. Nordström, T. Pacini, G2-manifolds and associative submanifolds via semi-Fano 3-folds, Duke Math. J. 164 (2015), no. 10, 1971-2092.

G. Calvaruso, A. Fino, Homogeneous geodesics of non-reductive homogeneous pseudo-Riemannian 4-manifolds, Bull. Braz. Math. Soc. (N.S.) 46 (2015), 23-64.

G. Calvaruso, A. Fino, Four-dimensional pseudo-Riemannian homogeneous Ricci solitons, Int. J. Geom. Methods Mod. Phys. 12 (2015), 1550056 (21 pages).

N. Enrietti, A. Fino, L. Vezzoni, The Pluriclosed Flow on Nilmanifolds and Tamed Symplectic Forms. J. Geom. Anal. 25 (2015), no. 2, 883-909.

M. Fernandez, A. Fino, V. Manero, G_2-structures on Einstein solvmanifolds, Asian J. Math. 19 (2015), 321-342.

A. Fino, P. Nurowski, Analog of selfduality in dimension nine. J. Reine Angew. Math. 699 (2015), 67-110.

A. Fino, A. Raffero, Coupled SU(3)-structures and Supersymmetry, Symmetry 2015, 7(2), 625-650.

A. Fino, L. Vezzoni, Special Hermitian metrics on compact solvmanifolds, J. Geom. Phys. 91 (2015), 40-53.

A. Fino, H. Kasuya, L. Vezzoni, SKT and Tamed symplectic structures on solvmanifolds, Tohoku Math. J. 67 (2015), 19-37.

E. Buzano, A. Fino, L. Vezzoni, The Calabi-Yau equation on the Kodaira-Thurston manifold, viewed as an S^1-bundle over a 3-torus, J. Differential Geom. 101 (2015), 175-195

A. Fino, H. Kasuya, Tamed symplectic structures on compact solvmanifolds of completely solvable type, preprint math.DG/1410.3610, to appear in Annali di Scuola Normale Superiore.

A. Fino, A. Otal, L. Ugarte, Six dimensional solvmanifolds with holomorphically trivial canonical bundle, preprint math.DG/1401.0512, to appear in International Mathematics Research Notices.

G. Calvaruso, A. Fino , Complex and paracomplex structures on homogeneous pseudo-Riemannian four-manifolds. Internat. J. Math. 24 (2013), no. 1, 28 pp.

N. Enrietti, A. Fino and G. Grantcharov, Tamed symplectic forms and generalized geometry. J. Geom. Phys. 71 (2013), 103-116.

A. Fino, L. Ugarte, On generalized Gauduchon metrics. Proc. Edinb. Math. Soc. (2) 56 (2013), no. 3, 733-753.

A. Fino, Y.Y. Li, S. Salamon and L. Vezzoni, The Calabi-Yau equation on 4-manifolds over 2-tori. Trans. Amer. Math. Soc. 365 (2013), no. 3, 1551-1575.

L. Vezzoni, A note on Canonical Ricci forms on 2-step nilmanifolds. Proc. Amer. Math. Soc. 141 (2013) 325--333.

G. Calvaruso, A. Fino, Five-dimensional K-contact Lie algebras. Monatsh. Math. 157 (2012), 35--59.

G. Calvaruso, A. Fino, Ricci solitons and geometry of non-reductive homogeneous 4-spaces. Canad. J. Math. 64 (2012), 778--804.

A. Fino, A. Tomassini, Blow-ups and Cohomology of Almost Complex Manifolds. Diff. Geom. Appl. 30 (2012), 520--529.

N. Enrietti, A. Fino, L. Vezzoni, Hermitian-Symplectic structures and SKT metrics. Journal of Symplectic Geometry 10, n. 2 (2012), 203--223.

A. J. Di Scala, L. Vezzoni, Quasi-Kahler manifolds with trivial Chern Holonomy. Math. Z. 271 (2012), 95--108.

A. J. Di Scala, J. Lauret, L. Vezzoni, Quasi-Kahler Chern-flat manifolds and complex 2-step nilpotent Lie algebras. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) XI (2012), 41--60.