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Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica (IMECC) (Institutional affiliation for the last research proposal) Birthplace: Brazil
Marcos Jardim graduated in Physics at the University of Campinas, obtained a Master's degree in Mathematics at the University of Campinas and a PhD in Mathematics from the University of Oxford, where he worked under the supervision of Simon Donaldson and Nigel Hitchin. He held post-doctoral positions at Yale University, University of Pennsylvania and University of Massachussets at Amherst; most recently, he has spent a sabbatical year at the University of Edinburgh in 2017. He is currently a Full Professor at the University of Campinas. His research concentrates on Gauge Theory and Algebraic Geometry, focusing on the study of vector bundles on algebraic varieties. He has published 36 papers on international journals, and supervised 13 masters and 10 PhD students, as well as 12 post-doctoral researchers. (Source: Lattes Curriculum)
Gauge theory is the study of differential equations involving connections on vector bundles over manifolds using methods from differential geometry, algebraic geometry and geometric analysis. This is area of research emerged in the late 1970s, especially after works by Michael Atiyah, Nigel Hitchin and simon Donaldson, among others, as a mathematical model for classical field theory in ma…
Instanton bundles are a class of algebraic vector bundles, first introduced in mathematical physics as solutions of the Yang-Mills equation over compactified space-time, and later much studied in algebraic geometry. The main questions (irreducibility, smoothness) about the moduli space of instanton bundles on 3-dimensional projective space have been recently settled, but there are many op…
This project will have as main areas of study algebraic geometry, complex geometry and global theory of holomorphic foliations. Its main goals are: show results about the existence of residues and localization of characteristic classes for holomorphic Lie algebroids; a concise study of non-integrable distributions in complex projective spaces; a characterization of nilpotent and semista…
(Only some records are available in English at this moment)
This project will cover aspects of the Mathematics of Solid Geometry, which deals with objects in three-dimensional Euclidean space. This project will especially focus on Polyhedra Classification, from the most usually taught in primary and higher education, to new classifications developed by the student and the supervisor. Basics concepts of Solid Geometry will be introduced with the go…
Moduli theory has been a central theme in Algebraic Geometry. To construct moduli spaces, one usually needs the concept of stability conditions. Motivated by the work in string theory, Bridgeland introduced the stability conditions on a triangulated category and proposed the existence of a stability manifold. Moreover, there exists a locally finite wall and chamber structure on this manif…
This project will consist in the study of Algebraic Varieties and Schemes with the intention of characterizing both objects and understanding the relationship between them. A special attention will be given to the schemes that cannot be represented with a variety structure, aiming to comprehend the advantages of the more modern definition compared to the classic one. During the course of …
(Only some records are available in English at this moment)
In this project, we are going to study the basic concepts of algebraic geometry necessary for the Riemann-Roch theorem. Furthermore we will give some applications of this theorem.
This research project has two aims. The first is to investigate Poisson structures on Hilbert schemes of points on Hirzebruch surfaces. We believe that this goal can be achieved by using the description of these Hilbert schemes in terms of quiver varieties given by Bartocci, Bruzzo, Lanza, and Rava, and by adapting to our needs some techniques of noncommutative Poisson geometry developed …
Gauge Theory emerged as an important area of mathematicas in the 1980s, after the work of Michael F. Atiyah, Simon K. Donaldson e Nigel J. Hitchin, among others. Since then, it has becaome an important tool for more traditional areas, like differential topology, complex geometry and algebraic geometry. This project will serve as an introduction to research in this area. The student will s…
(Only some records are available in English at this moment)
The main goal of this project is to give the beneficiary an opportunity to study with one of the leading researchers in Bridgeland stability, a topic in the state of the art within Algebraic Geometry that can relate to various other topics in both Algebraic Geometry and Physics. The idea is to study the stability properties of sheaves on P^3 with dimension 2 or less and how to translate …
The idea of this project consists in applying the tools of Bridgeland stability to moduli spaces of framed sheaves on Hirzebruch surfaces. In particular, three objectives are fixed: to study the chamber structure arising with the quiver description of Hilbert schemes of points of the total space of OP1(-n) (provided by the applicant in former works), to extend the already-mentioned quiver…
The study of moduli spaces of sheaves is a classical and relevant problem in algebraic geometry. The concept of stability is an important issue in this area, and the use of different notions can lead to a deeper understanding of the geometry of the moduli space of the object being studied.The present research project focuses on instanton sheaves on the 3 dimensional projective space. Thes…
(Only some records are available in English at this moment)
| 1 / 1 | Ongoing research grants |
| 21 / 21 | Completed research grants |
| 8 / 8 | Ongoing scholarships in Brazil |
| 21 / 19 | Completed scholarships in Brazil |
| 7 / 7 | Completed scholarships abroad |
| 58 / 56 | All research grants and scholarships |
| Associated processes | |
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
| Publications | 42 |
| Citations | 63 |
| Cit./Article | 1.5 |
| Data from Web of Science | |
BARTOCCI, CLAUDIO; LANZA, VALERIANO; RAVA, CLAUDIO L. S.. Moduli spaces of framed sheaves and quiver varieties. JOURNAL OF GEOMETRY AND PHYSICS, v. 118, n. SI, p. 20-39, AUG 2017. Web of Science Citations: 1. (15/07766-4)
VON FLACH, RODRIGO A.; JARDIM, MARCOS. Moduli spaces of framed flags of sheaves on the projective plane. JOURNAL OF GEOMETRY AND PHYSICS, v. 118, n. SI, p. 138-168, AUG 2017. Web of Science Citations: 0. (14/14743-8)
LANZA, VALERIANO; LO GIUDICE, ALESSIO. Bruzzo's Conjecture. JOURNAL OF GEOMETRY AND PHYSICS, v. 118, n. SI, p. 181-191, AUG 2017. Web of Science Citations: 1. (15/07766-4)
BERNARDI, ALESSANDRA; JELISIEJEW, JOACHIM; MARQUES, PEDRO MACIAS; RANESTAD, KRISTIAN. On polynomials with given Hilbert function and applications. COLLECTANEA MATHEMATICA, v. 69, n. 1, p. 39-64, JAN 2018. Web of Science Citations: 2. (14/12558-9)
MENET, GREGOIRE. On the integral cohomology of quotients of manifolds by cyclic groups. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, v. 119, p. 280-325, NOV 2018. Web of Science Citations: 1. (14/05733-9)
OMEGAR CALVO-ANDRADE; MAURÍCIO CÔRREA; ARTURO FERNÁNDEZ-PÉREZ. On non-Kupka points of codimension one foliations on P-3. Anais da Academia Brasileira de Ciências, v. 88, n. 4, p. 2067-2080, Dez. 2016. Web of Science Citations: 1. (14/23594-6)
MARCHESI, SIMONE; PRATA, DANIELA MOURA. Simplicity and exceptionality of syzygy bundles over P-n. Annali di Matematica Pura ed Applicata, v. 195, n. 1, p. 41-58, FEB 2016. Web of Science Citations: 1. (12/07481-1, 11/21398-7)
MARTENS, JOHAN; THADDEUS, MICHAEL. Compactifications of reductive groups as moduli stacks of bundles. COMPOSITIO MATHEMATICA, v. 152, n. 1, p. 62-98, JAN 2016. Web of Science Citations: 5. (09/05136-2)
JARDIM, MARCOS; VERBITSKY, MISHA. Moduli spaces of framed instanton bundles on CP3 and twistor sections of moduli spaces of instantons on C-2. ADVANCES IN MATHEMATICS, v. 227, n. 4, p. 1526-1538, JUL 10 2011. Web of Science Citations: 4. (09/12576-9, 05/04558-0)
CORREA, JR., MAURICIO; JARDIM, MARCOS; MARTINS, RENATO VIDAL. On the Singular Scheme of Split Foliations. Indiana University Mathematics Journal, v. 64, n. 5, p. 1359-1381, 2015. Web of Science Citations: 1. (14/14743-8)
BISWAS, INDRANIL; BRUZZO, UGO; GRANA OTERO, BEATRIZ; LO GIUDICE, ALESSIO. YANG-MILLS-HIGGS CONNECTIONS ON CALABI-YAU MANIFOLDS. ASIAN JOURNAL OF MATHEMATICS, v. 20, n. 5, p. 989-1000, 2016. Web of Science Citations: 0. (13/20617-2)
HENNI, ABDELMOUBINE AMAR; JARDIM, MARCOS; MARTINS, RENATO VIDAL. ADHM CONSTRUCTION OF PERVERSE INSTANTON SHEAVES. Glasgow Mathematical Journal, v. 57, n. 2, p. 285-321, MAY 2015. Web of Science Citations: 2. (09/12576-9, 11/01071-3)
JARDIM, MARCOS; VERBITSKY, MISHA. Trihyperkahler reduction and instanton bundles on CP3. COMPOSITIO MATHEMATICA, v. 150, n. 11, p. 1836-1868, NOV 2014. Web of Science Citations: 13. (09/12576-9, 11/01071-3)
JARDIM, MARCOS; MAICAN, MARIO; TIKHOMIROV, ALEXANDER S.. MODULI SPACES OF RANK 2 INSTANTON SHEAVES ON THE PROJECTIVE SPACE. PACIFIC JOURNAL OF MATHEMATICS, v. 291, n. 2, p. 399-424, DEC 2017. Web of Science Citations: 2. (16/03759-6, 14/14743-8)
KAPFER, SIMON; MENET, GREGOIRE. Integral cohomology of the generalized Kummer fourfold. ALGEBRAIC GEOMETRY, v. 5, n. 5, p. 523-567, SEP 2018. Web of Science Citations: 0. (14/05733-9)
BISWAS, INDRANIL; ANGEL CALVO, LUIS; FRANCO, EMILIO; GARCIA-PRADA, OSCAR. Involutions of Higgs moduli spaces over elliptic curves and pseudo-real Higgs bundles. JOURNAL OF GEOMETRY AND PHYSICS, v. 142, p. 47-65, AUG 2019. Web of Science Citations: 0. (15/06696-2, 12/16356-6)
CALVO-ANDRADE, OMEGAR. Foliations with a radial Kupka set on projective spaces. BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, v. 47, n. 4, p. 1071-1083, DEC 2016. Web of Science Citations: 2. (14/23594-6)
LO GIUDICE, ALESSIO; PUSTETTO, ANDREA. A compactification of the moduli space of principal Higgs bundles over singular curves. JOURNAL OF GEOMETRY AND PHYSICS, v. 110, p. 328-342, DEC 2016. Web of Science Citations: 0. (13/20617-2)
BARTOCCI, CLAUDIO; BRUZZO, UGO; LANZA, VALERIANO; RAVA, CLAUDIO L. S.. Hilbert schemes of points of phi(p1) (-n) as quiver varieties. Journal of Pure and Applied Algebra, v. 221, n. 8, p. 2132-2155, AUG 2017. Web of Science Citations: 1. (15/07766-4)
JARDIM, MARCOS; MARKUSHEVICH, DIMITRI; TIKHOMIROV, ALEXANDER S.. NEW DIVISORS IN THE BOUNDARY OF THE INSTANTON MODULI SPACE. MOSCOW MATHEMATICAL JOURNAL, v. 18, n. 1, p. 117-148, JAN-MAR 2018. Web of Science Citations: 2. (14/14743-8, 11/06464-3)
CALVO-ANDRADE, OMEGAR; RODRIGUEZ DIAZ, LAZARO O.; SA EARP, HENRIQUE N.. Gauge theory and G(2)-geometry on Calabi-Yau links. REVISTA MATEMATICA IBEROAMERICANA, v. 36, n. 6, p. 1753-1778, 2020. Web of Science Citations: 0. (14/24727-0, 14/13357-7, 14/23594-6)
JARDIM, M.; SILVA, D. D.. Instanton sheaves and representaTIONS OF QUIVERS. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, v. 63, n. 4, p. 984-1004, NOV 2020. Web of Science Citations: 0. (18/21391-1)
HENNI, ABDELMOUBINE AMAR; JARDIM, MARCOS. Monad constructions of omalous bundles. JOURNAL OF GEOMETRY AND PHYSICS, v. 74, p. 36-42, DEC 2013. Web of Science Citations: 2. (11/01071-3, 09/18249-0)
DALLAGNOL, LLOHANN; JARDIM, MARCOS. NONSINGULAR COMPLEX INSTANTONS ON EUCLIDEAN SPACETIME. INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, v. 5, n. 6, p. 963-971, SEP 2008. Web of Science Citations: 4. (05/04558-0)
CALVO-ANDRADE, O.; CORREA, M.; FERNANDEZ-PEREZ, A.. Higher codimensional foliations with Kupka singularities. INTERNATIONAL JOURNAL OF MATHEMATICS, v. 28, n. 3, MAR 2017. Web of Science Citations: 0. (14/23594-6)
OMEGAR CALVO-ANDRADE; MAURÍCIO CÔRREA; ARTURO FERNÁNDEZ-PÉREZ. On non-Kupka points of codimension one foliations on ℙ3. Anais da Academia Brasileira de Ciências, v. 88, n. 4, p. -, Dez. 2016. (14/23594-6)
JARDIM, MARCOS; MARKUSHEVICH, DIMITRI; TIKHOMIROV, ALEXANDER S.. Two infinite series of moduli spaces of rank 2 sheaves on P-3. Annali di Matematica Pura ed Applicata, v. 196, n. 4, p. 1573-1608, AUG 2017. Web of Science Citations: 2. (14/14743-8, 14/22807-6)
FRANCO, EMILIO; TORTELLA, PIETRO. Moduli spaces of Lambda-modules on abelian varieties. ADVANCES IN MATHEMATICS, v. 318, p. 459-496, OCT 1 2017. Web of Science Citations: 0. (15/06696-2, 11/17593-9, 12/16356-6)
HENNI, ABDELMOUBINE A.; JARDIM, MARCOS. Commuting matrices and the Hilbert scheme of points on affine spaces. ADVANCES IN GEOMETRY, v. 18, n. 4, p. 467-482, OCT 2018. Web of Science Citations: 0. (09/12576-9, 14/14743-8)
FRANCO, EMILIO; JARDIM, MARCOS; MARCHESI, SIMONE. Branes in the moduli space of framed sheaves. BULLETIN DES SCIENCES MATHEMATIQUES, v. 141, n. 4, p. 353-383, JUN 2017. Web of Science Citations: 4. (12/16356-6, 14/19676-7, 15/06696-2, 14/14743-8)
BRASSELET, JEAN-PAUL; CORREA, MAURICIO; LOURENCO, FERNANDO. Residues for flags of holomorphic foliations. ADVANCES IN MATHEMATICS, v. 320, p. 1158-1184, NOV 7 2017. Web of Science Citations: 1. (15/20841-5, 15/06697-9)
BROCHERO MARTINEZ, F. E.; CORREA, M.; RODRIGUEZ, A. M.. Poincar, problem for weighted projective foliations. BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, v. 48, n. 2, p. 219-235, JUN 2017. Web of Science Citations: 1. (15/20841-5)
MARCHESI, SIMONE; MARQUES, PEDRO MACIAS; SOARES, HELENA. MONADS ON PROJECTIVE VARIETIES. PACIFIC JOURNAL OF MATHEMATICS, v. 296, n. 1, p. 155-180, SEP 2018. Web of Science Citations: 0. (14/12558-9, 14/00498-1, 17/03487-9)
CALVO-ANDRADE, OMEGAR; CORREA, MAURICIO; JARDIM, MARCOS. Codimension One Holomorphic Distributions on the Projective Three-space. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, v. 2020, n. 23, p. 9011-9074, NOV 2020. Web of Science Citations: 2. (16/03759-6, 15/20841-5, 14/14743-8, 14/23594-6)
FU, LIE; MENET, GREGOIRE. On the Betti numbers of compact holomorphic symplectic orbifolds of dimension four. MATHEMATISCHE ZEITSCHRIFT, JAN 2021. Web of Science Citations: 0. (14/05733-9)
BARTOCCI, CLAUDIO; BRUZZO, UGO; LANZA, VALERIANO; RAVA, CLAUDIO L. S.. On the Irreducibility of Some Quiver Varieties. Symmetry Integrability and Geometry-Methods and Applications, v. 16, 2020. Web of Science Citations: 0. (15/07766-4)
JARDIM, MARCOS; MENET, GREGOIRE; PRATA, DANIELA M.; SA EARP, HENRIQUE N.. Holomorphic bundles for higher dimensional gauge theory. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, v. 49, n. 1, p. 117-132, FEB 2017. Web of Science Citations: 1. (09/10067-0, 11/21398-7, 14/14743-8, 14/05733-9, 14/24727-0)
FRANCO, EMILIO; GARCIA-PRADA, OSCAR; NEWSTEAD, P. E.. HIGGS BUNDLES OVER ELLIPTIC CURVES FOR REAL GROUPS. QUARTERLY JOURNAL OF MATHEMATICS, v. 70, n. 1, p. 105-146, MAR 2019. Web of Science Citations: 1. (12/16356-6, 15/06696-2)
FRANCO, EMILIO; JARDIM, MARCOS; MENET, GREGOIRE. Brane involutions on irreducible holomorphic symplectic manifolds. KYOTO JOURNAL OF MATHEMATICS, v. 59, n. 1, p. 195-235, APR 2019. Web of Science Citations: 0. (14/05733-9, 15/06696-2, 12/16356-6, 16/03759-6)
ALMEIDA, CHARLES; ANDRADE, ALINE V.. Lefschetz property and powers of linear forms in K[x, y, z]. FORUM MATHEMATICUM, v. 30, n. 4, p. 857-865, JUL 2018. Web of Science Citations: 0. (16/14376-0, 14/08306-4)
COSTA, LAURA; MARCHESI, SIMONE; MARIA MIRO-ROIG, ROSA. Tango bundles on Grassmannians. Mathematische Nachrichten, v. 289, n. 8-9, p. 950-961, JUN 2016. Web of Science Citations: 1. (13/10063-0)
ARRONDO, ENRIQUE; MARCHESI, SIMONE; SOARES, HELENA. Schwarzenberger bundles on smooth projective varieties. Journal of Pure and Applied Algebra, v. 220, n. 9, p. 3307-3326, SEP 2016. Web of Science Citations: 1. (12/07481-1)
BRUZZO, UGO; LO GIUDICE, ALESSIO. RESTRICTING HIGGS BUNDLES TO CURVES. ASIAN JOURNAL OF MATHEMATICS, v. 20, n. 3, p. 399-408, JUL 2016. Web of Science Citations: 4. (13/20617-2)
(References retrieved automatically from State of São Paulo Research Institutions)
SANTOS, Daniela Moura Prata dos. Representations of quivers and vector bundles over projectives spaces = : Representações de quivers e fibrados vetoriais sobre espaços projetivos. Tese (Doutorado) - Instituto de Matemática, Estatística e Computação Científica. Universidade Estadual de Campinas (UNICAMP). (07/07469-3)
MARTINO, Marcelo Gonçalves de. Teoria de calibre em dimensões dois e quatro. Dissertação (Mestrado) - Instituto de Matemática, Estatística e Computação Científica. Universidade Estadual de Campinas (UNICAMP). (09/02621-7)
JÚNIOR, Alcides de Carvalho. As equações de Seiberg-Witten. Dissertação (Mestrado) - Instituto de Matemática, Estatística e Computação Científica. Universidade Estadual de Campinas. (14/18855-5)
BARBOSA, Rodrigo de Menezes. Gauge theory on special holonomy manifolds = : Teoria de calibre em variedades de holonomia especial. Dissertação (Mestrado) - Instituto de Matemática, Estatística e Computação Científica. Universidade Estadual de Campinas (UNICAMP). (11/04214-0)
SANTOS, Patrícia Borges dos. ADHM construction of nested Hilbert scheme = A construção ADHM do esquema de Hilbert aninhado. Tese (Doutorado) - Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). (09/16646-1)
ALMEIDA, Charles Aparecido de. The geometry of the moduli space of torsion free sheaves on projective spaces : Geometria dos espaços de moduli de feixes sem torção em espaços projetivos. Tese (Doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica. (14/08306-4)