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Gauge theory and algebraic geometry

Grant number: 18/21391-1
Support Opportunities:Research Projects - Thematic Grants
Duration: May 01, 2019 - April 30, 2025
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Algebra
Principal Investigator:Marcos Benevenuto Jardim
Grantee:Marcos Benevenuto Jardim
Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
Pesquisadores principais:
Ethan Guy Cotterill ; Henrique Nogueira de Sá Earp
Associated researchers: Alan do Nascimento Muniz ; Rafael de Freitas Leão ; Simone Marchesi
Associated grant(s):22/09853-5 - The Aluffi Algebras and Free Divisors, AV.EXT
22/10067-4 - Asymptotic and polynomial stabilities in Bridgeland stability conditions, AV.EXT
Associated scholarship(s):23/06502-0 - Stability of sheaves on projective varieties, BP.PD
22/16369-2 - Algebraic curves and their applications to Coding Theory, BP.PD
23/03565-0 - Derived Categories and Fourier-Mukai Transforms, BP.IC
+ associated scholarships 22/15788-1 - Categories and applications on Algebraic Geometry and Algebraic Topology, BP.IC
22/03283-2 - Free plane algebraic curves, BP.MS
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
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

Abstract

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)

Articles published in Agência FAPESP Newsletter about the research grant:
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Scientific publications (14)
(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)
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)
CORREA, MAURICIO; JARDIM, MARCOS; MUNIZ, ALAN. Moduli of distributions via singular schemes. MATHEMATISCHE ZEITSCHRIFT, v. 301, n. 3, p. 23-pg., . (18/21391-1)
MIYAMOTO, HENRIQUE K.; COSTA, SUELI I. R.; EARP, HENRIQUE N. SA. Constructive Spherical Codes by Hopf Foliation. IEEE TRANSACTIONS ON INFORMATION THEORY, v. 67, n. 12, p. 7925-7939, . (18/21391-1, 16/05126-0, 17/20007-0, 13/25977-7)
FRANCO, EMILIO; JARDIM, MARCOS. Mirror symmetry for Nahm branes. EPIJOURNAL DE GEOMETRIE ALGEBRIQUE, v. 6, p. 29-pg., . (12/16356-6, 16/03759-6, 18/21391-1)
LOUBEAU, ERIC; MORENO, ANDRES J.; EARP, HENRIQUE N. SA; SAAVEDRA, JULIETH. Harmonic Sp(2)-Invariant G(2)-Structures on the 7-Sphere. JOURNAL OF GEOMETRIC ANALYSIS, v. 32, n. 9, p. 49-pg., . (17/20007-0, 18/21391-1)
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)
FONTES, AISLAN LEAL; JARDIM, MARCOS. Monads and moduli components for stable rank 2 bundles with odd determinant on the projective space. Geometriae Dedicata, v. 217, n. 2, p. 25-pg., . (18/21391-1)
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)
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)
LOTAY, JASON D.; EARP, HENRIQUE N. SA; SAAVEDRA, JULIETH. Flows of G(2)-structures on contact Calabi-Yau 7-manifolds. ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, v. 62, n. 2, p. 23-pg., . (18/21391-1)
GNERI, P. O.; JARDIM, M.; SILVA, D. D.. Derived categories of functors and quiver sheaves. JOURNAL OF ALGEBRA AND ITS APPLICATIONS, v. 21, n. 07, p. 26-pg., . (18/21391-1)
JARDIM, MARCOS; MACIOCIA, ANTONY; MARTINEZ, CRISTIAN. Vertical Asymptotics for Bridgeland Stability Conditions on 3-Folds. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, v. N/A, p. 53-pg., . (18/21391-1, 20/06938-4)
PORTILLA, LUIS E.; SA EARP, HENRIQUE N.. Instantons on Sasakian 7-manifolds. QUARTERLY JOURNAL OF MATHEMATICS, v. N/A, p. 57-pg., . (17/20007-0, 18/21391-1)
CAVALCANTE, ALANA; JARDIM, MARCOS; SANTIAGO, DANILO. Foliations by curves on threefolds. Mathematische Nachrichten, v. 296, n. 2, p. 22-pg., . (18/21391-1)

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