Symmetries in geometry, topology and mathematical physics

Grant number:	05/04558-0
Support type:	Research Projects - Thematic Grants
Duration:	November 01, 2006 - October 31, 2011
Field of knowledge:	Physical Sciences and Mathematics - Mathematics - Geometry and Topology

Principal researcher:	Alcibiades Rigas
Grantee:	Alcibiades Rigas

Home 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
Assoc. researchers:	Adriano Adrega de Moura ; Ricardo Antonio Mosna

Associated 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)

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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; DA SILVA, VITOR M. F. Decomposability criterion for linear sheaves. Central European Journal of Mathematics, v. 10, n. 4, p. 1292-1299, AUG 2012. Web of Science Citations: 2.

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. Web of Science Citations: 1.

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. Web of Science Citations: 3.

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.

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. Web of Science Citations: 3.

JARDIM, MARCOS; MARTINS, RENATO VIDAL. LINEAR AND STEINER BUNDLES ON PROJECTIVE VARIETIES. COMMUNICATIONS IN ALGEBRA, v. 38, n. 6, p. 2249-2270, 2010. Web of Science Citations: 5.

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.

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. Web of Science Citations: 4.

JARDIM, MARCOS; LEAO, RAFAEL F. On the eigenvalues of the twisted Dirac operator. Journal of Mathematical Physics, v. 50, n. 6 JUN 2009. Web of Science Citations: 3.

DURAN, C.; RIGAS, A. Equivariant homotopy and deformations of diffeomorphisms. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, v. 27, n. 2, p. 206-211, APR 2009. Web of Science Citations: 3.

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.

FREJLICH, PEDRO; JARDIM, MARCOS. Nahm transform for Higgs bundles. JOURNAL OF GEOMETRY AND PHYSICS, v. 58, n. 9, p. 1221-1230, SEP 2008. Web of Science Citations: 3.

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