Sonia Mazzucchi, born in Bolzano (Italy)

Curriculum vitae
Personal details:
Sonia Mazzucchi, born in Bolzano (Italy) on 25th December 1976.
married, three children.
Address:
viale Bolognini 46, Trento, Italy.
E-mail address:
[email protected]
Academic record:
• 1995-1999 Undergraduate student in the Faculty of Science of the University of Trento, Italy.
• Laurea in Fisica (best possible grade: 30 cum laude) , thesis “Sistemi di
riferimento quantistici” [Quantum reference frames], defended on November 16th, 1999 in Trento.
• 1999-2003 Ph.D.student at the Department of Mathematics of the University 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 University of Bonn.
• 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
Physics, Information Theory and Biology” (http://www.math−inf.uni−
greif swald.de/algebra/qp applications/).
• PhD in mathematics, thesis “Feynman path integrals”, defended on November the 3rd 2003 in Trento.
• In the period 1/2/2004 - 30/9/2006 research fellow of I.N.d.A.M. (Istituto Nazionale di Alta Matematica), as author of the research project
I.D.A. (Functional integration with applications in quantum mechanics
and quantum field theory) financially supported by the “Provincia Autonoma di Trento”.
The fellowship was suspended from September 2004 to January 2005 for
maternity (19/7/2004 birth of the first son).
The fellowship was interrupted on the 30th September 2006 for maternity
(30/9/2006 birth of the second son).
• 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 University.
• 30/1/2009 birth of the third child.
• 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 university of Trento with a 12 month fellowship on ”functional
integration”.
• 1/5/2011-31/3/2012 Post-Doc research fellow at CIRM (Centro Internazionale per la ricerca Matematica)-FBK, Trento (Italy) as author of
the research project ”Functional integration with applications to quantum 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 Internazionale per la ricerca Matematica)-FBK, Trento (Italy)
• Since September 2013 assistant professor (fixed term contract) 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 Superiore Pisa (I), June 2001
• Summer School in quantum probability and quantum computation , Trento
(I), July 2001.
• Stochastic differential equations and related topics, Oberwolfach (D), October 2001.
Presentation of a poster.
• School in evolution semigroups, Levico (TN) (I), November 2001.
• Stochastic differential equations and related topics, Levico (TN) (I), January 2002.
Presentation of two posters.
• Workshop Probabilistic methods: classical and quantum dynamical systems, 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 topics, at MSRI University of Berkeley (California), 9-12 December 2002.
Talk ”New developments of rigorous Feynman path integrals and application to a stochastic Schr¨odinger equation”.
• Young Researchers Symposium, in connection with the XIV International
Congress of Mathematical Physics, Instituto superiore tecnico, Lisbon,
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 developments in Feynman path integrals and applications”
• workshop Kolmororov equations ”Ennio De Giorgi” Center, Scuola Normale Superiore, Pisa, 17-18 October 2003.
Invited talk ”Some new developments in Feynman path integrals”.
• Stochastic differential equations and related topics, Levico (TN) (I), January 2004.
• school Mathematical methods in quantum mechanics 21-26 February 2005,
Bressanone (BZ) Italy. Invited talk ”New developments of rigorous Feynman path integrals”.
• Invited plenary speaker to the annual meeting of the German Mathematical 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 systems, Trento (I), November 2008. Talk ”Functional integral construction
of the solution of the Schr¨odinger equation for the inverse quartic oscillator”.
• Invited speaker at the meeting Feynman Path Integrals and their Applications, 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 ”Interplays 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 Sonderforschungbereich ”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 representations for the solutions of high order heat-type equations”.
• Speaker at the conference ”Operator and Geometric Analysis in Quantum 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 PseudoDifferential Operators , RIMS, Kyoto University, 7-10 October 2014.
Courses taught:
• Academic Year 2000/01:
Assistant Lecturer (course “Geometry 1” (undergrad. Mathematics and
Physics))
• Academic Year 2001/02:
Assistant Lecturer (course “Ordinary differential equations in Mathematical Physics” (undergrad. Mathematics ))
Assistant Lecturer (course “Partial differential equations in Mathematical
Physics” (undergrad. Mathematics and Physics))
Assistant Lecturer (course “Rational mechanics” (undergrad. Engineering
))
• Academic Year 2002/03:
Assistant Lecturer (course “Ordinary differential equations in Mathematical Physics” (undergrad. Mathematics ))
Assistant Lecturer (course “Partial differential equations in Mathematical
Physics” (undergrad. Mathematics and Physics))
Assistant Lecturer (course “Rational mechanics II” (undergrad. Engineering ))
• Academic Year 2003/04:
Assistant Lecturer (course “Ordinary differential equations in Mathematical Physics” (undergrad. Mathematics ))
Assistant Lecturer (course “Rational mechanics II” (undergrad. Engineering ))
• Academic Year 2004/05:
Assistant Lecturer (course “Partial differential equations in Mathematical
Physics” (undergrad. Mathematics and Physics))
Assistant Lecturer (course “Rational mechanics II” (undergrad. Engineering ))
• Academic Year 2005/06:
Assistant Lecturer (course “Analysis 1-2-3” (undergrad. Mathematics and
Physics))
Assistant Lecturer (course “Rational mechanics II” (undergrad. Engineering ))
• Academic Year 2009/10:
Lecturer (course “Feynman Path integrals” (Ph.D students in Mathematics))
• Academic Year 2010/11:
Assistant Lecturer (course “Analysis 2” (undergrad. Engineering ))
• Academic Year 2011/12:
Assistant Lecturer (course “Analysis 2” (undergrad. Engineering ))
Lecturer (course “Complements of mathematical analysis” (undergrad.
Engineering ))
• Academic Year 2012/13:
Assistant Lecturer (course “Analysis 2” (undergrad. Engineering ))
Lecturer (course “Complements of mathematical analysis” (undergrad.
Engineering ))
• Academic Year 2013/14:
Lecturer (course “Complements of mathematical analysis” (undergrad.
Engineering ))
• Academic Year 2014/15:
Lecturer (course “Analysis 2” (undergrad. Engineering ))
Refereeing/reviews:
• Refereeing for Mathematical Physics Electronic Journal, Journal of Differential 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 Probability with Applications to Physics, Information Theory and Biology (http://www.math−
inf.uni − greif swald.de/algebra/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 Functional integration with applications in quantum mechanics and quantum
field theory, financially supported by the Alexander von Humboldt foundation with an Alexander von Humboldt fellowship.
• 2007 - 2009 author and coordinator of the individual research project Functional 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 Functional integration with applications to quantum dynamical systems financially 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 Kolmogorov, equazioni differenziali stocastiche alle derivate parziali ed applicazioni 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 Kolmogorov, equazioni differenziali stocastiche alle derivate parziali ed applicazioni 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 Kolmororov 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 directed by Prof. A. Lunardi)
• Member of Research National Project (PRIN 2010-2011) Problemi differenziali di evoluzione: approcci deterministici e stocastici e loro interazioni (nationally directed by Prof. M. Fuhrman).
Publications:
Books:
• Albeverio S., Høegh-Krohn R. and Mazzucchi S.
Mathematical theory of Feynman path integrals - An Introduction, 2nd corrected 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 Applications 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 Ifferential Equations, Volume 2013. Article ID 297857, 7 pages (2013).
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 Misurazione 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 Symposium 2005 in honor of Prof. Kiyosi Ito, 75-92 Springer (2006).
• Albeverio, S. Mazzucchi, A survey on mathematical Feynman path integrals: construction, asymptotics, applications.
In: Fauser B., Tolksdorf J. Zeidler E. (eds.) Quantum Field Theory: Competitive Models. Birkauser Boston (2008) pag. 49-66.
• S. Albeverio, S. Mazzucchi, Infinite dimensional integrals and their asymptotics: some recent developments and applications.
In: Proceedings of the conference “Stochastic Partial Differential Equations 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.
Preprints:
• S. Bonaccorsi and S. Mazzucchi, High Order Heat-type Equations and
Random Walks on the Complex Plane.
arXiv:1402.6140 [math.PR] (2014). To appear in Stochastic processes and
their Applications.
• S. Mazzucchi, Infinite dimensional oscillatory integrals with polynomial
phase and applications to high order heat-type equations.
arXiv:1405.4501 [math.FA] (2014).
Further:
• Invited author and curator of the article Path integral: mathematical aspects on Scholarpedia:
http://www.scholarpedia.org/article/Path integral: mathematical aspects
• Collaboration with a group 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. Radiotherapy & 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.
Trento, 19-9-2014
Sonia Mazzucchi

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