Simona Settepanella |

Faculty of Science Mathematics Mathematics |

Associate Professor |

Last Updated :2020/09/10

- Natural sciences / Applied mathematics and statistics / Mathematical Modeling for Economics
- Natural sciences / Basic mathematics / Mathematical Modeling for Economics
- Natural sciences / Algebra

- 2016/04 - Today Hokkaido University Mathematics Department Associate Professor
- 2013/08 - 2016/03 Hokkaido University Mathematics Department Specially Appointed Lecturer
- 2008/08 - 2013/07 Scuola Sant'Anna di Studi Avanzati Research Fellow

**Productivity Decomposition in Heterogeneous Industries**Giovanni Dosi, Marco Grazzi, Le Li, Luigi Marengo, Simona SettepanellaJournal of Industrial Economics ( accepted for publication ) 2020/12 [Refereed][Not invited]**Algebraic Structure of Manin Schechtman Higher Braid Groups and Stratifications of Discriminantal Arrangements**P.Bailet, B. Guerville, A. Libgober, S. SettepanellaOberwolfach Annual Report 2019/12 [Not refereed][Invited]**On an explicit correspondence between $\nbc$-basis, chambers and minimal complex for real supersolvable arrangements**S. Settepanella, M. TorielliAustralasian Journal Of Combinatorics 72 (2) 223 - 245 2019/10 [Refereed][Not invited]**Pappus's Theorem in Grassmannian GR(3,C^n)**S. Sawada, S. Settepanella, S. YamagataArs Mathematica Contemporanea 16 (1) 257 - 276 2019/01 [Refereed][Not invited]**Strata of discriminantal arrangements**A. Libgober, S. SettepanellaJournal of Singularities (Special Volume in honor of E. Brieskorn ) 18 441 - 456 2018 [Refereed][Invited]- Sumire Sawada, Simona Settepanella, So YamagataCOMPTES RENDUS MATHEMATIQUE 355 (11) 1111 - 1120 1631-073X 2017/11 [Refereed][Not invited]

We show that points in specific degree-2 hypersurfaces in the Grassmannian Gr( 3, n) correspond to generic arrangements of n hyperplanes in C-3 with associated discriminantal arrangement having intersections of multiplicity three in codimension two. (C) 2017 Acadmie des sciences. Published by Elsevier Masson SAS. All rights reserved. - Pauline Bailet, Simona SettepanellaADVANCES IN APPLIED MATHEMATICS 90 46 - 85 0196-8858 2017/09 [Refereed][Not invited]

We study the first homology group H-1(F,C) of the Milnor fiber F of sharp arrangements (A) over bar in P-R(2). Our work relies on the minimal complex C-*(S(A)) of the deconing arrangement A and its boundary map. We describe an algorithm which computes possible eigenvalues of the monodromy operator h(1) of H-1(F, C). We prove that, if a condition on some intersection points of lines in A is satisfied, then the only possible nontrivial eigenvalues of h(1) are cubic roots of the unity. Moreover we give sufficient conditions for just eigenvalues of order 3 or 4 to appear in cases in which this condition is not satisfied. (C) 2017 Elsevier Inc. All rights reserved. - Giovanni Dosi, Marco Grazzi, Luigi Marengo, Simona SettepanellaJOURNAL OF INDUSTRIAL ECONOMICS 64 (4) 875 - 907 0022-1821 2016/12 [Refereed][Not invited]

The paper presents a new framework to assess firm level heterogeneity and to study the rate and direction of technical change. Building on the analysis of revealed short-run production functions by Hildenbrand (), we propose the (normalized) volume of the zonotope composed by vectors-firms as indicator of inter-firm heterogeneity. Moreover, the angles that the zonotope's main diagonal form with the axes provide a measure of the rates and directions of productivity change. The proposed framework also accounts for n-inputs and m-outputs and, crucially, the measures of heterogeneity and technical change do not require many of the standard assumptions from production theory. - Feichtner Eva-Maria, Settepanella SimonaEVOLUTIONARY AND INSTITUTIONAL ECONOMICS REVIEW 12 (1) 121 1349-4961 2015/06 [Refereed][Not invited]
- Settepanella Simona, Dosi Giovanni, Grazzi Marco, Marengo Luigi, Ponchio FedericoEVOLUTIONARY AND INSTITUTIONAL ECONOMICS REVIEW 12 (1) 223 - 234 1349-4961 2015/06 [Refereed][Not invited]
- G. Amendola, L. Marengo, D. Pirino, S. Settepanella, A. TakemuraEvolutionary and Institutional Economics Review 12 (1) 141 - 168 1349-4961 2015/06 [Refereed][Invited]
- Simona Settepanella, Michele TorielliAustralasian Journal of Combinatorics 75 (2) 223 - 245 2015/03/19 [Refereed][Not invited]

In this paper we give a very natural description of the bijections between

the minimal CW-complex homotopy equivalent to the complement of a supersolvable

arrangement $\mathcal{A}$, the $\textbf{nbc}$ basis of the Orlik-Solomon

algebra associated to $\mathcal{A}$ and the set of chambers of $\mathcal{A}$.

We use these bijections to get results on the first (co)homology group of the

Milnor fiber of $\mathcal{A}$ and to describe a bijection between the symmetric

group and the $\textbf{nbc}$ basis of the braid arrangement. - Sandro Manfredini, Simona SettepanellaTOPOLOGY AND ITS APPLICATIONS 176 51 - 56 0166-8641 2014/10 [Refereed][Not invited]

We describe the fundamental group and second homotopy group of ordered k-point sets in Gr(k,n) generating a subspace of fixed dimension. (C) 2014 Elsevier B.V. All rights reserved. **On the Configuration Spaces of Grassmannian Manifolds**S. Manfredini, S. SettepanellaAnn. Fac. Sci. Toulouse , 23 (2014), no. 2, 353-359 23 (2) 353 - 359 2014/03 [Refereed][Invited]**Social choice among complex objects**Luigi Marengo, Simona SettepanellaANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE 13 (4) 1039 - 1064 0391-173X 2014 [Refereed][Not invited]

We present a geometric model of social choice when the latter takes place among bundles of interdependent elements, that we will call objects. We show that the outcome of the social choice process is highly dependent on the way these bundles are formed. By bundling and unbundling the same set of constituent elements an authority enjoys a vast power of determining the social outcome. We provide necessary and sufficient conditions under which a social outcome may be a local or global optimum for a set of objects, and we show that, by appropriately redefining the set of objects, intransitive cycles may be broken and the median voter may be turned into a loser.**Braid groups in complex spaces**S. Manfredini, S. Parveen, S. SettepanellaBollettino dell'Unione Matematica Italiana 7 7 (2) 157 - 168 2014 [Refereed][Not invited]- M. W. Davis, S. SettepanellaPUBLICACIONS MATEMATIQUES 57 (2) 379 - 392 0214-1493 2013 [Refereed][Not invited]

Suppose R is the complement of an essential arrangement of toric hyperlanes in the complex torus (C*)(n) and pi = pi(1)(R). We show that H* (R; A) vanishes except in the top degree n when A is one of the following systems of local coefficients: (a) a system of nonresonant coefficients in a complex line bundle, (b) the von Neumann algebra N pi, or (c) the group ring Z pi. In case (a) the dimension of H-n is vertical bar e(R)vertical bar where e(R) denotes the Euler characteristic, and in case (b) the nth l(2) Betti number is also vertical bar e(R)vertical bar. - Gennaro Amendola, Simona SettepanellaJOURNAL OF MATHEMATICAL SOCIOLOGY 36 (1) 44 - 77 0022-250X 2012 [Refereed][Not invited]

Marengo and Settepanella (2010) have developed a geometric model of social choice when it takes place among bundles of interdependent elements, showing that by bundling and unbundling the same set of constituent elements an authority has the power of determining the social outcome. In this article, we will tie the model above to tournament theory, solving some of the mathematical problems arising in their work and opening new questions which are interesting from both a mathematical and social choice point of view. In particular, we will introduce the notion of u-local optima and study it from both a theoretical and a numerically probabilistic point of view; we will also describe an algorithm that computes the universal basin of attraction of a social outcome in O(M(3) log M) time (where M is the number of social outcomes). - Luca Moci, Simona SettepanellaJOURNAL OF PURE AND APPLIED ALGEBRA 215 (8) 1980 - 1989 0022-4049 2011/08 [Refereed][Not invited]

A toric arrangement is a finite set of hypersurfaces in a complex torus, every hypersurface being the kernel of a character. In the present paper, we build a CW-complex homotopy equivalent to the arrangement complement, with a combinatorial description similar to that of the well-known Salvetti complex. If the toric arrangement is defined by a Weyl group, we also provide an algebraic description, very handy for cohomology computations. In the last part, we give a description in terms of tableaux for a toric arrangement appearing in robotics. (C) 2010 Elsevier B.V. All rights reserved. - Emanuele Delucchi, Simona SettepanellaADVANCES IN APPLIED MATHEMATICS 44 (2) 124 - 144 0196-8858 2010/02 [Refereed][Not invited]

Polar orderings arose in recent work of Salvetti and the second author on minimal CW-complexes for complexified hyperplane arrangements. We study the combinatorics of these orderings in the classical framework of oriented matroids, and reach thereby a weakening of the conditions required to actually determine such orderings. A class of arrangements for which the construction of the minimal complex is particularly easy, called recursively orderable arrangements, can therefore be combinatorially defined. We initiate the study of this class, giving a complete characterization in dimension 2 and proving that every supersolvable complexified arrangement is recursively orderable. (C) 2009 Elsevier Inc. All rights reserved. - Simona SettepanellaTOPOLOGY AND ITS APPLICATIONS 156 (5) 1008 - 1012 0166-8641 2009/02 [Refereed][Not invited]

Consider the ring R := Q vertical bar tau. tau(-1)vertical bar of Laurent polynomials in the variable tau. The Artin's Pure Braid Groups (or Generalized Pure Braid Groups) act over R. where the action of every standard generator is the multiplication by tau. In this paper we consider the cohomology of these groups with coefficients in the module R (it is well known that such cohomology is strictly related to the untwisted integral cohomology, of the Milnor fibration naturally associated to the reflection arrangement). We compute this cohomology for the cases I(2)(m). H(3), H(4), F(4) and An with 1 <= n <= 7. (c) 2008 Elsevier B.V. All rights reserved. **On the Cohomology with local coefficients of Pure Braid Groups**Simona SettepanellaANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA 17 (1) 211 - 230 1224-1784 2009 [Refereed][Not invited]

The need to calculate local system cohomolgy of the complement of an hyper plane arrangement arises in various contexts. Nevertheless until now very few it's known on the direct computation of such cohomology. In this paper the author describes all generators of the first homology group of braid arrangement giving also a complete description of its first characteristic variety, fulfilling results obtained by D.Cohenand A.Suciuin [7]. Moreover she gives also a complete description of the first characteristic variety in the case of the generalized braid arrangement coming from the dihedral group.**Blocking Sets in the complement of hyperplane arrangements in projective space**S. SettepanellaJ. Discrete Math. Sci. Cryptography 12 (1) 101 - 107 2009 [Refereed][Not invited]- Mario Salvetti, Simona SettepanellaGEOMETRY & TOPOLOGY 11 1733 - 1766 1364-0380 2007 [Refereed][Not invited]

Using combinatorial Morse theory on the CW-complex S constructed in Salvetti [15] which gives the homotopy type of the complement to a complexified real arrangement of hyperplanes, we find an explicit combinatorial gradient vector field on S, such that S contracts over a minimal CW-complex. The existence of such minimal complex was proved before Dimca and Padadima [5] and Randell [14] and there exists also some description of it by Yoshinaga [19]. Our description seems much more explicit and allows to find also an algebraic complex computing local system cohomology, where the boundary operator is effectively computable. - S SettepanellaTOPOLOGY AND ITS APPLICATIONS 139 (1-3) 37 - 47 0166-8641 2004/04 [Refereed][Not invited]

Consider the ring R := Q[tau, tau(-1)] of Laurent polynomials in the variable tau. The Artin's pure braid groups (or generalized pure braid groups) act over R, where the action of every standard generator is the multiplication by tau. In this paper we consider the cohomology of such groups with coefficients in the module R (it is well known that such cohomology is strictly related to the untwisted integral cohomology of the Milnor fibration naturally associated to the reflection arrangement). We give a sort of stability theorem for the cohomologies of the infinite series A, B and D, finding that these cohomologies stabilize, with respect to the natural inclusion, at some number of copies of the trivial R-module Q. We also give a formula which computes this number of copies. (C) 2003 Elsevier B.V. All fights reserved.

- Discrete Morse Theory [Not invited]Simona SettepanellaPISA-HOKKAIDO-ROMA2 Summer School on Mathematics and Its Applications 2018 2018/08
- Multi-Factor Productivity and Evolutionary Accounting in Presence of (Persistently) Hetero- geneous Firms [Invited]Simona SettepanellaISS Conference, Seoul, (Korea) 2018/07
- Judgement aggregation and social choice: a graph model [Invited]Simona SettepanellaMathematical Analysis of Self- Organization with Constraints 2018/05
- Discriminantal arrangement, hypersurfaces in Grassmannian and Pappus’s Theorem [Invited]Simona SettepanellaWomen in Mathematics - a Panorama of Contributions 2017/07
- Intersection lattice of Discriminantal arrangement and hypersurfaces in Grassmannian [Not invited]Simona SettepanellaArrangements and beyond: Combinatorics, geometry, topology and applications 2017/06
- Homology graph of real arrangements and monodromy of Milnor Fiber [Invited]Simona SettepanellaHyperplane Arrangements and related topics 2017/02
- Discrete Morse Theory and minimal CW-complex [Not invited]Simona Settepanellaowards a New Paradim for Self-Organaization with constrains 2016/11
- Discrete Morse Theory and minimal CW-complex [Invited]Simona SettepanellaPerspectives on arrangements and configuration spaces 2016/09
- Strata of Discriminantal Arrangements [Invited]Simona SettepanellaSpecial Session on Combinatorics, at the Crossroads of Algebra, Geometry, and Topology, AMS Meeting 2016/09
- Arrow’s impossibility theorem on existence of global optimum and local alternatives: local optima [Invited]Simona SettepanellaTowards a New Paradim for Self-Organaization 2016/05
- Strata of Discriminantal Arrangements [Invited]Simona SettepanellaArrangements: topology,combinatorics and stability 2016/02
- Arrangements of hyperplanes and decision theory [Invited]Simona SettepanellaTowards a New Paradim for Self-Organaization 2015/05
- The nbc-minimal complex of supersolvable arrangements [Invited]Simona SettepanellaArrangements of plane curves and related problems 2015/03
- The nbc-minimal complex of supersolvable arrangements [Invited]Simona SettepanellaAlgebraic topology, geometric and combinatorial group theory 2015/02

- Algebra開講年度 : 2018課程区分 : 修士課程開講学部 : 理学院キーワード : Lie Groups, Lie Algebras
- Special Lecture II開講年度 : 2018課程区分 : 修士課程開講学部 : 理学院
- Special Lecture II開講年度 : 2018課程区分 : 博士後期課程開講学部 : 理学院
- Arts and Science Courses in English 2開講年度 : 2018課程区分 : 学士課程開講学部 : 国際本部
- Advanced Algebra開講年度 : 2018課程区分 : 学士課程開講学部 : 理学部
- Calculus I開講年度 : 2018課程区分 : 学士課程開講学部 : 全学教育キーワード : functions, differentiation, one and several variables.
- Calculus II開講年度 : 2018課程区分 : 学士課程開講学部 : 全学教育キーワード : integration, functions, one and several variables.