Symmetries in geometry, topology and mathematical physics

• Grant number: 05/04558-0
• Support Opportunities: Research Projects - Thematic Grants
• Start date: November 01, 2006
• End date: October 31, 2011
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Alcibiades Rigas
• Grantee: Alcibiades Rigas
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Pesquisadores principais: Carlos Eduardo Duran Fernandez ; Marcos Benevenuto Jardim
• Associated researchers: Adriano Adrega de Moura ; Ricardo Antonio Mosna
• Associated research grant(s): 09/12576-9 - Geometry of hyperkähler structures, AV.EXT
• Associated scholarship(s): 09/10067-0 - Instantons over G2-manifolds, BP.PD; 09/07953-8 - Geometry and Topology of Coboundaries, BP.DR; 09/05136-2 - Parabolic Higgs bundles on curves, BP.PD; + associated scholarships 09/02621-7 - Instantons with symmetries, BP.MS; 09/02990-2 - Introduction to Cluster Algebras via Quiver Representations, BP.MS; 07/05926-8 - Exotic phenomenas in Geometry and Topology, BP.MS; 07/06860-0 - Gauge theories: dynamical and topological aspects, BP.MS; 07/07456-9 - Representations of hyper loop algebras and multi current algebras, BP.DR; 07/07469-3 - Representation Theory and Algebraic Geometry, BP.DR; 07/07819-4 - Introduction to algebras and representations of quivers, BP.IC; 07/07855-0 - Introduction to differential geometry, BP.IC; 07/07448-6 - Introduction to Lie Theory, BP.IC - associated scholarships

Abstract

The main theme of the proposal is the study of the various ways the concept of symmetry appears in algebra, geometry, topology and mathematical physics through a) actions of groups and algebras b) in its infinitesimal version, where the study of symmetries is encoded in representations of algebras, and c) in the study of deformations of algebraic structures and of group actions. As an example, we consider the study of exotic structures on manifolds, where the symmetries appear through exotic actions of groups and global properties of geodesics and of connections on principal fiber bundles with maximal symmetry. This path leads us to the study of special geometric structures relevant to mathematical physics. (AU)

Scientific publications

(12)

(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)

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. (05/04558-0, 09/12576-9)

JARDIM, MARCOS; LEAO, RAFAEL F.. On the eigenvalues of the twisted Dirac operator. Journal of Mathematical Physics, v. 50, n. 6, JUN 2009. (05/04558-0)

JARDIM, MARCOS; MARTINS, RENATO VIDAL. LINEAR AND STEINER BUNDLES ON PROJECTIVE VARIETIES. COMMUNICATIONS IN ALGEBRA, v. 38, n. 6, p. 2249-2270, 2010. (05/04558-0)

JARDIM, MARCOS; MARTINS, RENATO VIDAL. The ADHM variety and perverse coherent sheaves. JOURNAL OF GEOMETRY AND PHYSICS, v. 61, n. 11, p. 2219-2232, NOV 2011. (05/04558-0)

JARDIM‚ M.; LEÃO‚ R.. On the Spectrum of the Twisted Dolbeault Laplacian on Line Bundles over Kähler Manifolds. Advances in Applied Clifford Algebras, v. 20, n. 3, p. 669-676, 2010. (05/04558-0)

FREJLICH, PEDRO; JARDIM, MARCOS. Nahm transform for Higgs bundles. JOURNAL OF GEOMETRY AND PHYSICS, v. 58, n. 9, p. 1221-1230, SEP 2008. (05/04558-0)

JARDIM, MARCOS; DA SILVA, VITOR M. F.. Decomposability criterion for linear sheaves. Central European Journal of Mathematics, v. 10, n. 4, p. 1292-1299, AUG 2012. (05/04558-0)

JARDIM, MARCOS; LEAO, RAFAEL F.. On the spectrum of the twisted Dolbeault Laplacian over Kahler manifolds. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, v. 27, n. 3, p. 412-419, JUN 2009. (05/04558-0)

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. (05/04558-0)

DURAN, C.; RIGAS, A.. Equivariant homotopy and deformations of diffeomorphisms. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, v. 27, n. 2, p. 206-211, APR 2009. (05/04558-0)

BRUZZO, UGO; CHUANG, WU-YEN; DIACONESCU, DUILIU-EMANUEL; JARDIM, MARCOS; PAN, G.; ZHANG, YI. D-branes, surface operators, and ADHM quiver representations. Advances in Theoretical and Mathematical Physics, v. 15, n. 3, p. 849-911, JUN 2011. (05/04558-0)

CORREA, JR., MAURICIO; JARDIM, MARCOS. BOUNDS FOR SECTIONAL GENERA OF VARIETIES INVARIANT UNDER PFAFF FIELDS. ILLINOIS JOURNAL OF MATHEMATICS, v. 56, n. 2, p. 343-352, SUM 2012. (05/04558-0)