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Geometria differenziale e complessa

Differential and Complex Geometry

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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 

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.

 

 

 

Prodotti della ricerca

On nearly parallel G_2-manifolds: formality and associative submanifolds
In corso di stampa Marisa Fernandez; Anna Fino; Alexei Kovalev; Vicente Munoz https://iris.unito.it/handle/2318/1944590

Optical geometries
In corso di stampa Anna Fino; Arman Taghavi-Chabert; Thomas Leistner https://iris.unito.it/handle/2318/1944592

Closed G_2-Structures on Unimodular Lie Algebras with Non-trivial Center
In corso di stampa Fino A.; Raffero A.; Salvatore F. https://iris.unito.it/handle/2318/1850013

CYT and SKT metrics on compact semi-simple Lie groups
2023-01-01 A. Fino, G. Grantcharov https://iris.unito.it/handle/2318/1906034

Exact G_2-structures on compact quotients of Lie groups
2023-01-01 A. Fino, L. Martin-Merchan , A. Raffero https://iris.unito.it/handle/2318/1872459

Almost Robinson geometries
2023-01-01 A. Fino, A. Taghavi-Chabert, T. Leistner https://iris.unito.it/handle/2318/1906033

Hermitian structures on a class of almost nilpotent solvmanifolds
2022-01-01 Fino, Anna; Paradiso, Fabio https://iris.unito.it/handle/2318/1871398

Infinite families of homogeneous Bismut Ricci flat manifolds
In corso di stampa Fabio Podestà; Alberto Raffero https://iris.unito.it/handle/2318/1890774

Special solutions to the Type IIA flow
In corso di stampa Alberto Raffero https://iris.unito.it/handle/2318/1941150

Bismut Ricci flat manifolds with symmetries
2023-01-01 Fabio Podestà; Alberto Raffero https://iris.unito.it/handle/2318/1890772

Purely coclosed G_2 -structures on 2-step nilpotent Lie groups
2022-01-01 del Barco V.; Moroianu A.; Raffero A. https://iris.unito.it/handle/2318/1786699

On the Dynamical Behaviour of the Generalized Ricci Flow
2021-01-01 Raffero A.; Vezzoni L. https://iris.unito.it/handle/2318/1786700

Closed G_2-structures with a transitive reductive group of automorphisms
2021-01-01 Podestà, Fabio; Raffero, Alberto https://iris.unito.it/handle/2318/1877697

Homogeneous 8-manifolds admitting invariant Spin(7)-structures
2020-01-01 Dmitri Alekseevsky, Anna Fino, Ioannis Chrysikos, Alberto Raffero https://iris.unito.it/handle/2318/1758403

Remarks on homogeneous solitons of the G_2-Laplacian flow
2020-01-01 Anna Fino; Alberto Raffero https://iris.unito.it/handle/2318/1758419

On G2-Structures, Special Metrics and Related Flows
2020-01-01 Fernandez M.; Fino A.; Raffero A. https://iris.unito.it/handle/2318/1742543

On the automorphism group of a closed G2-structure
2019-01-01 Podestà, Fabio; Raffero, Alberto https://iris.unito.it/handle/2318/1676269

On the automorphism group of a symplectic half-flat 6-manifold
2019-01-01 Podestà, Fabio; Raffero, Alberto* https://iris.unito.it/handle/2318/1684879

Homogeneous symplectic half-flat 6-manifolds
2019-01-01 Podestà, Fabio; Raffero, Alberto* https://iris.unito.it/handle/2318/1676268

Special Types of Locally Conformal Closed G2-Structures
2018-01-01 Bazzoni, Giovanni; Raffero, Alberto https://iris.unito.it/handle/2318/1684878

Convexity theorems for the gradient map on probability measures
2018-01-01 Biliotti, Leonardo*; Raffero, Alberto https://iris.unito.it/handle/2318/1676270

A remark on the quaternionic Monge-Ampère equation on foliated manifolds
2023-01-01 Giovanni Gentili; https://iris.unito.it/handle/2318/1866344

On the pluriclosed flow on Oeljeklaus-Toma manifolds
2022-01-01 Fusi, E; Vezzoni, L https://iris.unito.it/handle/2318/1934410

Pluriclosed and Strominger Kähler–like metrics compatible with abelian complex structures
2022-01-01 A. Fino, N. Tardini, Luigi Vezzoni https://iris.unito.it/handle/2318/1877313

A parabolic approach to the Calabi-Yau problem in HKT geometry
2022-01-01 Lucio Bedulli, Giovanni Gentili, Luigi Vezzoni https://iris.unito.it/handle/2318/1865468

The quaternionic Calabi Conjecture on abelian Hypercomplex Nilmanifolds Viewed as Tori Fibrations
2022-01-01 Giovanni Gentili; https://iris.unito.it/handle/2318/1797277

Solutions to the Hull-Strominger system with torus symmetry.
2021-01-01 A.Fino, G. Grantcharov, L. Vezzoni https://iris.unito.it/handle/2318/1829954

Hermitian curvature flow on unimodular lie groups and static invariant metrics
2020-01-01 Lafuente R.A.; Pujia M.; Vezzoni L. https://iris.unito.it/handle/2318/1758226

Stability of geometric flows of closed forms
2020-01-01 Bedulli L.; Vezzoni L. https://iris.unito.it/handle/2318/1728632

Quantitative stability for hypersurfaces with almost constant mean curvature in the hyperbolic space
2020-01-01 Ciraolo G.; Vezzoni L. https://iris.unito.it/handle/2318/1758228

A remark on the Laplacian flow and the modified Laplacian co-flow in G 2 -geometry
2020-01-01 Bedulli L.; Vezzoni L. https://iris.unito.it/handle/2318/1758227

A scalar Calabi-type flow in Hermitian geometry: short-time existence and stability
2020-01-01 Bedulli, L; Vezzoni, L https://iris.unito.it/handle/2318/1797265

On the umbilic set of immersed surfaces in three-dimensional space forms
2020-01-01 Catino G.; Roncoroni A.; Vezzoni L. https://iris.unito.it/handle/2318/1765844

Bubble-Tree Convergence and Local Diffeomorphism Finiteness for Gradient Ricci Shrinkers
2023-01-01 Reto Buzano; Louis Yudowitz https://iris.unito.it/handle/2318/1908290

Gaussian upper bounds for the heat kernel on evolving manifolds
2023-01-01 Buzano R.; Yudowitz L. https://iris.unito.it/handle/2318/1928530

Geometric convergence results for closed minimal surfaces via bubbling analysis
2022-01-01 Lucas Ambrozio, Reto Buzano, Alessandro Carlotto, Ben Sharp https://iris.unito.it/handle/2318/1808277

A Local Singularity Analysis for the Ricci Flow and its Applications to Ricci Flows with Bounded Scalar Curvature
2022-01-01 Reto Buzano; Gianmichele Di Matteo https://iris.unito.it/handle/2318/1831385

The moduli space of two-convex embedded spheres
2021-01-01 Buzano R.; Haslhofer R.; Hershkovits O. https://iris.unito.it/handle/2318/1808250

Global regularity of second order twisted differential operators
2020-01-01 Ernesto Buzano; Alessandro Oliaro https://iris.unito.it/handle/2318/1716633

On the topology of leaves of singular Riemannian foliations
2023-01-01 Radeschi, Marco; Khalili Samani, Elahe https://iris.unito.it/handle/2318/1945037

Maximality of Laplacian algebras, with applications to Invariant Theory
2023-01-01 Mendes R.A.E.; Radeschi M. https://iris.unito.it/handle/2318/1945018

How highly connected can an orbifold be?
2022-01-01 Lange, Christian; Radeschi, Marco https://iris.unito.it/handle/2318/1945038

ON THE STRUCTURE OF BESSE CONVEX CONTACT SPHERES
2022-01-01 Mazzucchelli, M; Radeschi, M https://iris.unito.it/handle/2318/1945033

Polar foliations on symmetric spaces and mean curvature flow
2022-01-01 Liu X.; Radeschi M. https://iris.unito.it/handle/2318/1945031

Odd-dimensional orbifolds with all geodesics closed are covered by manifolds
2021-01-01 Amann M.; Lange C.; Radeschi M. https://iris.unito.it/handle/2318/1945036

Torus actions on rationally elliptic manifolds
2021-01-01 Galaz-Garcia F.; Kerin M.; Radeschi M. https://iris.unito.it/handle/2318/1945022

Laplacian algebras, manifold submetries and the Inverse Invariant Theory Problem
2020-01-01 Mendes R.A.E.; Radeschi M. https://iris.unito.it/handle/2318/1945019

SINGULAR RIEMANNIAN FOLIATIONS AND THEIR QUADRATIC BASIC POLYNOMIALS
2020-01-01 Mendes R.A.E.; Radeschi M. https://iris.unito.it/handle/2318/1945016

Virtual immersions and minimal hypersurfaces in compact symmetric spaces
2020-01-01 Mendes R.A.E.; Radeschi M. https://iris.unito.it/handle/2318/1945025

Ricci curvature, the convexity of volume and minimal Lagrangian submanifolds
In corso di stampa Tommaso Pacini https://iris.unito.it/handle/2318/1948193

Extremal length in higher dimensions and complex systolic inequalities
2021-01-01 Pacini, Tommaso https://iris.unito.it/handle/2318/1743429

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

Corti Alessio, Haskins Mark, Nordstrom Johannes, Pacini Tommaso (2015)
G_2-manifolds and associative submanifolds via semi-Fano 3-folds.
https://iris.unito.it/handle/2318/1616213

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. 128 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.

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