Curriculum

Personal Data                                                                                                                                                      Curriculum in Italiano 

I was born in La Spezia (Italy) on May 1979
I am married and I have two children.
My current address: Via Carlo Alberto 10, 10124, Torino (Italy).
E-mail : luigi.vezzoni@unito.it
I'm member of UMI (Unione Matematica Italiana).

Current Employment

March 2022-present Full Professor at the University of Torino.

Past Employments

November 2014- February 2022 Associated Professor at the University of Torino.

2008-2014 Italian Researcher (tenured assistant professor) at the University of Torino.

Education

2006-2008 Italian postdoc fellowship (Assegno di Ricerca) at the University of Torino. 

I was a Ph.D. student at the University of Pisa and I got the Ph.D. title in 2007 with the Thesis "The Geometry of some Special SU(n)-structures" [PDF].  My Supervisor was Prof. Paolo de Bartolomeis. 

I studied at the University of Florence and I got the Italian Laurea in Mathematics on 20 June 2003.

Research interests

Special Structures on Real and Complex manifolds. Complex and almost Complex Geometry. Symplectic and almost Kähler structures. Partial differential equations on real and complex manifolds. Parabolic flows and evolution equations.

Talks 

• Geometric Flows and Special Hermitian metrics on Lie groups , Geometry Webinar Sur/AmSul, 20213

• Geometric flow of closed forms, Columbia University, 2023 

• Metriche Speciali e Flussi Geometrici in Gruppi di Lie. Università di Parma, 2023

• Geometric flows of special metrics: short-time existence and stability, Differential Geometry @ L’Aquila 2023, L' Aquila, 2023

• The Calabi-Yau problem in Hypercomplex manifolds, Osaka University, Osaka, 2023

• The Calabi-Yau problem in Hypercomplex manifolds, 7th workshop on complex geometry and Lie groups, Lecce, 2023 

• Flows of Geometric Structures, Special Riemannian Metrics and Curvature Functionals, Centro de Giorgi, Pisa, 2022

• The Calabi-Yau problem in HKT Geometry, Virtual seminar on geometry with symmetries, online seminar 2022

• Introduction to HKT geometry, Generalized Ricci flow Learning Seminar, online seminar, 2022

• The Calabi-Yau problem in HKT Geometry, Quaternioni sul Conero III, 2021

• The Calabi-Yau problem in HKT Geometry, Geometry Webinar Sur/AmSul, 2021 

• Geometric flows of Hermitian metrics on Lie groups, The 6th Workshop "Complex Geometry and Lie groups", online workshop, 2021

• A geometric flow of balanced metrics, Bridging the Gap between Kähler and non-Kähler Complex Geometry, Birs, Banff (Canada), 2019

• Geometric flows of Balanced Metrics, Almost Complex Geometry Seminars, CUNY, New York (USA), 2019

• Special Hermitian metrics and Geometric flows on Lie groups, Geometric Analysis and Homogeneous Geometry, Brisbase (Australia), 2019 

• Flussi di Metriche Hermitiane in Gruppi di Lie, Università di Firenze, 2019

• The quantitative Alexandrov Theorem, Politecnico di Milano, Milano, 2019  

• A quantitative version of a Theorem of Alexandrov, Geometric Analysis, parallel session at The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications. Taiwan, 2018 

• Geometric flows on complex homogeneous spaces and Special Hermitian metrics, Workshop PRIN "Varietà reali e complesse: geometria, topologia e analisi armonica'', Scuola Normale Superiore, Pisa, 2018. 

• The quantitive Alexandrov Theorem, Scuola Normale Superiore, Pisa, 2017. 

• The quantitive Alexandrov Theorem, Munster, Germany, 2017. 

• A quantitative version of a Theorem of Alexandrov, Workshop on Geometric Analysis - Homage to Olga Gil-Medrano, Valencia, 2017.

• A quantitative version of a Theorem of Alexandrov, Variational and Geometrical Models for PDEs, Palermo, 2017.

• A quantitative version of a Theorem of Alexandrov, Università dell'Aquila, 2017.

• The Calabi-Yau equation on the Kodaira-Thurston manifold, MDS, Sofia, Bulgaria, 2017. 

• The Calabi-Yau problem for Fibrations and generalized Monge-Ampère equations. Young Geometric Analysts' Forum 2017, TSIMF, Sanya, Cina, 2017. 

• The Calabi-Yau problem on the Kodaira-Thurston manifold, FIU, Florida, USA, 2017.  

• A quantitative version of a Theorem of Alexandrov. Complex and Riemannian Geometry days. Cagliari, Italy. 2016.  

• The Calabi-Yau problem in torus bundles and generalized Monge-Ampère equations. VI Workshop on Differential Geometry. La Falda (Cordoba), Argentina, 2016.

• Un'introduzione alla superfici a curvatura quasi costante. Seminari del Dipartimento di Matematica Informatica. Palermo 2106. 

• The Calabi-Yau problem in toric fibrations and Monge-Ampère equation. The 4^th workshop on complex Geometry and Lie groups. Nara, Japan, 2016.

• Evolution of special Hermitian metrics. International Conference on Geometric and Nonlinear Analysis, Xinyang, Hénan, China, 2015.

• A quantitative version of a theorem of Alexandrov. Geometric Properties for Parabolic and Elliptic PDE's 4th Italian-Japanese Workshop, Palinuro, 2015. 

• The Calabi-Yau problem in symplectic Geometry and Monge-Ampère equation, University of Texas at Austin, 2015.

• A recent pinching theorem for hypersurfaces in the Euclidean space. University of Turin, 2015.

• Evolution of closed sections of vector bundles, ICM Satellite conference on Geometric Analysis, Sungkyunkwan University, Suwon, Korea, 2014. 

• The Calabi-Yau equation in toric fibrations, First Joint International Meeting RSME-SCM-SEMA-SIMAI-UMI, Bilbao, Spagna, 2014.

• Equazioni ellittiche in varietà almost Kähler. Giornata di Geometria Milano Torino, Dipartimento di Mathematica ''Federigo Enriques", Università di Milano, 2014.

• L'equazione di Calabi-Yau in varietà simplettiche, Workshop PRIN "Varietà reali e complesse: geometria, topologia e analisi armonica'', Scuola Normale Superiore, Pisa, 2014.

• Metriche Hermitiane Speciali, Workshop Firb, Firenze 2013.

• Riemannian foliations with special holonomy. Journées de Géométrie Différentielle, Université Libanaise de Beirut, 2013.

• A parabolic flow of balanced structures. American University of Beirut. 2013.

• Un flusso parabolico per le metriche bilanciate. Politecnico di Torino, 2013.

• L'equazione di Calabi-Yau per varietà  almost Kähler. Firenze, 2012.

• Special almost complex structures and the Calabi-Yau equations. Symmetries in Differential Geometry and Mathematical Physics, Luxemburgh, 2012.

• The Calabi-Yau equation for solvmanifolds, Incontro di Geometria Brasile-Italia, Salvador de Bahia, 2012.

• The Calabi-Yau equation for T^2-fibrations, Workshop on geometric structures on manifolds and their applications, Castle Rauischholzhausen, 2012.

• L'equazione di Calabi-Yau nelle Nilvarietà,  XIX Congresso dell'Unione Matematica Italiana, Bologna, 2011.

• Strutture quasi complesse dominate e strutture quasi complesse calibrate da forme simplettiche, New Trends in Differential Geometry. L'Aquila, 2011. 

• L'equazione di Calabi-Yau per fibrazioni Lagrangiane, Politecnico di Torino, 2011. 

• The Calabi-Yau equation on nilmanifolds, Marrakech,  2011.

• The Calabi-Yau equation for Lagrangian fibrations, Coimbra, 2010.

• The Calabi-Yau equation on nilmanifolds, XIX International Fall Workshop on Geometry and Physics. Oporto, 2010.

• Chern flat and Ricci flat almost Hermitian structures,  Northern German Differential Geometry Day. Hamburg, 2009.

• Il flusso della Curvatura Hermitiana, Politecnico di Torino, 2009.

• Contact Connections, Workshop in CR and Sasakian Geometry. Luxembourg 2009.

• Varietà Chern-piatte,  Progressi recenti in Geometria Reale e Complessa, Levico 2008.

• Connessione di Chern, identità di Gray e integrabilità. Firenze 2008.

• The Ricci tensor of an SU(3)-manifold, Berlin 2007.

Short visits abroad

July 2016: Università degli Studi di Palermo. 

April 2015: University of Texas at Austin.

March 2013: American University of Beirut.

December 2010: University of Coimbra

December 2009: "Max Plank" Institute at Amburg.

January 2007: Humbolt University, Berlin.

Services

October 2022-present  Deputy Director for research of the Mathematics Department of the University of Torino.

Support Journal Editor of the Journal "Complex Manifolds."

Co-organizer of Differential Geometry workshop in Lerici, April 8-10 2024, Lerici (Italy)  [link]

Co-organizer of  A Complex Differential Geometry Meeting at UniTo, June 17-19 2023, Torino (Italy)  [link]

Co-organizer of A Geometric Analysis Meeting at UniTo, June 15-17 2022, Torino (Italy)  [link]

Co-organizer of  Informal Geometry Wokshop in "Paradiso",  3rd-4th-5th of February, 2022, Cogne (Italy) [link]

Co-organizers Giornata di Benvenuto 2020/2021/2022. [link]

Co-organizer of "Pluripotential Theory, Geometric Analysis and Calibrated Geometry" 2-4 May 2018, Torino (Italy),  [link]. 

Co-organizer of  Informal Geometry Workshop in "Paradiso", 22-24 January 2018, Cogne (Valle D'Aosta - Italy) [link].

Co-organizer of "Differential Geometry Days", 5-7 April 2017, Torino. [link].

Co-organizer of "Perspectives in Geometry", 26-28 January 2017, Firenze. [link].

Co-organizer of "A Differential Geometry Day in memory of Sergio Console", 13 May 2016, Torino [link]. 

Co-organizer of "New perspectives in differential geometry: special metrics and quaternionic geometry", 16-20 November 2015, Roma.

Co-organizer of "Workshop in memory of Sergio Console",  23-26 February 2015, Torino [link].

Co-organizer of "Workshop: Complex Geometry and Lie Groups", 16-20 June 2014, Torino  [link].

Co-organizer of the workshop "Browsing through Mathematics", 28 April 2014, Torino. [link].

Co-organizer of "Carnival Differential Geometry school", 24-27 February 2014, Torino [link].

Co-organizer of "Workshop Firb", 23-25 October 2013, Firenze [link].

Co-organizer of ''Giornata di Geometria Torino-Milano", 7-06-13, Torino. [link].

Co-organizer of "Turin Differential Geometry Day", 17-7-09, Torino. [link].

Supervision of Post-Doc students

• Michela Zedda, October 2013--June 2015. 

• Udhav Fowadar,  February 2024--

• Giovanni Gentili, February 2024--

Supervision of graduate Thesis 

• Elia Fusi, University of Torino. (In progress).

• Giovanni Gentili, New advances in HKT Geometry, University of Torino.  [Thesis]. 

• Mattia Pujia, Evolution of Hermitian Metrics on Lie Groups, University of Torino. [Thesis].

• Alberto Roncoroni, Symmetry and Quantitative Stability Results for Problems in Geometric Analysis and Functional Inequalities, University of Pavia [Thesis].  (joint supervision with Giulio Ciraolo). 

Supervision of undergraduate Thesis (University of Torino)

• Ettore Lo Giudice, Some aspects of the Geometric flow, Master degree in Mathematics.

• Mauro Valezano, Introduzione alle curve geodetiche, Bachelor's degree in Mathematics.

• Alessandro Pedrani, Il Teorema di Gauss-Bonnet, Bachelor's degree in Mathematics.

• Simone Siclari, L'equazione di Calabi-Yau nella varietà di Kodaira-Thurston, Master degree in Mathematics. 

• Silvia Avandero, Geodetiche su superfici e varietà Riemanniane, Bachelor's degree in Mathematics.

• Gabriele Beltramo, Il Teorema di Seifert e Van Kampen, Bachelor's degree in Mathematics.

• Gemma Taricco, Metodi topologici per lo studio della chiralità delle molecole, Bachelor's degree in Mathematics. 

• Samuele Lancini, Il teorema di Calabi-Yau. Master degree in Mathematics.

• Samuele Lancini, Ellisoidi Generalizzati. Bachelor's degree in Mathematics.

• Giorgio Tortone, Il Teorema di Poincaré-Hopf per superfici e varietà. Bachelor's degree in Mathematics.

Teaching (at the University of Torino) [CampusNet]

2018-2019 / 2019-2020 / 2020-2021 /2021-2022 / 2022-2023 / 2023-2024 

Geometria 1, Undergraduate course in Mathematics

Istituzioni di Geometria, Undergraduate course in Mathematics

2016-2017

Matematica e Fisica, Undergraduate course in Biology

Geometria Superiore, Undergraduate course in Mathematics

Geometria Differenziale, Undergraduate course in Mathematics

2015-2016

Matematica e Fisica, Undergraduate course in Biology

Geometria Superiore, Undergraduate course in Mathematics

2014-2015

Geometria 2, Undergraduate course in Mathematics

Geometria Complessa, Undergraduate course in Mathematics

Geometria Differenziale, Undergraduate course in Mathematics

Analisi 2, Undergraduate course in Physics

2013-2014

Geometria Uno, Undergraduate course in Mathematics

Geometria 2, Undergraduate course in Mathematics

Geometria 3, Undergraduate course in Mathematics

Geometria 4, Undergraduate course in Mathematics

2012-2013

Geometria e Algebra Lineare I, Undergraduate course in Physics

Laboratorio di Geometria per le applicazioni, Undergraduate course in Mathematics

Geometria 4, Undergraduate course in Mathematics

Flusso di Ricci e strutture Geometriche speciali, Graduate course in Mathematics

2011-2012

Metodi Geometrici, Undergraduate course.

Geometria 4, Undergraduate course in Mathematics.

Geometria Differenziale, Undergraduate course in Mathematics

2010-2011

Precorso di Matematica, Undergraduate course in Mathematics.

Geometria 3, Undergraduate course in Mathematics.

Geometria 4, Undergraduate course in Mathematics.

Geometria Simplettica e Kalheriana, Graduate course in Mathematics.

2009-2010

Esercitazioni di Matematica A, Undergraduate course in Chemistry.

Esercitazioni di Geometria III, Undergraduate course in Mathematics.

Geometria IV, Undergraduate course in Mathematics.

Other Activities (Attività di terza missione)

I'm currently vice president of the Italian association Scuola di Formazione scientifica "Luigi Lagrange" whose main activity consists in the organization of a periodic campus for students from the high school (http://www.campusmfs.it/).

Beside the organization of the campus, I did the following talks and short courses:

Divulgative talks (for students of high school)

• La Geometria della Teoria dell Stringhe, "Matematica al Forte", April 2015, Bard (AO). 

• Pillola di scienze: Dalla formula di Eulero alla classificazione delle superfici compatte. "Campus invernale di Matematica, Fisica e Astrofisica 2014", February 2014, Sansicario (To).

• La formula di Eulero: un viaggio nella topologia. ''Campus invernale di Matematica, Fisica e Astrofisica 2014'', February 2014, Sansicario (To).

• Pillola di scienze: Dalla formula di Eulero alla classificazione delle superfici compatte. "Campus invernale di Matematica, Fisica e Astrofisica 2013", December 2013, Sansicario (To).

• La formula di Eulero: un viaggio nella topologia. "Campus invernale di Matematica, Fisica e Astrofisica 2013", December 2013, Sansicario (To).

Divulgative courses (for students of high school)

• Geometrie non Euclidee (10 h),  "Campus estivo di Matematica Fisica e Astrofisica", July 2106, Bardonecchia (To).

• Matematica 2, (12 h), "Campus estivo di Matematica Fisica e Astrofisica", July 2106, Bardonecchia (To).

• Matematica 1, (12 h), "Campus estivo di Matematica Fisica e Astrofisica", July 2106, Bardonecchia (To).

• Introduzione agli aspetti matematici della relatività generale (10 h) "Campus sulla Relatività ristretta e generale", April 2016, Marina di Massa (MS) 

• Geometrie delle curve e delle superfici, (10 h) ''Campus invernale di Matematica, Fisica e Astrofisica 2015'', January 2015, Bardonecchia (To)

• Geometrie delle curve e delle superfici,  (10 h) ''Campus invernale di Matematica, Fisica e Astrofisica 2015'', December 2015, Bardonecchia (To)

• Dalla Geometria Elementare agli universi impossibili, (10 h), "Campus di Matematica, Fisica, Astrofisica e Nuove tecnologie", December 2014, Bardonecchia (To).

• Matematica 1, (24 h), "Campus estivo di Matematica Fisica e Sport", July 2014, Acqui Terme (AT).