Curriculum vitae

Academic record: • 1995-1999 Undergraduate student in the Faculty of Science of the Univer- sity of Trento, Italy. • Laurea in Fisica (best possible grade: 30 cum laude) , thesis “Sistemi di riferimento quantistici” [Quantum reference frames], defended on Novem- ber 16th, 1999 in Trento. • 1999-2003 Ph.D.student at the Department of of the Uni- versity of Trento, Italy. • In the period 31/1/2001 - 28/2/2002 guest of the Professor David Elworthy at the Institute of mathematics of the University of Warwick. • In the period 28/4/2002 - 31/5/2002 guest of Professor Sergio Albeverio at the Institute of applied mathematics of the . • In the period 15/9/2002-15/2/2003 Marie Curie fellow at the Institute of applied mathematics of the University of Bonn, with the support of the EU Research Training Network ”Quantum Probability with Applications to , and Biology” (http://www.math−inf.uni− greifswald.de/algebra/qp applications/). • PhD in mathematics, thesis “Feynman path integrals”, defended on Novem- ber the 3rd 2003 in Trento. • In the period 1/2/2004 - 30/9/2006 research fellow of I.N.d.A.M. (Isti- tuto Nazionale di Alta Matematica), as author of the research project I.D.A. (Functional integration with applications in and quantum field theory) financially supported by the “Provincia Au- tonoma di Trento”.

• 1/1/2007 - 31/3/ 2007 Alexander von Humboldt fellow at the Institute of applied mathematics of the University of Bonn. • 1/4/2007 -30/4/2009 ”Francesco Severi” fellow of I.N.d.A.M. (Istituto Nazionale di Alta Matematica) at the math department of Trento Uni- versity. • 1/8/2009-31/1/2010 Alexander von Humboldt fellow at the Hausdorff Centre for Mathematics, University of Bonn (Germany) . • 1/5/2010-30/4/2011 research fellow at the department of mathematics of the with a 12 month fellowship on ”functional integration”. • 1/5/2011-31/3/2012 Post-Doc research fellow at CIRM (Centro Inter- nazionale per la ricerca Matematica)-FBK, Trento (Italy) as author of the research project ”Functional integration with applications to quan- tum dynamical systems”. • 1/4/2012-30/6/2012 Alexander von Humboldt fellow at the Hausdorff Centre for Mathematics, University of Bonn (Germany) . • 15/7/2012-14/8/2013 Post-Doc research fellow at CIRM (Centro Inter- nazionale per la ricerca Matematica)-FBK, Trento (Italy) • September 2013-April 2015 assistant professor (fixed term contract) at the department of mathematics of Trento University. • Since 1st Mai 2015 assistant professor (tenured track) at the department of mathematics of Trento University.

Meetings attended: • Summer School in probability , Saint Flour (France), August 2000. • Stochastic differential equations and related topics, Scuola Normale Supe- riore Pisa (I), June 2001 • Summer School in quantum probability and quantum computation , Trento (I), July 2001. • Stochastic differential equations and related topics, Oberwolfach (D), Oc- tober 2001. Presentation of a poster. • School in evolution semigroups, Levico (TN) (I), November 2001. • Stochastic differential equations and related topics, Levico (TN) (I), Jan- uary 2002. Presentation of two posters. • Workshop Probabilistic methods: classical and quantum dynamical sys- tems, Trento (I), March 2002. Invited talk ”A representation of Belavkin equation via Feynman path integrals”. • Invited speaker at the workshop Feynman path integrals and related top- ics, at MSRI University of Berkeley (California), 9-12 December 2002. Talk ”New developments of rigorous Feynman path integrals and applica- tion to a stochastic Schr¨odinger equation”. • Young Researchers Symposium, in connection with the XIV International Congress of Mathematical Physics, Instituto superiore tecnico, , 25-26 July 2003. • Invited speaker at the XIV International Congress of Mathematical Physics, University of Lisbon, July 28 - August 2, 2003. Talk ”Some new develop- ments in Feynman path integrals and applications”

• workshop Kolmororov equations ”Ennio De Giorgi” Center, Scuola Nor- male Superiore, Pisa, 17-18 October 2003. Invited talk ”Some new developments in Feynman path integrals”.

• Stochastic differential equations and related topics, Levico (TN) (I), Jan- uary 2004.

• school Mathematical methods in quantum mechanics 21-26 February 2005, Bressanone (BZ) Italy. Invited talk ”New developments of rigorous Feyn- man path integrals”.

• Invited plenary speaker to the annual meeting of the German Mathemat- ical society, Bonn, September 18-22 2006. Talk ”Feynman path integrals as infinite dimensional oscillatory integrals”.

• Invited speaker to the joint meeting UMI-DMV, Perugia, June 18-22 2007. Invited talk ”Infinite dimensional oscillatory integrals with polynomially growing phase function”.

• Workshop Probabilistic methods: classical and quantum dynamical sys- tems, Trento (I), November 2008. Talk ”Functional integral construction of the solution of the Schr¨odinger equation for the inverse quartic oscilla- tor”.

• Invited speaker at the meeting Feynman Path Integrals and their Applica- tions, 18-19 January 2010, Mathematics department, Swansea University. Invited talk “The quartic oscillator: a Feynman path integral approach”.

• Invited speaker at first CIRM-HCM Joint Meeting Stochastic Analysis, SPDEs, Particle Systems, Optimal Transport, 24-30 January 2010, Levico Terme (Trento), Italy. Invited talk “Functional integral representations for the solution of the Schr¨odinger equation”.

• school Mathematical methods in quantum mechanics 14-29 February 2011, Bressanone (BZ) Italy.

• workshop Deterministic and stochastic methods in evolution problems, 7-9 September 2011, Parma, Italy. Invited talk “Probabilistic representations for the solution of higher order PDEs”.

• Invited speaker at the meeting ”Quantum Physics and Bethe Ansatz” at the Dublin Institute of Advanced Studies, Dublin 8-10 October 2012. Invited talk ”Feynman path integrals as infinite dimensional oscillatory integrals”. • Invited speaker at the 2013 Joint Meeting American Mathematical Society - Mathematical Association of America, in the AMS special session on ”In- terplays Between Feynman Operational Calculus, Wiener and Feynman Integrals, Physics and Analysis on Wiener Space”, 9-12 January 2013. Invited talk ”Feynman path integrals as infinite dimensional oscillatory integrals”. • Invited speaker at the colloquium of the Berlin-Brandenburg Sonderforschung- bereich ”Space-Time-Matter” in Potsdam (Germany), 5th February 2013. Invited talk ”Feynman path integrals as infinite dimensional oscillatory integrals” • Conference ”Stochastic Partial Differential Equations and Applications - IX”, Levico (TN), 6-11 January 2014. Invited talk ”Probabilistic repre- sentations for the solutions of high order heat-type equations”. • Speaker at the conference ”Operator and Geometric Analysis in Quan- tum Theory”, Levico Terme (Trento), 15-19 September 2014. Invited talk ”Infinite dimensional integration techniques and applications to quantum mechanics”. • Invited plenary speaker at the Workshop on Path Integral and Pseudo- Differential Operators, RIMS, Kyoto University, 7-10 October 2014. In- vited talk ”Feynman Path Integrals as Infinite DImensional Oscillatory Integrals”. • Invited plenary speaker at the Workshop ”Feynman integral with har- monic analysis and related topics”, NIMS (National Institute for Mathe- matical Sciences) Daejeon, South Korea, 20-22 Mayo 2015. Invited talk ”Infinite dimensional integration of oscillatory type and applications ”. • Invited speaker at the Workshop ”Classic and Stochastic Geometric Me- chanics”, CIB (Centre Interfacultaire Bernoulli), Ecole´ polytechnique fd´rale´ de Lausanne, 08 - 11 June 2015. SInvited talk ”A probabilistic represen- tation for the solution of high-order heat-type equations”.

Courses taught: • Academic Year 2000/01: Assistant Lecturer (course “ 1” (undergrad. Mathematics and Physics)) University of Trento • Academic Year 2001/02: Assistant Lecturer (course “Ordinary differential equations in Mathemat- ical Physics” (undergrad. Mathematics )) University of Trento Assistant Lecturer (course “Partial differential equations in Mathematical Physics” (undergrad. Mathematics and Physics) University of Trento) Assistant Lecturer (course “Rational mechanics” (undergrad. )University of Trento) • Academic Year 2002/03: Assistant Lecturer (course “Ordinary differential equations in Mathemat- ical Physics” (undergrad. Mathematics ) University of Trento) Assistant Lecturer (course “Partial differential equations in Mathematical Physics” (undergrad. Mathematics and Physics) University of Trento) Assistant Lecturer (course “Rational mechanics II” (undergrad. Engineer- ing )University of Trento) • Academic Year 2003/04: Assistant Lecturer (course “Ordinary differential equations in Mathemat- ical Physics” (undergrad. Mathematics ) University of Trento) Assistant Lecturer (course “Rational mechanics II” (undergrad. Engineer- ing ) University of Trento) • Academic Year 2004/05: Assistant Lecturer (course “Partial differential equations in Mathematical Physics” (undergrad. Mathematics and Physics) University of Trento) Assistant Lecturer (course “Rational mechanics II” (undergrad. Engineer- ing ) University of Trento) • Academic Year 2005/06: Assistant Lecturer (course “Analysis 1-2-3” (undergrad. Mathematics and Physics) University of Trento) Assistant Lecturer (course “Rational mechanics II” (undergrad. Engineer- ing ) University of Trento) • Academic Year 2009/10: Lecturer (course “Feynman Path integrals” (Ph.D students in Mathemat- ics) University of Trento)

• Academic Year 2010/11: Assistant Lecturer (course “Analysis 2” (undergrad. Engineering ) Uni- versity of Trento)

• Academic Year 2011/12: Assistant Lecturer (course “Analysis 2” (undergrad. Engineering ) Uni- versity of Trento) Lecturer (course “Complements of mathematical analysis” (undergrad. Engineering ) University of Trento)

• Academic Year 2012/13: Assistant Lecturer (course “Analysis 2” (undergrad. Engineering ) Uni- versity of Trento) Lecturer (course “Complements of mathematical analysis” (undergrad. Engineering ) University of Trento) • Academic Year 2013/14: Lecturer (course “Complements of mathematical analysis” (undergrad. Engineering ))

• Academic Year 2014/15: Lecturer (course “Analysis 2” (undergrad. Engineering ) University of Trento) Lecturer (with Prof. S. Albeverio) of the course ”Mathematical theory of Feynman path-integrals” (Ph.D students in Mathematics, University of Milan)

Refereeing/reviews:

• Refereeing for Mathematical Physics Electronic Journal, Journal of Dif- ferential Equations, J. Phys. A: Math. Theor., J. Math. Phys., Journal of Function spaces and Applications. • Reviews for Math Reviews (American Mathematical Society). • Member of the editorial board of Frontiers in Mathematical Physics

Languages: Italian (mother language), English, German.

Partecipation in/coordination of research projects:

• 2002-2003 member of the EU Research Training Network Quantum Proba- bility with Applications to Physics, Information Theory and Biology (http://www.math− inf.uni − greifswald.de//qp applications/) • 2004 - 2006 author and coordinator of the individual research project I.D.A. (Functional integration with applications in quantum mechanics and quantum field theory) financially supported by PAT (Provincia Autonoma di Trento). • 2006-2007 author and coordinator of the individual research project Func- tional integration with applications in quantum mechanics and quantum field theory, financially supported by the Alexander von Humboldt foun- dation with an Alexander von Humboldt fellowship. • 2007 - 2009 author and coordinator of the individual research project Func- tional integrals and application to quantum theory financially supported by I.N.d.A.M. (Istituto Nazionale di Alta Matematica) with a ”Francesco Severi” fellowship. • 2011-2013 author and coordinator of the individual research project Func- tional integration with applications to quantum dynamical systems finan- cially supported by CIRM (Centro Internazionale per la ricerca Matematica)- FBK, Trento (Italy), with a Post-Doc fellowship.

• Member of Research National Project (PRIN 2002) Equazioni di Kol- mogorov, equazioni differenziali stocastiche alle derivate parziali ed appli- cazioni alla dinamica delle popolazioni e alla teoria dei campi quantistici (nationally directed by Prof. G. Da Prato)

• Member of Research National Project (PRIN 2004) Equazioni di Kol- mogorov, equazioni differenziali stocastiche alle derivate parziali ed appli- cazioni alla dinamica delle popolazioni e alla teoria dei campi quantistici (nationally directed by Prof. G. Da Prato)

• Member of Research National Project (PRIN 2006) Equazioni di Kolmoro- rov e applicazioni (nationally directed by Prof. G. Da Prato)

• Member of Research National Project (PRIN 2008) Problemi di evoluzione: analisi di modelli deterministici e stocastici ed applicazioni (nationally di- rected by Prof. A. Lunardi)

• Member of Research National Project (PRIN 2010-2011) Problemi dif- ferenziali di evoluzione: approcci deterministici e stocastici e loro inter- azioni (nationally directed by Prof. M. Fuhrman).

Projects submitted as PI:

• Futuro in Ricerca (FIRB) 2008. Project ”Integrazione funzionale e appli- cazioni” (Functional integration and applications)

• Futuro in Ricerca (FIRB) 2013. Project ”Integrazione funzionale e appli- cazioni ad equazioni di evoluzione” (Functional integration and applica- tions to evolution equations) . Publications: Books:

• Albeverio S., Høegh-Krohn R. and Mazzucchi S. Mathematical theory of Feynman path integrals - An Introduction, 2nd cor- rected and enlarged edition, Lecture Notes in Mathematics, Vol. 523. Springer, Berlin (2008).

• S. Mazzucchi, Mathematical Feynman path integrals and applications. World Scientific Publishing Co. Singapore (2009).

• F. Bigolin, S. Mazzucchi, Esercizi di Calcolo Differenziale e Integrale vol.1 Funzioni di una variabile reale . ARACNE editrice (2011)

Articles in journals/contributions to books:

• S. Mazzucchi. On the observables describing a quantum reference frame. J. Math. Phys. 42 2477-2489 (2001) • S. Albeverio, G. Guatteri, S. Mazzucchi. Phase space Feynman path integrals. J. Math. Phys. 43 2847-2857 (2002)

• S. Albeverio, G. Guatteri, S. Mazzucchi. A representation of the Belavkin equation via Feynman path integrals. Probab. Theory Relat. Fields 125, 365-380 (2003).

• S. Albeverio, G. Guatteri, S. Mazzucchi, A representation of the Belavkin equation via phase space Feynman path integrals, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 7 (2004), no. 4, 507–526.

• S. Albeverio and S. Mazzucchi. Generalized infinite-dimensional Fresnel integrals. C. R. Acad. Sci. Paris 338 n.3, 255-259, (2004).

• S. Albeverio and S. Mazzucchi. Some New Developments in the Theory of Path Integrals, with Applica- tions to Quantum Theory. J. Stat. Phys. 115 n.112, 191-215, (2004).

• S. Albeverio and S. Mazzucchi. Generalized Fresnel integrals. Bull. Sci. Math. 129 (2005), no. 1, 1–23.

• S. Albeverio, S. Mazzucchi, Feynman path integrals for polynomially growing potentials J. Funct. Anal. 221 no. 1 (2005), 83–121. • S. Mazzucchi, Feynman path integrals Encyclopedia of Mathematical physics, eds. J.P. Francoise, G.L. Naber and Tsou S.T. Oxford: Elsevier, 2006, (ISBN 978-0-1251-2666-3), volume 2 page 307. • S. Albeverio, S. Mazzucchi, Feynman path integrals for the time dependent quartic oscillator, C. R. Math. Acad. Sci. Paris 341 (2005), no. 10, 647– 650. • S. Albeverio, S. Mazzucchi, The time dependent quartic oscillator - a Feynman path integral approach. J. Funct. Anal. 238,471-488 (2006) • S. Albeverio, L. Cattaneo, L. Di Persio, S. Mazzucchi, A rigorous approach to the Feynman-Vernon influence functional and its applications. I. J. Math. Phys. 48 (2007), no. 10, 102109. • S. Mazzucchi, Feynman path integrals for the inverse quartic oscillator. J. Math. Phys. 49, 093502 (2008) (15 pages). • S. Albeverio, S. Mazzucchi. An asymptotic functional-integral solution for the Schroedinger equation with polynomial potential. J. Funct. Anal. 257 (2009), no. 4, 1030–1052. http://dx.doi.org/10.1016/j.jfa.2009.02.005. • S. Albeverio, S. Mazzucchi. Infinite dimensional oscillatory integrals with polynomial phase function and the trace formula for the heat semigroup. From probability to geometry. Volume in honour of the 60th birthday of Jean-Michel Bismut. Ast´erisque 327 (I), (2009), 17-45. • G. Greco, S. Mazzucchi and E. Pagani, Peano on derivative of measures: strict derivative of distributive set functions. Rend. Lincei Mat. Appl. 21 (2010), 305–339. • S. Mazzucchi. Functional-integral solution for the Schr¨odinger equation with polynomial potential: a white noise approach. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 14, 4, 675-688 (2011). • S. Mazzucchi, Probabilistic representations for the solution of higher order differential equations. International Journal of Partial Differential Equations, Volume 2013. Ar- ticle ID 297857, 7 pages (2013). • S. Bonaccorsi, S. Mazzucchi. High order heat-type equations and random walks on the complex plane. Stochastic Processes and their Applications, Volume 125, Issue 2, February 2015, Pages 797-818. • S. Albeverio and S. Mazzucchi, An introduction to Infinite-dimensional Oscillatory and Probabilistic Integrals. In R. dalang, M. Dozzi, F. Flan- doli, F. Russo (editors) stochastic Analysis: A Series of Lectures. p. 1-54, Birkh¨auser (2015). • S. Albeverio and S. Mazzucchi. Infinite dimensional oscillatory integrals as projective systems of functionals. Journal of the Mathematical Society of Vol. 67, No. 4 (October, 2015), p. 1295 - 1316.

• G.H. Greco, S. Mazzucchi, The Originality of Peano’s 1886 Existence The- orem on Scalar Differential Equations. to appear in Journal of Convex Analysis, Volume 23 (2016).

Refereed Proceedings:

• S. Mazzucchi, Some new developments in Feynman path integrals and applications in Proceedings of the XIV International Congress of Mathematical Physics 505–511, World Sci. Publ., Hackensack, NJ, 2005.

• S. Albeverio, S. Mazzucchi, Integrali di Cammino di Feynman e Mis- urazione Quantistica, in Atti del colloqui di Matematica 2001-2003, Note di matematica e fisica, Edizioni Cerfim Locarno, anno 16, vol. 12, 123-156, 2003.

• S. Albeverio and S. Mazzucchi, Feynman path integrals for time-dependent potentials. ”Stochastic Partial Differential equations and Applications” Proceedings of the VIII Conference held in Trento, January 2004. Edited by G. Da Prato and L. Tubaro.

• S. Albeverio and S. Mazzucchi, Theory and applications of infinite dimensional oscillatory integrals. in : ”Stochastic Analysis and Applications”, Proceedings of the Abel Sym- posium 2005 in honor of Prof. Kiyosi Ito, 75-92 Springer (2006).

• Albeverio, S. Mazzucchi, A survey on mathematical Feynman path inte- grals: construction, asymptotics, applications. In: Fauser B., Tolksdorf J. Zeidler E. (eds.) : Com- petitive Models. Birkauser Boston (2008) pag. 49-66.

• S. Albeverio, S. Mazzucchi, Infinite dimensional integrals and their asymp- totics: some recent developments and applications. In: Proceedings of the conference “Stochastic Partial Differential Equa- tions and Applications” Levico (TN) 2008.

• S. Albeverio, S. Mazzucchi, The trace formula for the heat semigroup with polynomial potential, in: R.Dalang, M.Dozzi, F.Russo (Editors). Stochastic analysis, random fields and applications VI. Progress in Probability 63, Birkh¨user Verlag (2011), 3-21. • S. Mazzucchi, Feynman path integrals for quantum open systems. RIMS Kˆokyˆuroku No.1958, ”Introductory Workshop on Path Integrals and Pseudo- Differential Operators” Differential Operators” (2015), p. 96-116.

• S. Mazzucchi, Generalized Feynman-Kac formulae for the solution of high order heat-type equations. RIMS Kˆokyˆuroku No.1958, ”Introductory Work- shop on Path Integrals and Pseudo-Differential Operators” Differential Operators” (2015), p. 143-159.

Preprints: • S. Mazzucchi, Infinite dimensional oscillatory integrals with polynomial phase and applications to high order heat-type equations. arXiv:1405.4501 [math.FA] (2014).

• S. Albeverio and S. Mazzucchi, A unified approach to infinite dimensional integration . arXiv:1411.2853 [math.PR] (2014).

• G.H. Greco, S. Mazzucchi and E. Pagani. Peano on definition of surface area. arXiv:1412.2691 [math.HO] (2014)

Further:

• Invited author and curator of the article Path integral: mathematical as- pects on Scholarpedia: http://www.scholarpedia.org/article/Path integral: mathematical aspects

• Invited author and curator of the article Probabilistic integral: mathemat- ical aspects on Scholarpedia: http://www.scholarpedia.org/article/Probabilistic integral: mathematical aspects

• Collaboration with a of the medical physics units of the Trento ”Santa Chiara” hospital, and development of a mathematical method for the analysis of particular diagnostic images. The details are described in the paper: L. Menegotti, A. Delana, A. Martignano, V. Vanoni, S. Mazzucchi. 2D dosimetry with Gafchromic EBT: IMRT planning verification. Radio- therapy & Oncology 2006, 81(supplement 1):363. The technique developed in this article has been sold by the authors to an industrial company (ISP World Headquarters, International Specialty Products, 1361 Alps Road, Wayne, New Jersey 07470 USA), that has patented and practically implemented it.