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Gauge theory and algebraic geometry

Grant number: 18/21391-1
Support type:Research Projects - Thematic Grants
Duration: May 01, 2019 - April 30, 2024
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Algebra
Principal researcher:Marcos Benevenuto Jardim
Grantee:Marcos Benevenuto Jardim
Home Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
Pesquisadores principais:
Henrique Nogueira de Sá Earp
Assoc. researchers:Rafael de Freitas Leão ; Simone Marchesi
Associated scholarship(s):21/11603-4 - The generalized Ricci curvature on contact Calabi-Yau 7-manifolds, BP.MS
21/10550-4 - Logarithmic sheaves for complete intersection schemes, BP.DR
21/07249-0 - Symmetries in exceptional holonomy problems, BP.PD
+ associated scholarships 21/08026-5 - Special geometries and calibrated submanifolds, BP.PD
21/05051-9 - Octonions and cross product, BP.IC
21/07190-6 - Algebraic topology via problems, BP.IC
20/15525-5 - Supersymmetric Yang-Mills theory on contact Calabi-Yau 7-manifolds, BP.MS
21/02706-4 - Classification of polyhedra, BP.IC
20/03499-0 - Stability conditions on higher dimensional varieties and moduli spaces, BP.PD
20/15054-2 - Spectrum of the Laplacian on Hermitian Vector Bundles over Homogeneous Spaces, BP.DD
20/16173-5 - Schemes and algebraic varieties, BP.IC
20/06938-4 - Geometry of moduli spaces of sheaves via wall-crossing, BP.PD
19/23499-7 - Noether-Lefschetz theory in toric varieties, BP.PD
19/20843-9 - Moduli problems in algebraic geometry, BP.MS
19/22453-3 - Spectra of the Laplacian on homogeneous spaces, BP.MS
19/21140-1 - Moduli spaces of pfaffian representations of cubic three-folds and instanton bundles, BP.PD - associated scholarships


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 mathematical physics, and had inumerous applications to more tradicional areas of mathematics, like differential topology, algebraic geometry, complex geometry, Riemannian geometry, geometric analysis and representation theory.At the core of the theory is a 1-1 correspondence between solutions of certain equations (e.g. the Yang--Mills anti-self-duality equation) and holomoprhic vector bundles with certain properties (e.g. stability). The research group in Gauge Theory and Algebraic Geometry of the Department of Mathematics at IMECC-UNICAMP focuses on the interaction between these two areas, also working on specific problems in each of them. (AU)

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Scientific publications (5)
(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)
ALMEIDA, C.; JARDIM, M.; TIKHOMIROV, A. S.; TIKHOMIROV, S. A.. New moduli components of rank 2 bundles on projective space. SBORNIK MATHEMATICS, v. 212, n. 11, p. 1503-1552, . (16/14376-0, 14/08306-4, 18/21391-1, 16/03759-6)
CALVO-ANDRADE, OMEGAR; CORREA, MAURICIO; JARDIM, MARCOS. Codimension one distributions and stable rank 2 reflexive sheaves on threefolds. Anais da Academia Brasileira de Ciências, v. 93, n. 3, . (18/21391-1)
MIYAMOTO, HENRIQUE K.; COSTA, SUELI I. R.; EARP, HENRIQUE N. SA. onstructive Spherical Codes by Hopf Foliation. IEEE TRANSACTIONS ON INFORMATION THEORY, v. 67, n. 12, p. 7925-7939, . (17/20007-0, 16/05126-0, 18/21391-1, 13/25977-7)
JARDIM, M.; SILVA, D. D.. Instanton sheaves and representaTIONS OF QUIVERS. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, v. 63, n. 4, p. 984-1004, . (18/21391-1)
VON FLACH, RODRIGO A.; JARDIM, MARCOS; LANZA, VALERIANO. Obstruction theory for moduli spaces of framed flags of sheaves on the projective plane. JOURNAL OF GEOMETRY AND PHYSICS, v. 166, . (15/07766-4, 18/21391-1)

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