Curriculum vitae et studiorum of Anna Martellotti Born in Perugia, on July, 11.th 1955 Institution: Mathematics and Informatics Department, University of Perugia; Address: Via Pascoli, 06123 PERUGIA, Italy. Phone: 0039-075-585-5041 Fax: 0039-075-585-5024 e-mail: [email protected] Languages: Fluent english, good french, basic german. Studies - Degree in Mathematics at the University of Perugia, 1978 (Dissertation: Sopra una definizione dell'Integrale Multiplo del Calcolo delle Variazioni alla Lebesgue-Serrin). Career - C.N.R. scholarship for undergraduate students (Perugia, 14.IV.1977 - 14.IV.1978). - National Institute for High Mathematics scholarship for postgraduate students (Rome, Istituto Nazionale di Alta Matematica F. Severi 1.XI.1978 - 30.IX.1979 and 15.XI.1979 - 14.XI.1980). - National Institute for High Mathematics research scholarship (Perugia 1.XII.1980 - 30.XI.1982) - Professore a contratto for Calculus I at the Engineering Faculty of Ancona University (1.XI.1982 - 1.X.1983). - Ricercatore (lecturer) in Mathematics at the University of Perugia (1.I.1984 - 27.I.1988). - Associate professor of Mathematics at the Engineering Faculty of Ancona University (28.I.1987 - 31.X.1991). - Associate professor of Mathematics at the University of Perugia (from 1.XI.1991) Teaching experience Undergraduate courses: Calculus 1 and Calculus 2, Statistics and Probability, Applied Mathematics in different Engi- neering faculties (Ancona, Terni, Perugia); Calculus for Life science students; Calculus 1 for Physics students; Calculus 1 and 2 for Earth Science students; Calculus 1, Functional Analysis, Calculus of Variations for Mathematics students. Graduate courses: Mathematical Methods in structure analysis (postgraduate course for engineers; Academic Year 1990-91), Probability Theory (PhD students at the University of Florence, Academic Year 1998), Mathematical methods for economics (PhD students at the University of Perugia, 2000-2009) 1 Postgraduate courses: Minicourse for postgraduate students on Finitely additive phenomena at the 5.th Workshop of Real Analysis and Measure Theory, Gorizia, August-September 1999. Scientific memberships - Italian Mathematical Union (U.M.I.) since 1978; - Italian National Group for Mathematical Analysis, Probability and their Applications (G.N.A.M.P.A. formerly G.N.A.F.A.) since 1979; - American Mathematical Association (since 1999); - Italian Association of Mathematics Applied to Economic and Social Sciences (A.M.A.S.E.S.) (2007); - Member of the Editorial Board of Mathematica Slovaca and of Australian Journal of Mathe- matical Analisys and Applications; - Scientific Committee of the Centro Studi Interfacolt`a Lamberto Cesari; - Participation in the national research projects of Real Analysis and Measure Theory since 1984; - Referee for several international journals: Journal of Mathematical Analysis and Applications, Atti Seminario Matematico e Fisico dell'Universit`adi Modena, Annali dell'Universit`adi Ferrara, Collectanea Mathematica, New Zealand Journal of Mathematics, Indian Journal of Pure and applied mathematics, Topological Methods of Nonlinear Analysis, Journal of Mathematical Analysis (ZAA), Positivity, Mediterranean Journal of Mathematics. - Member of the Graduate Committee for the PhD Program in Mathematical and Statistical Methods for Economic and Social Sciences, University of Perugia, since 2001. - Member of the committee for the final PhD exams in Math´ematiques Appliqu´ees of the Uni- versity of Paris I (Panth´eon-Sorbonne) in 2004, and for the PhD in Mathematics at the University of Bari in 2007. Academic activity A. M. has been a member of the National committees for several national competitions for perma- nent university positions: for lecturers (ricercatori) at the universities of Perugia 1992 and 2009, Trieste 1994, Caserta 1999, Cosenza 2003; and for associate professor at the University of Salerno 2001. Stays abroad and invitations - Visiting professorship (September - October 1989) at the Department of Mathematics, Univer- sity of Florida, Gainesville, participation in the research seminars , three lectures. - Invited lectures in the Colloquim of Georgia Institute of Technology, Atlanta GA October 1989. - From September to December 1990 CNR scholarship at the Department of Mathematics of the University of Florida, Gainesville Fla, (research lectures and joint research). 2 - Upon invitation of the Polish Academy of Sciences, lectures in Wroclaw and Poznan in November 1991 - Upon invitation of the Polish Academy of Sciences, joint research in Warsaw in July 2004. - Upon invitation of the D.A.A.D. (Deutscher Akademischer Austausch Dienst) and of the Uni- versity of W¨urzburg (Germany) has held the Giovanni Prodi Chair in Nonlinear Analysis in the Summer Semester 2008 (April-July), and taught a course in Mathematical Methods in Economics. - Invited speaker in several international meetings, both in Italy and abroad (Mondello 1997, W¨urzburg2000, Brest 2002, Mondello 2003, Paris 2004, Cetraro 2005, Bonn 2008). - A.M. has held several invited lectures in italian and abroad universities (Modena, Ancona, Genova, Trieste, Caserta, Napoli, Cosenza, Palermo, Novara, Berlin, Potenza) Scientific interests - Finitely additive measures: ranges, countably additive restrictions, integration and Radon- Nikodym theorems, multivalued integration; - Minimax relationships; - Stochastic processes: Quasi-martingales and Decomposition Theorems; - Different topics in Functional Analysis and Mathematical Economics: Proximinal subspaces of functional spaces, Drop property in Banach spaces, Compact-friendly operators in functional spaces, structure results in L1(µ), geometry of Banach spaces, fixed point theorems . - Different topics in Mathematical Economics: Equiulibrium theory, core-walras equivalence, TU games Some scientific achievements In the study of ranges, the first example of a finitely additive measure that does not enjoy the Liapounoff Property of the range has been given in [1]; the same example is suitable also to prove several other pathologies of the finitely additive case (see [29]). The investigation of countably additive restrictions also includes the proof of the important Hered- 2 itarily Overlapping Boundary Property (H.O.B.P.) [8], a geometric property of the ranges of R - valued strongly non-atomic measures (both finitely and countably additive). By virtue of the H.O.B.P. the first finitely additive Radon-Nikodym Theorem has been obtained in [14] besides the new results concerning proximinal subspaces of C(K) ([27]). For what concerns Vector integration, it could be said that A. M. jointly with other authors has given a wide range of results: for instance in [23] the best way to define vector integration in a Choquet sense is given. The systematic study of Radon-Nikodym Property for finitely additive measures has stemmed from the first interesting characterization of an exact Radon-Nikodym Theorem for a pair of non-negative finitely additive measures µ and ν: If µ ν and they are both strongly non atomic, dµ then exists iff the range of the pair (µ, ν) contains all its exposed points. dν A. M. and Anna Rita Sambucini have been the first authors that faced the finitely additive version of multivalued integration, and their main contributions are the geometric and topological properties of multivalued integrals of Banach valued correspondences in several dfferent settings, some of special interest towards applications in Equilibrium Theory ([32]). 3 Among the minimax results that have been obtained jointly with Anna Salvadori in the late eighties, the vector version of the Hahn-Banach Theorem obtained in [9] is worth of mention. A. M. has also given some contributions in different fields of Functional Analysis; among them we mention the elegant characterization of proximinality for a subspace V of finite codimension in C(K), which enables to check its proximinality by means of only finitely many elements in the annihilator of V [27], and the completely new point of view of [30] and [33] in defining the Drop Property by means of different classes of `small' sets in a Banach space. General Equilibrium Theory is an important branch of Mathematical Economics. In a series of recent papers the core-walras equivalence has been given for very general models of economies: finitely additive economies, with infinite-dimensional commodity space in the (unusual in the finite- ly additive setting) individualistic approach; they are therefore suitable for modelling economies in infinite time horizon, without restrictions in the mechanism of coalition forming. They represent also an increasing line of generalizations of the milestone paper by Rustichini and Yannelis. Scientific papers 1. D. Candeloro - A. Martellotti Sacchetti, Su alcuni problemi relativi a misure scalari subadditive e applicazioni al caso dell’additivit`afinita, Atti Sem. Mat. Fis. Univ. Modena 27 (1978) 284-296. 2. D. Candeloro - A. Martellotti Sacchetti, Sul rango di una massa vettoriale, Atti Sem. Mat. Fis. Univ. Modena 28 (1979) 102-111. 3. D. Candeloro - A. Martellotti, Continuous finitely additive measures which are ex- tensions of non-atomic measures, Atti Sem. Mat. Fis. Univ. Modena 29 (1980) 328-344. 4. A. Martellotti, Topological properties of the range of a group-valued finitely additive measure, J. Math. Anal. Appl. 110 (1985) 411-423. 5. A. Martellotti, L'integrale di Fubini-Tonelli alla Weierstrass-Burkill lungo coppie di curve continue, Atti Sem. Mat. Fis. Univ. Modena 34 (1985-86) 95-114. 6. D. Candeloro - A. Martellotti, Una panoramica su