About Me

Education

1999: Laurea in Mathematics, University of Genova. Thesis title: “Algebre commutative di operatori corrispondenti alle trasformazioni affini del piano tempo-frequenza” (“Commutative operator algebras corresponding to affine transformations in the time- frequency plane”). Advisor: Filippo De Mari. Mark: 110/110 cum laude.

2004: “Dottorato di Ricerca” (Italian PhD) in Mathematics and its Applications, University of Genova. Thesis title: “Multicontact mappings on Hessenberg manifolds”, Advisor: Filippo De Mari.

2017: FULT certificate (Foundations of University Learning and Teaching), UNSW;

2017-2018: GCULT (Graduate Certificate for University Learning and Teaching), UNSW;

Italian National Habilitation to the role of Associate Professor in Geometry and that of Associate Professor in Analysis.

Research interests

Differential geometry and geometric analysis on sub-Riemannian spaces. Quasiconformal mappings. Harmonic analysis. Geometric Group Theory. Geometric methods in PDE's. Geometric Control Theory.

Current position

Since June 2022: Senior Lecturer, UNSW, Sydney. Responsabilities: Director of Undergraduate Studies.

Academic positions

2000–03: PhD fellowship, based at the Politecnico di Torino.

2003–04: Research Fellow at the University of Genova.

2004–06: Assistant and Postdoctoral Fellow, University of Bern.

2006–07: Research Fellow, University of Genova.

2008–11: Research Fellow, University of Milano Bicocca.

2012-2014: Research Fellow, CIRM, Trento.

2015-2019: Senior Research Fellow at UNSW, Sydney.

2019-2022: Lecturer, UNSW, Sydney.

Visiting

June 2008: Visiting Fellow, University of New South Wales (UNSW).

July 2010: Visiting Fellow, UNSW.

February 2011: Visiting Fellow, Aalto University of Helsinki.

March 2011: Visiting Fellow, ETH Zurich.

June 2011: Visiting Fellow, ETH Zurich.

January–February 2012: Visiting Fellow, Université de Paris-Sud, Orsay.

May 2012: Visiting Fellow, Université de Paris-Sud.

October 2012: Visiting Fellow, University of Jyvӓskylӓ, Finland.

October–November 2012, Visiting Fellow, UNSW.

February 2013, Visiting Fellow, University of Jyvӓskylӓ.

October–November 2013, Visiting Fellow, UNSW.

March-April 2014, Visiting Fellow, Polytechnic Institute of Massachussets.

October 2014: Visiting Fellow, UNSW.

November-December 2014: Visitor, Institut Henri Poincare.

March 14–March 29 2016: Visitor, Nara Women’s University, Japan.

January-February 2018: Visiting fellow, University of Jyvӓskylӓ.

Grants

2003: University of Genova of approximately € 3000. Grant: “Training of young re- searchers at foreign centers of excellence”, for a pre-doctoral research course at the University of Orleans.

2004: Swiss National Science Foundation of approximately CHF 100000. Grant on the rigidity of Carnot groups, to finance my postdoctoral position in Bern: Application written with H. M. Reimann.

2010: GNAMPA Grant of € 3500: “Harmonic analysis and Riemannian manifolds”. Application written with A. Martini and M. Vallarino.

2011: GNAMPA Grant of € 4000: “Harmonic analysis and Riemannian manifolds”. Application written with M.Vallarino.

2012: GNAMPA Grant of € 5000: “Harmonic analysis on manifolds, Wiener spaces and Lie groups”. Application written with A. Carbonaro and M. Vallarino. 2013: GNAMPA Grant of € 3000: “Harmonic and Geometric Analysis on Lie groups and subRiemannian spaces”. Application written with N. Arcozzi, V. Casarino and P. Ciatti.

2013: GNAMPA Grant of € 3000: “Harmonic and Geometric Analysis on Lie groups and subRiemannian spaces”. Application written with N. Arcozzi, V. Casarino and P. Ciatti.

2014: GNAMPA Grant of € 2100: “Harmonic and Geometric Analysis on manifolds and Lie groups”. Application written with A. Carbonaro and M. Vallarino.

2015: GNAMPA Grant of € 2100: “Alcune questioni di analisi armonica per opera- tori differenziali non ellittici”. Application written with P. Ciatti, A. Martini and V. Casarino.

2015: AustMS grant of AUD3790 and contribution of the School of Mathematics and Statistics of UNSW of about AUD3000, for the organization of the workshop “Analysis and Geometry in non-Riemannian spaces”, held at UNSW in 2-4 November, 2015.

2022: ARC (Australian Research Council) Grant for DP scheme. Chief investigator. Amount: 375K.

Conferences organized

“Geometric and Harmonic Analysis on sub-Riemannian Spaces”, 16–18 March 2009, University of Milano Bicocca.

Webpage: http://www.matapp.unimib.it/∼ ottazzi/Workshop.htm

School & Workshop “Harmonic Analysis and Related Topics”, 21–25 February 2011, University of Milano Bicocca.

Webpage: http://www.matapp.unimib.it/hart/

“Analysis and Geometry in non-Riemannian spaces”, 2-4 November, 2015, University of New South Wales.

Webpage: http://conferences.science.unsw.edu.au/SR2015/

Teaching

2000–01: Introductory calculus lecturer at the Politecnico di Torino.

2001–04: First year calculus tutor at the University of Genova.

2004–05: Lecturer of the honours course “Nilpotent Lie groups” (in English) and as- sistant in second year calculus at the University of Bern (in German). 2005–06: Lecturer of the honours course “Hopf bifurcation” (in English) and assistant to the course “Wavelets” (in German), containing a laboratory module with the Matlab Wavelet Tool, at the University of Bern.

2007–08: Assistant to the first year calculus course and lecturer in the web-teaching project at the Politecnico of Torino.

2008–09: Assistant to “Mathematics and Statistics” for biologists, and to first year calculus for chemists at the University of Milano Bicocca.

2009–10: Assistant to “Mathematics and Statistics” for biologists, and to first year calculus for chemists at the University of Milano Bicocca. Lecturer of the introductory courses of mathematics for social sciences and for sciences at the University of Milano Bicocca.

2010–11: Assistant to “Mathematics and Statistics” for biologists, and to first year calculus for chemists at the University of Milano Bicocca. Lecturer of the introductory courses of mathematics for social sciences and for sciences at the University of Milano Bicocca.

2011–12: Assistant to first year calculus for chemists, lecturer of the introductory courses of mathematics for social sciences, and lecturer and coordinator of the intro- ductory courses of mathematics for sciences at the University of Milano Bicocca.

2012–13: Assistant to the second year calculus course for engineers at the University of Trento.

2014–15: Lecturer of "Analysis III" for Physics students, University of Trento.

2014–15: Tutor of Linear Algebra I and II, Tutor of Higher Complex Analysis, UNSW.

2017: Lecturer of Complex Analysis MATH2069 in S1 (364 students) and Lecturer of Higher Complex Analysis MATH2621 in S2 (about 95 students), UNSW. Tutor of MATH2069, MATH2621 and MATH1231 (Calculus and Linear Algebra).

2018: Coordinator and lecturer of MATH2069 (Complex Analysis and Vector Calculus), UNSW.

2019 : Tutor of MATH2011 (Multivariable Calculus); UNSW. Course authority of MATH2069; UNSW.

2020 : Course authority of MATH2069, Lecturer of MATH1241 Higher Calculus, Tutor of MATH1041 (Statistics), MATH1081 (Discrete Maths), and MATH5535 (Lie groups); UNSW.

2021 : Course authority of MATH2069 , Lecturer of MATH1241 Higher Calculus, Lecturer of MATH1231 Calculus; UNSW.

2022 : Course authority of MATH2621 Higher Complex Analysis, Lecturer of MATH1241 Higher Calculus, UNSW.

Invited lectures

I have given lectures and conference presentations at the following:

Convegno di Analisi Armonica, 26–29 May 2003, Padova.

Young researcher days of the HARP Network, 16–17 June 2003, Orleans (France).

XVII Congresso UMI, 8–13 September 2003, Milano.

Convegno Nazionale di Analisi Armonica, 21–26 May 2007, Caramanico Terme (Italy).

Conference in Geometric Analysis and its applications, 21–24 January 2008, Bern.

Workshop in analisi e geometria subriemanniana, 8–10 July 2008, Genova.

Convegno Nazionale di Analisi Armonica, 15–19 June 2009, Bardonecchia (Italy).

5th Asian Mathematical Conference, 22–26 June 2009, Kuala Lumpur.

Workshop on non-Riemannian mapping theory and geometry, 12–15 May 2010, Bern.

Seminar series at Aalto University, February 2011, Helsinki.

New function spaces in PDEs and Harmonic Analysis, May 1–June 4, 2011, Naples.

XXX Convegno di Analisi Armonica, 7–11 June 2010, Gargnano (Italy).

XXXI Convegno di Analisi Armonica, May 30–June 4, 2011, Rome.

“Martin’s Days”—Conference in honor of Hans Martin Reimann’s 70th birthday, November 11–13, 2011, Bern.

XXXIII Convegno di Analisi Armonica, June 17–20, 2013, Alba.

“La notte dei ricercatori” (Researchers night), Event for the popularization of science, September 27, 2013, Trento.

IHP Trimester, Geometry, Analysis and Dynamics on Sub-Riemannian Manifolds, September 1 - December 12, 2014.

Rencontres Mathematiques de Rouen: SR Geometry, CR Geometry and Analysis on manifolds, June 17th to 19th, 2015.

Ninth School on Analysis and Geometry in Metric Spaces, Levico, July 6-10, 2015.

Complex Analysis and Geometry, Special Session of AustMS Meeting, Flinders University, Adelaide, September 28-October 1, 2015.

Complex Analysis and Geometry, Special Session of AustMS Meeting, Australian National University, Canberra, December 2016 [Invited speaker].

CIME-CIRM Course on New Trends on Analysis and Geometry in Metric Spaces, Levico, June 26-20, 2017. [Invited speaker]

Complex Analysis and Geometry, Special Session of AustMS Meeting, Macquarie University, December 2017.

Harmonic Analysis, Special Session of AustMS Meeting, Macquarie University, December 2017.

Sub-Riemannian Geometry and Beyond, 19-23 February 2018, University of Jyvӓskylӓ, Finland.

Geometry and Symmetries, Special Session of AustMS Meeting, UNSW, December 2022.

And I have given short courses or lecture series at the following:

Workshop on Group Representation and Visual Cortex, 20–21 September 2010, Bologna.

University of Paris-Sud, 7–18 May 2012, Paris.

University of Genoa, May 2011, Genova.

ETH Zurich, June 6–10, 2011, Zurich.

Other service

Qualification aux fonctions de Mâıtre de Conférences, France, Campagne 2012.

Reviewer for Zentralblatt MATH and the AMS.

Referee for international journals and the Swiss National Foundation.

Activities for the popularization of science.

Languages

Italian is my mother tongue, and I also know English (IELTS overall mark: 8), French, and German.

Publications

(1) Cowling M. Ganji M., Ottazzi A., Schmalz G., CR embeddings of CR manifolds. Annali di Matem- atica Pura ed Applicata, Published Online Firstin 2022: https://doi.org/10.1007/s10231-022-01241-7 .

(2) Cowling M., Li J., Ottazzi A., Wu Q., Conformal and CR mappings on Carnot groups. Proc. Amer. Math. Soc. Ser. B, 7 (2020), 67-81.

(3) Ottazzi A., Vittone D., On the codimension of the abnormal set in step two Carnot groups. ESAIM: Control, Optimisation and Calculus of Variations. Volume 25, (2019), Article Number 18, Number of page(s) 17.

(4) Capogna L., Citti G., Le Donne E., Ottazzi A., Conformality and Q-Harmonicity in sub-Riemannian manifolds. Journal des Math ́ematiques Pures et Appliqu ́ees. Volume 122, February 2019, Pages 67- 124. DOI: doi.org/10.1016/j.matpur.2017.12.006.

(5) Martini A., Ottazzi A., Vallarino M., A multiplier theorem for sub-Laplacians with drift on Lie groups, Revista Matem ́atica Iberoamericana 35 (2019), no. 5, 1501–1534.

(6) Ottazzi A., Schmalz G., Normal forms for singular multi-contact structures and applications to second order ODEs, Differential Geometry and its Application, 52 (2017), 78–93.

(7) Cowling M., Ottazzi A., Structure of stratified groups I. Product decompositions, J. Lie Theory, 27 (2017), 177–183.

(8) Martini A., Ottazzi A., Vallarino M., Spectral multipliers for sub-Laplacians on NA groups, Jour- nal d’Analyse Mathematique, (2018) 136: 357. DOI: doi.org/10.1007/s11854-018-0063-6

(9) Ottazzi A., Schmalz G., Singular multi-contact structures. J. Math. Anal. Appl., 443 (2016), 1220–1231.

(10) Le Donne E., Montgomery R., Ottazzi A., Pansu P., Vittone D., Sard Property for the endpoint map on some Carnot groups, Annales de l’Institut Henri Poincare (C) Analyse non lineaire, 33 (2016), no. 6, 1639–1666.

(11) Cowling M. Ottazzi A., Global quasiconformal maps of Carnot groups, Conformal Geometry and Dynamics 19 (2015), 221–239.

(12) Le Donne E., Ottazzi A., Isometries between open sets of Carnot groups and global isometries of sub-Finsler Lie groups, J. Geom. Anal. 26 (2016), no. 1, 330–345.

(13) Cowling M.G., Ottazzi A., Conformal maps of Carnot groups, Ann. Acad. Sci. Fenn. Math. 40 (2015), 203–213.

(14) Ottazzi A., Vallarino M., Spectral multipliers of Laplacian with drift in Damek Ricci spaces, Math. Nachr. 287 (2014), no. 16, 1837–1847.

(15) Le Donne E., Ottazzi A., Warhurst B., Ultra-rigid tangents of sub-Riemannian nilpotent groups, Annales de l’Institut Fourier 64 (2014), no. 6, 2265–2282.

(16) Ottazzi A., Warhurst B., A Liouville type theorem for Carnot groups: a case study, Chapter in Trends in Harmonic Analysis, Springer-Indam Series 3 (2013), 371–380.

(17) Ottazzi A., Warhurst B., Contact and 1-quasiconformal maps on Carnot groups., J. Lie Theory 21 (2011), 787–811.

(18) Ottazzi A., Warhurst B., Algebraic prolongation and rigidity of Carnot groups. Monats. Math. 162 (2011), 179–195.

(19) Ottazzi A., Warhurst B., Rigidity of Iwasawa nilpotent Lie groups via Tanaka’s theory. Note Mat. 30 (2010), 141–146.

(20) Demari F., Ottazzi A., Rigidity of Carnot groups relative to multicontact structures. Proc. Amer. Math. Soc. 138 (2010), 1889–1895.

(21) Ottazzi A., Polynomial bases for split simple Lie algebras. Publ. Math. 76 (2010), 157–171.

(22) Ottazzi A., Classes of nonrigid Carnot groups. Bull. Malaysian Math. Soc. 35 (2010), 567–571.

(23) Ottazzi A., A sufficient condition for nonrigidity of Carnot groups. Math. Zeits. 259 (2008), 617–629.

(24) Ottazzi A., Multicontact vector fields on Hessenberg manifolds, J. Lie Theory 15 (2005), 357–377.

Preprints

(25) Cowling M., Kivioja V., Le Donne E., Nicolussi Golo S., Ottazzi A., From homogeneous metric spaces to Lie groups. Submitted. Preprint: arXiv:1705.09648.

(26) Nicolussi S., Ottazzi A., Polarised Lie groups contactomorphic to stratified groups. Submitted. Preprint: arXiv:1807.03854 .

(27) Cowling M. Ganji M., Ottazzi A., Schmalz G., CR embeddings of nilpotent Lie groups. Submitted. Preprint: arXiv:2210.07515 .

(28) Peng Chen, Michael G. Cowling, Ming-Yi Lee, Ji Li, Alessandro Ottazzi, Flag Hardy space theory on Heisenberg groups and applications. Preprint: arXiv:2102.07371.