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Andrea Bonfiglioli

Associate Professor

Department of Mathematics

Academic discipline: MAT/05 Mathematical Analysis

Curriculum vitae

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1) Born in Bologna, May 17th 1974.
2) Degree in Mathematics cum laude at the University of Bologna (July 17th 1998) with the thesis "Equations of Levi-type Curvature" (advisor Ermanno Lanconelli).
3) PhD in Mathematics at the University of Bologna (from A.Y. 1998/99; PhD degree: March 29th 2003) with the thesis "Second Order Differential Operators on Stratified Lie Groups" (advisor E. Lanconelli).
4) October 2000: I qualified as a teacher for the Competition Class A047 (Mathematics in Secondary Schools of the Emilia-Romagna region), having been ranked at the top of the list for the competition in Ordinary Chairs for Qualifications and Examinations (2000).
5) From November 1st 2002, to October 31st 2006: Research grant in Mathematics within the Research Program "Sub-Elliptic Equations on Homogeneous Lie Groups", University of Bologna.
6) November 1st 2006 - September 14th 2014: Assistant Professor in Mathematical Analysis (SSD MAT/05), University of Bologna.
7) November 21st 2013: I obtained the National Scientific Qualification (A.S.N.: Abilitazione Scientifica Nazionale; 2012 session) as Associate Professor in Italian Universities (Settore Concorsuale 01/A3: Analisi Matematica, Probabilità e Statistica Matematica).
8) September 15th 2014 - present: Associate Professor in Mathematical Analysis (Settore Concorsuale 01/A3: Analisi Matematica, Probabilità e Statistica Matematica).

Further professional information:
1) October 12th-December 3rd 2000: I collaborated in the Event "Mathematics, Art and Technology (Bologna 2000)" sponsored by U.M.I. (Italian Mathematical Union) during the World Mathematical Year 2000. I collaborated in the related exhibition, providing the catalogue.
2) September 2010 - May 2012: I worked with the Publisher Zanichelli (Bologna, Italy) as an editor/proofreader/co-author in the Project "MATutor".
3) A.Y.'s from 2012/13 to 2015/16: I attended the "National Plan for Scientific Degrees" ("Piano Nazionale per le Lauree Scientifiche") of the M.I.U.R. Italian Ministry of Education, class of Mathematics (Dept. of Mathematics, Bologna) and I was responsible for associated laboratories.
4) From A.Y. 2012/13: I am a member of the Education Committee (Commissione Didattica) of the Degrees in Mathematics of Bologna; member of the Quality Assurance Committe (Presidio Q.A.) for the first-cycle and second-cycle Degrees in Mathematics (Bologna).
5) For thirteen academic years (from 1999/2000) I collaborated with C.E.U.R. (European Centre for University and Research) for tutoring in Mathematics at the Excellence Residence "Camplus - Alma Mater" in Bologna.
6) June 2008 - September 2010: I worked for a supporting activity at the Institute for the Blind "F. Cavazza" (Bologna), for the special teaching of Mathematics in the presence of the visual impairment.
7) I have published with Springer-Verlag (as a co-author) two monographs (XXVI+800 pages; XLV+539 pages) in the venues Springer Monographs in Mathematics and Lecture Notes in Mathematics: see references [20] and [27] in the list of publications.
8) I have refereed in: Applicable Analysis; Computer Physics Communications; SCIENCE CHINA Mathematics; Potential Analysis; Calculus of Variations and PDE's; Mathematische Nachrichten; Rendiconti Lincei: Matematica e Applicazioni.

TEACHING ACTIVITY (University of Bologna):
My teaching activity has been continuative since 1998/99. Up to 2006, I have lectured at the Faculties of Chemistry, Engineerings, Information Sciences, "MM.FF.NN." Sciences. I have also lectured for the "Master Course in Mathematical Finance" (Bologna) and for the PhD in Mathematics (Bologna). Presently, my teaching courses are: Advanced Analysis 2, Geometric Analysis (two-year Degree in Mathematics), Mathematical Analysis 1, and Institutions of Mathematics 2 (Environmental Sciences, Ravenna).

Assigned Degree-Theses and PhD-Theses:
1. I contributed to parts of the PhD Thesis "Sui sub-Laplaciani reali e su una classe di operatori ultraparabolici sui gruppi di Lie stratificati" by dr. Chiara Cinti (PhD XVII cicle, Bologna).
2. A.Y. 2011/12: advisor for the two-year degree thesis in Mathematics "La Soluzione Fondamentale per i Sub-Laplaciani sui Gruppi Nilpotenti di Passo Due" (by dr. Andrea Tamagnini); advisor for the three-year degree thesis in Mathematics of Mirko Ruffilli.
3. A.Y. 2012/2013: advisor for the two-year degree thesis in Mathematics of dr. Erika Battaglia; collaboration for the PhD Thesis of dr. Beatrice Abbondanza (PhD XXVI Cicle, Bologna). Advisor for the three-year degree thesis in Mathematics of Tommaso Zamagni.
4. A.Y. 2013/2014: advisor for the three-year degree thesis in Mathematics of the students: Francesco di Fabio; Stefano Murtagh; Righini Alberto (co-advisor).
5. A.Y. 2014/2015: advisor for the two-year degree thesis in Mathematics of dr. Mirko Ruffilli (thesis "Stime Integrali su Gruppi di Tipo H e Principio Forte di Continuazione Unica"); co-advisor for the three-year degree thesis in Mathematics of Annachiara Bartolini.
6. A.Y. 2015/16: I am advisor for the PhD Theses of dr. Stefano Biagi (PhD XXVII Cicle, Bologna) and of dr. Erika Battaglia (PhD XXVIII Cicle, Bologna).


My research activity primarily deals with the study of differential operators of the second-order with nonnegative characteristic form, not elliptic, falling in the hypoellipticity class introduced by Hörmander. Among these operators, particularly relevant are the sub-Laplacians L on Carnot groups G, which locally approximate every Hörmander operator. Starting from the vector fields generating the Lie algebra of a stratified group G, one can shape more general differential operators, for instance, with low regularity on the coefficients or of a non-variational type: these are also a subject of my research.

The main motivation of my studies derives from the attention paid (over the past three decades) to subelliptic PDOs on stratified groups: the interest in these algebraic structures in the PDE context is both theoretical and in the applications. Indeed, linear and non-linear partial differential equations, in variational or non-variational form appear in various contexts: the geometric theory of the functions with several complex variables; complex mathematical modeling of crystalline materials; curvature problems for Cauchy-Riemann manifolds; control theory; sub-Riemannian geometry; diffusion processes; mathematical modeling of human or computer vision; Mathematical Finance, etc.

Among the algebraic-geometric structures often associated with these equations, one encounters with the stratified groups (also referred to as Carnot groups), a sub-class of the nilpotent Lie groups, whose associated Lie algebra admits a stratification, i.e., a decomposition in layers the form g+[g;g]+[[g;g];g]+.... This decomposition enriches these groups in a remarkable way, making them relatively simple to be studied with elementary and direct methods. Naturally associated with the Carnot groups are their sub-Laplacians, differential operators of the second-order which are sums of squares of vector fields generating the first layer g. The usual additive group on R^N and the classic Laplace operator Δ are certainly the simplest examples of (Abelian) stratified group and of sub-Laplacian (strictly elliptic);
the well-known Heisenberg group H^n and the associated Kohn-Laplacian Δ_H are, instead, the first nontrivial example of a (non-commutative) stratified group, and of a degenerate-elliptic sub-Laplacian. It is immediately evident from the Heisenberg-group example that, although the sub-Laplacians share many properties with elliptic operators, one cannot expect all the classical results to apply in the non-Euclidean setting as well, let alone can the methods be the same as in the non-degenerate elliptic case.

My scientific work is divided into the following topics, closely related to each other:

- The study of the structure of the Carnot groups and their sub-Laplacians L.
- The study of the heat operator H = L-partial_t on Carnot groups and of some non-divergence operators modeled on L and H on more general structures than the Carnot groups.
- The Potential Theory for L and for operators in divergence or non-divergence form on Lie groups whatsoever (not necessarily Carnot).
- Applications of the celebrated Campbell-Baker-Hausdorff-Dynkin Theorem (CBHD, in the sequel) to the theory of Lie groups, of ODEs and PDEs.

In the following, we provide a very brief description of these research topics.

(1) Throughout my scientific activity, I have studied the structure of Carnot groups and the analytic properties of the associated sub-Laplacians. For example, in the papers [8, 9, 10, 12, 20, 27, 28, 29, 30, 34], together with specific problems of analysis, it is supplied part the algebraic-geometric background needed for the close study of stratified groups, always following a direct analytical approach. In particular, we compare the classical definition of Carnot group to a more operative definition of homogeneous Carnot group, extremely useful in the analytical context. Some topics that we deepened, of interest for mathematical analysis, are therefore geometrical: for example, we investigated the free and nilpotent algebras, the process of lifting of stratified groups to free groups, the equivalence of sub-Laplacians modulo diffeormorphisms, the so-called formula of Campbell-Baker-Hausdorff-Dynkin, the construction of Carnot groups by means of vector fields on R^N, the H-type algebras and groups, Taylor's formula for homogeneous groups, the notion of convexity etc. One of the classes of Carnot groups that I studied more closely is that of the H-type groups: having characterized such groups in sufficient explicitness, we studied a non-existence result for a semi-linear problem with critical exponent on all the half-spaces (characteristic and not) of the H-type groups (see [7, 8]). This result improves recent investigations in this setting.
Besides, I studied more general structures than the Carnot groups: the homogeneous groups [21], and groups (not necessarily nilpotent) which one can construct on RN starting from certain Hörmander vector fields (see [24, 25, 26, 29]). In the first setting, I proved the analogue of Taylor's formula (with applications to Schauder estimates and to problems of real analyticity); within the second structures, we proved the existence and the good properties of the fundamental solution, including a property of left-translation invariance; also, we provided necessary and sufficient conditions for a set of Hörmander vector fields to be left-invariant on some Lie group.

(2) The quoted algebraic and geometric background needed for the study of the stratified groups and their sub-Laplacians is widely and thoroughly treated in the monograph [20], whose goal is precisely to providing detailed analytical and geometrical features of sub-Laplacians on stratified groups, together with the Potential Theory associated with them. More recently, I have been able to deepen the algebraic study of these groups, starting from one of the most important and significant results on Lie groups: the formula that brings the names of Baker, Campbell, Dynkin and Hausdorff. The study of this formula (with complete demonstrations) is approached with algebraic methods (associated with certain tensor algebras of formal series), with analysis techniques (of certain ordinary differential equations), and of differential geometry (of Lie groups). A unitary and self-contained treatise with all these different approaches appears in the monograph [27]; some side observations of purely algebraic nature are collected in [28] and a proof of a formula of Campbell-Hausdorff type relative to a context of ordinary differential equations is studied in [26] (and improved in [39]).

We explicitly remark that there still are open issues on the formula of Baker-Campbell-Hausdorff-Dynkin, i.e., its q-analog, appearing in the theory of quantum mechanics. We obtained (joint work with Jacob Katriel) some definitive results in this setting in [40].

(3) A significant part of my research is devoted to the Potential Theory for sub-Laplacians L on stratified groups. Starting from the good properties of the fundamental solution Γ of L, it is possible to reconstruct much of the classical theory such as: Harnack-Liouville theorems; characterizations of subharmonicity for L; average formulas for L and representation theorems; formulas of Poisson&Jensen type; capacity and energy for L; the formula of Pizzetti on Heisenberg groups and H-type groups. See the works [1, 2, 3, 5, 13, 15, 17, 22]. As significant applications of Potential Theory, we obtained: maximum principles on unbounded domains [3]; finne regularity properties [15]; the study of the Dirichlet problem associated with L with L^p data and the Hardy spaces associated with them [17]. Another application is given for the study of the Eikonal equation and theorems of Bôcher-type for singularity removal [19].
Very recently, I have dealt with Potential Theory for operators in divergence-form, but not necessarily under the form of sums of squares of Hörmander vector fields, nor necessarily left-invariant on Lie groups.

It is shown that in the presence of a positive fundamental solution (and vanishing at infinity) one can give a complete theory of subharmonic functions and their associated mean-value operators [33, 35, 37]. Some of the characterizations of subharmonicity provided in the cited works are new even in the case of the classical Laplacian (see also the recent paper [36]). In the framework of not necessarily stratified groups, and using representation formulas, we very recently proved some Lp-Liouville theorems, [43]. Outside the framework of Hörmander operators, we also demonstrated a Harnack inequality and maximum-propagation principles for hypoelliptic divergence-form operators with possibly infinite-degenerate coefficients; see [41].

(4) Another direction of my research has been devoted to the heat operator on Carnot groups (Gaussian estimates for the fundamental solution and its derivatives, Harnack inequality, nonnegative caloric functions): see [4, 6, 11, 14, 18]. These results apply to the study of a non-divergence class of operators with non-smooth coefficients. These operators are the linearizations of some fully nonlinear operators (e.g., curvature operators, Levi-Monge-Ampère operators). In particular, we have proved the Harnack inequality and the existence of the relevant fundamental solution, by using an adaptation of the Levi Parametrix method. Such method is based on uniform Gaussian estimates for the "frozen" operators, which are also obtained by using Lifting results. The approach used is consistent with the direct approach used in the study of stratified groups, in particular by making use of elements of Potential Theory. Useful for the study of these linearized operators is the notion of horizontal convexity (h-convexity) on Carnot groups, [23]. In this regard, we obtained both algebraic and differential-geometric results on h-convexity: in particular we have shown that h-convex functions "lift" to h-convex functions when a Carnot group is lifted to its free nilpotent group. Also, an example is given of a gauge function on a group of step two with unexpected properties of non-convexity, negatively answering to a problem so far open. Weak characterizations of h-convexity were then obtained in a recent work [34].

Invited talks and events:
1) Seminar "Liouville-type theorems for sub-Laplacians on Carnot groups and applications", during the meeting "Liouville Theorems in Riemannian and Sub-Riemannian settings", Bologna, November 23rd-24th 2006, Dept. of Mathematics, Bologna.
2) Talk "Some Results on Convex Functions on Carnot Groups: Lifting and Gauge-Functions", during the meeting "Viscosity, metric and control theoretic methods in nonlinear PDE's: analysis, approximations, applications", Rome, September 3rd-5th 2008, La Sapienza.
3) Seminar "Subharmonic functions in sub-Riemannian settings: Characterizations of subharmonicity", Pisa, February 22nd 2012, during the "A one day workshop on Symmetry, Subharmonicity and Nonsmooth Vector Fields", Department of Mathematics, Pisa University.
4) Seminar "Gruppi di Lie associati ad alcune classi di operatori di Hörmander", Dept. of Mathematics, Padova University (February 21st 2013), during the "Seminario di Equazioni Differenziali e Analisi Complessa".
5) Talk "Infinito in Matematica: Alcune suggestioni", Dept. of Mathematics, Bologna University (April 12th 2013), during the "Giornata Matematica per gli studenti Liceo Righi".
6) Talk "L'Infinito in Matematica", during the "Convegno Scientifico sul P.L.S.", Città della Scienza, Naples, December 12th-13th 2013.
7) Talk "Maximum principles and Harnack inequality for divergence-form hypoelliptic operators" (June 25th 2014), during the Conference "CR Geometry and PDEs - VI" (June 23-27, 2014, Levico Terme, Trento, Italy).
8) From September 7th, to October 3rd, 2014: Invitation to the Trimester "Geometry, Analysis and Dynamics on Sub-Riemannian Manifolds" (September 1st - December 12th, Paris, 2014) at the Institut Henri Poincaré (I.H.P.), Paris.
9) Talk: "Maximum principle and Harnack inequality for hypoelliptic degenerate non-Hörmander operators" (September 10th, 2014), at the Institut Henri Poincaré (I.H.P.) in Paris, for the seminars "Séminaire de géométrie sous-Riemannienne", during the Trimester "Geometry, Analysis and Dynamics on Sub-Riemannian Manifolds".

Departmental seminars:
1) Gruppi di Carnot associati a campi vettoriali, Mathematical Analysis Seminar, January 15th 2002, Dept. of Mathematics, Bologna.
2) Un teorema di Liouville non lineare sui semispazi dei gruppi di passo due, Mathematical Analysis Seminar, February 25th 2003, Dept. of Mathematics, Bologna.
3) La formula di Taylor sui gruppi omogenei e applicazioni, Mathematical Analysis Seminar, March 6th 2008, Dept. of Mathematics, Bologna.
4) I teoremi di Campbell, Baker, Hausdorff e Dynkin. Storia, prove, problemi aperti, Mathematical Analysis Seminar, May 20th 2010, Dept. of Mathematics, Bologna.
5) Algebras of complete Hörmander vector fields, and Lie-group construction, Mathematical Analysis Seminar, March 27th 2014, Dept. of Mathematics, Bologna.

[1] Liouville-type theorems for real sub-Laplacians (con E. Lanconelli) Manuscripta Math. 105, 111--124 (2001).
[2] Expansion of the Heisenberg integral mean via iterated Kohn Laplacians: a Pizzetti-type formula, Pot. Analysis 17, 165--180 (2002).
[3] Maximum Principle on unbounded domains for sub-Laplacians: a Potential Theory approach (con E. Lanconelli), Proc. Amer. Math. Soc. 130, 2295--2304 (2002).
[4]Uniform Gaussian estimates of the fundamental solutions for heat operators on Carnot groups (con E. Lanconelli, F. Uguzzoni), Adv. Differential Equations 7, 1153-1192 (2002).
[5] Subharmonic functions on Carnot groups (con E. Lanconelli), Math. Ann. 325, 97--122 (2003).
[6] Levi's parametrix for some sub-elliptic non-divergence form operators (con E. Lanconelli, F. Uguzzoni), Electron. Res. Announc. Math. Sci. 9, 10--18 (2003).
[7] Some non-existence results for critical equations on step-two stratified groups (con F. Uguzzoni), C. R. Acad. Sci. Paris Sér. I Math. 336, 817--822 (2003).
[8] Nonlinear Liouville theorems for some critical problems on H-type groups (con F. Uguzzoni), J. Funct. Anal. 207, 161--215 (2004).
[9] Homogeneous Carnot groups related to sets of vector fields, Bollettino U.M.I. (8) 7-B, 79--107 (2004).
[10] Families of diffeomorphic sub-Laplacians and free Carnot groups (con F. Uguzzoni), Forum Math. 16, 403--415 (2004).
[11] Fundamental solutions for non-divergence form operators on stratified groups (con E. Lanconelli, F. Uguzzoni), Trans. Amer. Math. Soc. 356, 2709--2737 (2004).
[12] A note on lifting of Carnot groups (con F. Uguzzoni), Rev. Mat. Iberoamericana 21, 1013--1035 (2005).
[13] A Poisson-Jensen type representation formula for subharmonic functions on stratified Lie groups (con C. Cinti), Pot. Analysis 22, 151--169 (2005).
[14] Representation formulas and Fatou-Kato theorems for heat operators on stratified groups (con F. Uguzzoni) Rendiconti di Matematica, Serie VII, 25, 53--67 (2005).
[15] The theory of energy for sub-Laplacians with an application to quasi-continuity (con C. Cinti) Manuscripta Math. 118, 283--309 (2005).
[16] Maximum principle and propagation for intrinsicly regular solutions of differential inequalities structured on vector fields (con F. Uguzzoni) J. Math. Anal. Appl. 322, 886--900 (2006).
[17] Dirichlet problem with L^p-boundary data in contractible domains of Carnot groups (con E. Lanconelli), Ann. Sc. Norm. Super. Pisa, Cl. Sci. 5, 579--610 (2006).
[18] Harnack inequality for non-divergence form operators on stratified groups (con F. Uguzzoni) Trans. Amer. Math. Soc. 359, 2463—2481 (2007).
[19] Gauge functions, Eikonal equations and Bocher's theorem on stratified Lie groups (con E. Lanconelli) Calc. Var. Partial Diff. Equations 30, 277--291 (2007).
[20] Stratified Lie Groups and Potential Theory for their sub-Laplacians, Monografia (ca. 800 pagine) (con E. Lanconelli, F. Uguzzoni), Springer Monographs in Mathematics, vol. XXVI. New York, NY: Springer-Verlag, 2007 (XXVI p. + 800 p.). ISSN: 1439-7382, ISBN-10 3-540-71896-6.
[21] Taylor formula for homogeneous groups and applications, Math. Z. 262, 255--279 (2009).
[22] Pizzetti's formula for H-type groups, Potential Analysis 31, 311--333 (2009).
[23] Lifting of convex functions on Carnot groups and lack of convexity for a gauge function, Archiv der Math. 93, 277--286 (2009).
[24] On left invariant Hörmander operators in R^N. Applications to Kolmogorov-Fokker-Planck equations (con E. Lanconelli), Journal of Mathematical Sciences 171, n.1, 22--33 (2010).
[25] On left-invariant Hörmander operators in R^N: applications to the Kolmogorov-Fokker-Planck equations (con E. Lanconelli), (Russian) Sovrem. Mat. Fundam. Napravl. 36, 24--35 (2010).
[26] An ODE's version of the formula of Baker, Campbell, Dynkin and Hausdorff and the construction of Lie groups with prescribed Lie algebra, Mediterr. J. Math. 7, 387--414 (2010).
[27] Topics in Noncommutative Algebra. The Theorem of Campbell, Baker, Hausdorff and Dynkin (con R. Fulci), Lecture Notes in Mathematics, vol. 2034, Springer-Verlag, 2011 (XXII p.+ 498 p.). ISBN 978-3-642-22596-3
[28] A new proof of the existence of free Lie algebras and an application (con R. Fulci), ISRN Algebra, Volume 2011 (2011), Article ID 247403, 11 pages. doi:10.5402/2011/247403
[29] Lie groups related to Hörmander operators and Kolmogorov-Fokker-Planck equations (con E. Lanconelli), Commun. Pure Appl. Anal. 11, 1587--1614 (2012).
[30] A new characterization of convexity in free Carnot groups (con E. Lanconelli), Proc. Amer. Math. Soc. 140, 3263--3273 (2012).
[31] Matrix exponential groups and Kolmogorov-Fokker-Planck equations (con E. Lanconelli), J. Evol. Equ. 12, 59--82 (2012)
[32] The early proofs of the Theorem of Campbell, Baker, Hausdorff and Dynkin (con R. Achilles), Arch. Hist. Exact Sci. 66, 295--358 (2012).
[33] On the Dirichlet problem and the inverse mean value theorem for a class of divergence form operators (con B. Abbondanza), J. London Math. Soc., 1--26 (2012); doi: 10.1112/jlms/jds050.
[34] H-convex distributions in stratified groups (con E. Lanconelli, V. Magnani, M. Scienza), Proc. Amer. Math. Soc. 141 (2013), 3633–3638.
[35] Subharmonic functions in sub-Riemannian settings (con E. Lanconelli), J. Eur. Math. Soc. (JEMS) 15 (2013), no. 2, 387–441.
[36] On the convergence of the Campbell-Baker-Hausdorff-Dynkin series in infinite-dimensional Banach-Lie algebras (con S. Biagi), Linear Multilinear Algebra 62 (2014), 1591–1615.
[37] Convexity of average operators for subsolutions to subelliptic equations (con E.Lanconelli e A.Tommasoli), Anal. PDE 7 (2014), 345–373.
[38] Normal families of functions for subelliptic operators and the theorems of Montel and Koebe (con E. Battaglia), J. Math. Anal. Appl. 409 (2014), 1–12.
[39] A completeness result for time-dependent vector fields and applications (con S.Biagi), Commun. Contemp. Math. 17 (2015), no. 4, 1450040, 1-26.
[40] The q-deformed Campbell-Baker-Hausdorff-Dynkin theorem (con R.Achilles e J.Katriel), Electron. Res. Announc. Math. Sci. 22 (2015), 32–45.

[41] The strong maximum principle and the Harnack inequality for a class of hypoelliptic non-Hörmander operators (con E.Battaglia e S.Biagi) Ann. Inst. Fourier (Grenoble) 66, 589-631 (2016).
[42] A Hadamard-type open map theorem for submersions and applications to completeness results in control theory (con A.Montanari e D.Morbidelli), Ann. Mat. Pura Appl. 195, 445-458 (2016).
[43] Weighted L^p-Liouville theorems for hypoelliptic partial differential operators on Lie groups (with A.E.Kogoj), J. Evol. Equ. 16, 569-585 (2016).

[44] Generating q-commutator identities and the q-BCH formula (with J. Katriel),
Advances in Mathematical Physics, Volume 2016, Article ID 9598409, 26 pages;

[45] The existence of a global fundamental solution for homogeneous H\"ormander operators
via a global Lifting method (with S. Biagi), Proc. London Math. Soc. 114 (2017), 855-889.

[46] An invariant Harnack inequality for a class of subelliptic operators under global doubling and Poincaré assumptions, and applications (with E. Battaglia), J. Math. Anal. Appl. 460, 302-320, 2018.

[47] On the Baker-Campbell-Hausdorff Theorem: non-convergence and prolongation issues (with. S. Biagi, M. Matone), to appear in Linear Multilinear Algebra (2019).

[48] "An Introduction to the Geometrical Analysis of Vector Fields - with Applications to Maximum Principles and Lie Groups." (with S. Biagi) World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2019. xxv+423 pp. ISBN: 978-981-3276-61-1

Scientific papers (informative and dissemination):

1) Bonfiglioli, A., Valentini, C. (editori): Matematica Arte e Tecnologia: da Escher alla Computer Graphics, Edizioni Aspasia, Bologna (2000).
2) "Matematica Arte e Tecnologia: da Escher alla Computer Graphics" Bologna, 12 ottobre - 3 dicembre 2000 (with C. Valentini), in "Matematica, Arte, Tecnologia, Cinema" Atti della Mostra e del Convegno, Bologna 2000, Springer Italia (2001).
3) Mathematics meets Art: Escher, Reutersvärd and Saffaro at Bologna 2000 (with C.Valentini), in "Mathematics, Art, Technology, and Cinema" a cura di M. Emmer, Springer Verlag, 2003, 33--38.
4) Analisi del Laboratorio P.L.S. "L'Infinito Matematico: Alcune Suggestioni" (374-378.), in: "L'insegnamento della matematica e delle scienze nella società della conoscenza. Il Piano Lauree Scientifiche (PLS) dopo 10 anni di attività" (Atti del Convegno Scientifico sul PLS; Napoli, Dicembre 2013). Casa Editrice Mondadori: collana "Mondadori Università" (2014). A cura di: G.Anzellotti, L.M.Catena, M.Catti, U.Cosentino, J.Immè, N.Vittorio. ISBN 978-88-6184-408-7.
5) Alcune considerazioni e suggestioni sull'infinito in matematica, in: "Parliamo tanto e spesso di didattica della matematica", Atti del Convegno "Incontri con la Matematica" n.28 (Castel S.Pietro Terme, novembre 2014); Collana: Incontri con la Matematica, a cura di B.D'Amore e S.Sbaragli, 2014. ISBN 88-371-1901-1

Departmental seminars:

-Gruppi di Carnot associati a campi vettoriali, in: Seminario di Analisi Matematica, Dipartimento di Matematica dell'Università di Bologna; Anno Accademico 2001/2002, 27-46, Tecnoprint: Bologna (2002).
- Un teorema di Liouville non lineare sui semispazi dei gruppi di passo due, in: Seminario di Analisi Matematica, Dipartimento di Matematica dell'Università di Bologna; Anno Accademico 2002/2003, 25-33, Tecnoprint: Bologna (2003).
- Gauge functions, eikonal equation and Bôcher theorem on stratified Lie groups (con E. Lanconelli), in: Mathematical Analysis Seminar, University of Bologna Department of Mathematics: Academic Year 2005/2006 (Italian), 55-63, Tecnoprint: Bologna (2007).
- Taylor formula for homogeneous groups and applications, in: "Bruno Pini" Mathematical Analysis Seminar: University of Bologna Department of Mathematics: Academic Year 2007/2008 (Italian), 43-69, Tecnoprint: Bologna (2008).
- I Teoremi di Campbell, Baker, Hausdorff e Dynkin. Storia, prove, problemi aperti in: "Bruno Pini" Mathematical Analysis Seminar (electronic, ISSN 2240-2829), University of Bologna Department of Mathematics: Academic Year 2009/2010 (Italian), 1-47 (2008).
- Algebras of complete Hörmander vector fields, and Lie-group construction, in: Mathematical Analysis Seminar (2014), Dept. of Mathematics, Bologna.

Membership in Research Projects:
1) Accepted proposal "Senior Fellowship" granted by I.S.A. (Istituto di Studi Avanzati) of Bologna; three-month guest: Prof. Jacob Katriel (Technion - Israel Institute of Technology).
2) Member of the Organizing Committee for the Meeting "Geometric methods in PDE's", INDAM Meeting on the occasion of the 70th birthday of Ermanno Lanconelli; Cortona 27-31/5/2013.
3) Scientific Coordinator of the G.N.A.M.P.A. Project 2012, "Equazioni alle Derivate Parziali Lineari e non-Lineari in Contesti sub-Riemanniani" (June 2012/May 2013).
4) Member of the P.R.I.N. Program 2009 (Programmi di Ricerca Scientifica di Rilevante Interesse Nazionale). Title: "Equazioni di diffusione in ambiti sub-riemanniani e problemi geometrici associati". Coordinator: Prof. I. Capuzzo Dolcetta, Responsabile scientifico: Prof. E. Lanconelli; Ateneo: Università degli Studi di Bologna, protocollo: 2009KNZ5FK 005.
5) Member of the P.R.I.N. Program 2007 (Programmi di Ricerca Scientifica di Rilevante Interesse Nazionale). Title: "Equazioni subellittiche e problemi geometrici associati". Coordinator: Prof. I. Capuzzo Dolcetta, Responsabile scientifico: Prof. E. Lanconelli; Ateneo: Università degli Studi di Bologna, protocollo: 2007WECYEA 003.
6) Member of the R.F.O. Project 2010 (Ricerca Fondamentale Orientata). Coordinator: Prof. B. Franchi.
7) Member of the G.A.L.A. Project (Geometrical Analysis in Lie groups and Applications). Coordinator: Prof. G. Citti. STREP EU-FP6; September 2006-2009.
8) Member of the A.G.A.P.E. Project (Analysis in Lie Groups and Applications to Perceptual Emergences). Coordinator: Prof. G. Citti. University of Bologna; March 2011-2016.
9) Member of Progetto Giovani Ricercatori 1998. Title: "Moto per curvatura di Levi di ipersuperfici reali in C^n". Coordinator: Prof. A. Montanari; E.F. 1998.
10) Member of Progetto Giovani Ricercatori 1999. Title: "Equazioni differenziali degeneri non ipoellittiche in finanza matematica". Coordinator: Prof. A.Pascucci; E.F. 1999.
11) Coordinator of Progetto Giovani Ricercatori 2000. Title: "Disuguaglianza di Harnack e teoremi di esistenza per una classe di equazioni non lineari con forma caratteristica semidefinita positiva" E.F. 2000.

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Bologna, July 8th, 2019.
Prof. Andrea Bonfiglioli