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Journal of Algebra, ISSN 0021-8693, 05/2015, Volume 430, pp. 260 - 302
In this paper we consider L∞-algebras equipped with complete descending filtrations. We prove that, under some mild conditions, an L∞ quasi-isomorphism U:L→L˜... 
Simplicial sets | L-infinity algebras | Algebra
Journal Article
Compositio Mathematica, ISSN 0010-437X, 09/2015, Volume 151, Issue 9, pp. 1763 - 1790
Journal Article
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, ISSN 1073-7928, 03/2019, Volume 2019, Issue 5, pp. 1503 - 1542
We study higher-order analogues of Dirac structures, extending the multisymplectic structures that arise in field theory. We define higher Dirac structures as... 
FORMS | MATHEMATICS | FORMALISM | L-INFINITY-ALGEBRAS | GEOMETRY
Journal Article
Advances in Mathematics, ISSN 0001-8708, 10/2019, Volume 354, p. 106754
Over a field of characteristic zero, every deformation problem with cohomology constraints is controlled by a pair consisting of a differential graded Lie... 
Links | Milnor fibers | Weight filtration | Deformation theory | Fundamental group | L-infinity algebras and modules | TOPOLOGY | MATHEMATICS | SYSTEMS | HOMOTOPY | COHOMOLOGY JUMP LOCI
Journal Article
Advances in Mathematics, ISSN 0001-8708, 06/2019, Volume 349, pp. 869 - 910
Given a complex variety X, a linear algebraic group G and a representation ρ of the fundamental group π1(X,x) into G, we develop a framework for constructing a... 
Hodge theory | [formula omitted] algebras | Representation varieties | Complex algebraic geometry | Formal deformation theory | Fundamental groups | MATHEMATICS | L-infinity algebras | Algebraic Geometry | Mathematics
Journal Article
Advances in Mathematics, ISSN 0001-8708, 01/2016, Volume 288, pp. 527 - 575
Given a Lie group G, one constructs a principal G-bundle on a manifold X by taking a cover U→X, specifying a transition cocycle on the cover, and descending... 
Simplicial manifolds | String 2-group | Bundle gerbes | MATHEMATICS | CATEGORIES | L-INFINITY-ALGEBRAS
Journal Article
JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, ISSN 1446-7887, 02/2020, Volume 108, Issue 1, pp. 120 - 144
Given a vector field on a manifold M, we define a globally conserved quantity to be a di fferential form whose Lie derivative is exact. Integrals of conserved... 
MATHEMATICS | conservation laws | homotopy co-momentum map | L-INFINITY-ALGEBRAS | multisymplectic manifolds | GEOMETRY | Differential Geometry | Mathematics
Journal Article
Journal of Algebra, ISSN 0021-8693, 09/2015, Volume 438, pp. 90 - 118
We give some formality criteria for a differential graded Lie algebra to be formal. For instance, we show that a DG-Lie algebra L is formal if and only if the... 
Differential graded Lie algebras | [formula omitted]-algebras | Spectral sequences | L ∞ -algebras | KAHLER-MANIFOLDS | MATHEMATICS | MODELS | SPACES | OBSTRUCTIONS | L-infinity-algebras | HOMOTOPY-THEORY | DEFORMATION-THEORY | MODULI | Algebra
Journal Article
Applied Categorical Structures, ISSN 0927-2852, 8/2017, Volume 25, Issue 4, pp. 489 - 503
We construct a symmetric monoidal category S Lie ∞ MC ${\mathfrak {S}}\mathsf {Lie}_{\infty }^{\text {MC}}$ whose objects are shifted L ∞ -algebras equipped... 
Geometry | Enriched categories | Convex and Discrete Geometry | Mathematics | Theory of Computation | L-infinity algebras | Mathematical Logic and Foundations
Journal Article
International Mathematics Research Notices, ISSN 1073-7928, 2013, Volume 2013, Issue 16, pp. 3790 - 3855
We use Chen's iterated integrals to integrate representations up to homotopy. That is, we construct an A(infinity) functor integral : Rep(infinity)(A) -> (R)... 
MATHEMATICS | LIE BRACKETS | L-INFINITY-ALGEBRAS | DEFORMATIONS
Journal Article
JOURNAL OF LIE THEORY, ISSN 0949-5932, 2016, Volume 26, Issue 4, pp. 1037 - 1067
Multisymplectic geometry admits an operation that has no counterpart in symplectic geometry, namely, taking the product of two multisymplectic manifolds... 
MATHEMATICS | strong homotopy Lie algebra | moment map | Multisymplectic manifold | L-INFINITY-ALGEBRAS | GEOMETRY
Journal Article
Journal of Homotopy and Related Structures, ISSN 2193-8407, 6/2016, Volume 11, Issue 2, pp. 309 - 332
By using homotopy transfer techniques in the context of rational homotopy theory, we show that if $$C$$ C is a coalgebra model of a space $$X$$ X , then the... 
Algebra | L_\infty $$ L ∞ -algebra | Functional Analysis | Mapping space | Secondary 54C35 | Algebraic Topology | Rational homotopy | Mathematics | Number Theory | Primary 55P62 | algebra | MATHEMATICS | L-infinity-algebra | LIE-ALGEBRA | HOMOLOGICAL ALGEBRA | WHITEHEAD PRODUCTS | CONE | L-INFINITY-ALGEBRAS | DEFORMATION-THEORY | Mathematics - Algebraic Topology
Journal Article
Communications in Contemporary Mathematics, ISSN 0219-1997, 06/2017, Volume 19, Issue 3, p. 1650034
We study the extension of a Lie algebroid by a representation up to homotopy, including semidirect products of a Lie algebroid with such representations. The... 
Representation up to homotopy | integration | Lie 2-groupoids | Courant algebroids | Lie 2-algebroids | BRACKETS | MATHEMATICS, APPLIED | REPRESENTATIONS | HOMOTOPY | L-INFINITY-ALGEBRAS | MATHEMATICS | GROUPOIDS | GEOMETRY
Journal Article
Journal of Geometry and Physics, ISSN 0393-0440, 12/2014, Volume 86, pp. 497 - 533
We disclose the mathematical structure underlying the gauge field sector of the recently constructed non-abelian superconformal models in six space–time... 
Superconformal models | [formula omitted]-manifolds | Tensor hierarchy | [formula omitted]-infinity algebras | Q-manifolds | L-infinity algebras | MATHEMATICS | GAUGE ALGEBRA | POISSON SIGMA-MODELS | PHYSICS, MATHEMATICAL | Analysis | Algebra
Journal Article
Letters in Mathematical Physics, ISSN 0377-9017, 9/2018, Volume 108, Issue 9, pp. 2055 - 2097
We describe some $$L_{\infty }$$ L∞ model for the local period map of a compact Kähler manifold. Applications include the study of deformations with associated... 
Geometry | 32G20 | 14D07 | Theoretical, Mathematical and Computational Physics | Complex Systems | Group Theory and Generalizations | Yukawa algebra | L-infinity algebras | 13D10 | Physics | Formal period maps | LIE-ALGEBRAS | SPACE | COHOMOLOGY | DEFORMATIONS | CONSTRUCTION | MANIFOLDS | PHYSICS, MATHEMATICAL | HOMOTOPY-THEORY | GEOMETRY | Analysis | Algebra
Journal Article
JOURNAL OF NONCOMMUTATIVE GEOMETRY, ISSN 1661-6952, 2019, Volume 13, Issue 1, pp. 297 - 361
Given a differential graded (dg) symmetric Frobenius algebra A we construct an unbounded complex D* (A, A), called the Tate-Hochschild complex, which arises as... 
A-infinity algebras | string topology | MATHEMATICS | MATHEMATICS, APPLIED | Tate-Hochschild complex | Frobenius algebras | DUALITY | L-infinity algebras | PHYSICS, MATHEMATICAL | HOMOLOGY
Journal Article
Compositio Mathematica, ISSN 0010-437X, 1/2011, Volume 147, Issue 1, pp. 105 - 160
We prove a version of Kontsevich's formality theorem for two subspaces (branes) of a vector space X. The result implies, in particular, that the Kontsevich... 
coisotropic submanifolds | Koszul algebras | L-algebras and morphisms | A-bimodules | Koszul duality | deformation quantization | MATHEMATICS | COMPLEX | L-infinity-algebras and morphisms | A(infinity)-bimodules | FORMALITY THEOREM | Quantization | Theorems | Deformation | Vector spaces | Subspaces | Branes | Quantum Algebra | Mathematics | Mathematical Physics | Physics
Journal Article
Advances in Theoretical and Mathematical Physics, ISSN 1095-0761, 2012, Volume 16, Issue 5, pp. 1485 - 1589
Recent work applying higher gauge theory to the superstring has indicated the presence of "higher symmetry". Infinitesimally, this is realized by a "Lie... 
LORENTZ | HIGHER GAUGE-THEORY | BRANES | 2-GROUPS | SPINORS | PHYSICS, MATHEMATICAL | L-INFINITY-ALGEBRAS | OCTONIONS | PHYSICS, PARTICLES & FIELDS
Journal Article
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