 Research group
 EGSA  Differential Equations, Geometry, Control and Dynamical Systems, and Applications
 Department
 Department of Applied Mathematics III
 School
 Terrassa School of Engineering (EET)
 m.immaculada.galvezupc.edu
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Scientific and technological production


Groupoids and Faa di Bruno formulae for Green functions in bialgebras of trees
Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew
Advances in mathematics
Date of publication: 20140320
Journal article
Read the abstract View Share Reference managersWe prove a Faa di Bruno formula for the Green function in the bialgebra of Ptrees, for any polynomial endofunctor P. The formula appears as relative homotopy cardinality of an equivalence of groupoids. (C) 2013 Elsevier Inc. All rights reserved. 
Thomason cohomology of categories
Gálvez Carrillo, Maria Immaculada; Neumann, Frank; Tonks, Andrew
Journal of pure and applied algebra
Date of publication: 2013
Journal article
Read the abstract Access to the full text Share Reference managersWe investigate cohomology and homology theories of categories with general coefficients given by functors on simplex categories first studied by Thomason. These generalize Baues¿Wirsching cohomology and homology of a small category, and coincide with Gabriel¿Zisman cohomology and homology of the simplicial nerve of the category. Thus Baues¿Wirsching cohomology of categories is seen to be a special case of simplicial cohomology. We analyze naturality and functoriality properties of these theories and construct associated spectral sequences for functors between small categories.
We investigate cohomology and homology theories of categories with general coefficients given by functors on simplex categories first studied by Thomason. These generalize Baues–Wirsching cohomology and homology of a small category, and coincide with Gabriel–Zisman cohomology and homology of the simplicial nerve of the category. Thus Baues–Wirsching cohomology of categories is seen to be a special case of simplicial cohomology. We analyze naturality and functoriality properties of these theories and construct associated spectral sequences for functors between small categories.
Postprint (author’s final draft) 
GEOMATRIA ALGEBRAICA, SIMPLECTICA, ARITMETICA Y APLICACIONES
Alberich Carramiñana, Maria; Amoros Torrent, Jaume; Barja Yañez, Miguel Angel; Elgueta Montó, Josep; Fernández Sánchez, Jesús; Ventura González Alonso, Daniel; Barbieri Solha, Romero; Miranda Galceran, Eva; Pascual Gainza, Pedro; Roig Marti, Agustin; Roig Maranges, Abdo; Feliu Trijueque, Elsienda; Gálvez Carrillo, Maria Immaculada; Casanellas Rius, Marta
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Estructuras Ainfinito en la opérada de cactus
Gálvez Carrillo, Maria Immaculada; Lombardi, Leandro; Tonks, Andrew
Encuentro de Topología
Presentation's date: 20121019
Presentation of work at congresses
Read the abstract View Share Reference managersDiversas versiones de la opérada de cactus inicialmente definida por Voronov han sido estudiadas. Es conocida su equivalencia débil con la opérada de pequeños discos. Se conoce pues que la opérada de cactus admite una acción de la opérada de Gerstenhaber salvo homotopía. En este proyecto, nuestro objetivo es obtener una realización explícita de dicha acción. Por el momento, hemos construido una acción explícita de la opérada A8 en la opérada de cactus, que presentamos en este póster 
André spectral sequences for Baues¿Wirsching cohomology of categories
Gálvez Carrillo, Maria Immaculada; Neumann, Frank; Tonks, Andrew
Journal of pure and applied algebra
Date of publication: 20120430
Journal article
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Homotopy BatalinVilkovisky Algebras
Gálvez Carrillo, Maria Immaculada; Tonks, Andrew; Vallette, Bruno
Journal of noncommutative geometry
Date of publication: 2012
Journal article
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Central cohomology operations and Ktheory
Gálvez Carrillo, Maria Immaculada; Whitehouse, Sarah
Date: 201204
Report
Read the abstract Access to the full text Share Reference managersFor stable degree zero operations, and also for additive unstable operations of bidegree (0,0), it is known that the centre of the ring of operations for complex cobordism is isomorphic to the corresponding ring of connective complex Ktheory operations. Similarly, the centre of the ring of BP operations is the corresponding ring for the Adams summand of plocal connective complex Ktheory. Here we show that, in the additive unstable context, this result holds with BP replaced by BPfor any n. Thus, for all chromatic heights, the only central operations are those coming from Ktheory 
Groupoids and Faa di Bruno formulae for Green functions in bialgebras of trees
Gálvez Carrillo, Maria Immaculada; Tonks, Andrew; Kock, Joachim
Date: 201207
Report
Read the abstract Access to the full text Share Reference managersWe prove a Faa di Bruno formula for the Green function in the bialgebra of Ptrees, for any polynomial endofunctor P. The formula appears as relative homotopy cardinality of an equivalence of groupoids. For suitable choices of P, the result implies also formulae for Green functions in bialgebras of graphs 
Thomason cohomology of categories
Gálvez Carrillo, Maria Immaculada; Neumann, Frank; Tonks, Andrew
Date: 201208
Report
Read the abstract Access to the full text Share Reference managersWe introduce cohomology and homology theories for small categories with general coefficient systems from simplex categories first studied by Thomason. These theories generalize at once BauesWirsching cohomology and homology and other more classical theories. We analyze naturality and functoriality properties of these theories and construct associated spectral sequences for functors between small categories. 
André spectral sequences for BauesWirsching cohomology of categories
Gálvez Carrillo, Maria Immaculada; Neumann, Frank; Tonks, Andrew
Date: 20111216
Report
Read the abstract Access to the full text Share Reference managersWe construct spectral sequences in the framework of BauesWirsching cohomology and homology for functors between small categories and analyze particular cases including Grothendieck fibrations. We also give applications to more classical cohomology and homology theories including HochschildMitchell cohomology and those studied before by Watts, Roos, Quillen and others 
Homotopy BatalinVilkovisky algebras
Gálvez Carrillo, Maria Immaculada; Tonks, Andrew; Vallette, Bruno
Date: 20110330
Report
Read the abstract Access to the full text Share Reference managersThis paper provides an explicit cofibrant resolution of the operad encoding BatalinVilkovisky algebras. Thus it defines the notion of homotopy BatalinVilkovisky algebras with the required homotopy properties. To define this resolution we extend the theory of Koszul duality to operads and properads that are defind by quadratic and linear relations. The operad encoding BatalinVilkovisky algebras is shown to be Koszul in this sense. This allows us to prove a PoincareBirkhoffWitt Theorem for such an operad and to give an explicit small quasifree resolution for it. This particular resolution enables us to describe the deformation theory and homotopy theory of BValgebras and of homotopy BValgebras. We show that any topological conformal field theory carries a homotopy BValgebra structure which lifts the BValgebra structure on homology. The same result is proved for the singular chain complex of the double loop space of a topological space endowed with an action of the circle. We also prove the cyclic Deligne conjecture with this cofibrant resolution of the operad BV. We develop the general obstruction theory for algebras over the Koszul resolution of a properad and apply it to extend a conjecture of LianZuckerman, showing that certain vertex algebras have an explicit homotopy BValgebra structure. 
Álgebras de vértices, opéradas y complejo de De Rham quiral
Gálvez Carrillo, Maria Immaculada
Date: 20111216
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Homotopy Gerstenhaber structures and vertex algebras
Gálvez Carrillo, Maria Immaculada; Gorbounov, V.; Tonks, Andrew
Applied categorical structures
Date of publication: 2010
Journal article
Read the abstract Access to the full text Share Reference managersWe provide a simple construction of a G∞algebra structure on an important class of vertex algebras V, which lifts the Gerstenhaber algebra structure on BRST cohomology of V introduced by Lian and Zuckerman. We outline two applications to algebraic topology: the construction of a sheaf of G∞ algebras on a Calabi–Yau manifold M, extending the operations of multiplication and bracket of functions and vector fields on M, and of a Lie∞ structure related to the bracket of Courant
Postprint (author’s final draft) 
Infinite sums of Adams operations and cobordism.
Gálvez Carrillo, Maria Immaculada; Whitehouse, Sarah
Mathematische Zeitschrift
Date of publication: 2005
Journal article
Read the abstract Access to the full text Share Reference managersThe elements of various algebras of stable degree zero operations in plocal Ktheory can be described explicitly as certain infinite sums of Adams operations [11, 9]. Here we show how to make sense of the same expressions for MU(p) and BP, thus identifying the “Adams subalgebra” of the algebras of operations. We prove that the Adams subalgebra is the centre of the ring of degree zero operations
Postprint (author’s final draft) 
Differential operators and the Witten genus for projective spaces and Milnor manifolds
Gálvez Carrillo, Maria Immaculada; Tonks, Andrew
Mathematical proceedings of the Cambridge Philosophical Society
Date of publication: 2003
Journal article
Read the abstract Access to the full text Share Reference managersA $genus$ (in the sense of Hirzebruch [4]) is a multiplicative invariant of cobordism classes of manifolds. Classical examples include the numerical invariants given by the signature and the $\widehat{A}$ and Todd genera. More recently genera were introduced which take as values modular forms on the upper halfplane, $\frak{h}=\{\,\tau\;\;\mathrm{Im}(\tau)>0\,\}$. The main examples are the elliptic genus $\phi_{ell}$ and the Witten genus $\phi_W$; we refer the reader to the texts [7] or [9] for details
Postprint (author’s final draft)
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