Burgos Gil, José I. (José Ignacio) 1962
Overview
Works:  19 works in 56 publications in 4 languages and 732 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Dedicatee, Opponent, 958 
Publication Timeline
.
Most widely held works by
José I Burgos Gil
Regulators : Regulators III Conference, July 1222, 2010, Barcelona, Spain by Regulators(
Book
)
9 editions published in 2012 in English and held by 186 WorldCat member libraries worldwide
9 editions published in 2012 in English and held by 186 WorldCat member libraries worldwide
Arithmetic geometry of toric varieties : metrics, measures and heights by
José I Burgos Gil(
Book
)
9 editions published in 2014 in English and held by 173 WorldCat member libraries worldwide
We show that the height of a toric variety with respect to a toric metrized line bundle can be expressed as the integral over a polytope of a certain adelic family of concave functions. To state and prove this result, we study the Arakelov geometry of toric varieties. In particular, we consider models over a discrete valuation ring, metrized line bundles, and their associated measures and heights. We show that these notions can be translated in terms of convex analysis, and are closely related to objects like polyhedral complexes, concave functions, real MongeAmpère measures, and LegendreFenchel duality. We also present a closed formula for the integral over a polytope of a function of one variable composed with a linear form. This formula allows us to compute the height of toric varieties with respect to some interesting metrics arising from polytopes. We also compute the height of toric projective curves with respect to the FubiniStudy metric and the height of some toric bundles"Page 4 of cover
9 editions published in 2014 in English and held by 173 WorldCat member libraries worldwide
We show that the height of a toric variety with respect to a toric metrized line bundle can be expressed as the integral over a polytope of a certain adelic family of concave functions. To state and prove this result, we study the Arakelov geometry of toric varieties. In particular, we consider models over a discrete valuation ring, metrized line bundles, and their associated measures and heights. We show that these notions can be translated in terms of convex analysis, and are closely related to objects like polyhedral complexes, concave functions, real MongeAmpère measures, and LegendreFenchel duality. We also present a closed formula for the integral over a polytope of a function of one variable composed with a linear form. This formula allows us to compute the height of toric varieties with respect to some interesting metrics arising from polytopes. We also compute the height of toric projective curves with respect to the FubiniStudy metric and the height of some toric bundles"Page 4 of cover
The regulators of Beilinson and Borel by
José I Burgos Gil(
Book
)
1 edition published in 2001 in English and held by 143 WorldCat member libraries worldwide
1 edition published in 2001 in English and held by 143 WorldCat member libraries worldwide
Feynman amplitudes, periods, and motives : international research workshop, periods and motives : a modern perspective on
renormalization : July 26, 2012, Instituto de Ciencias Matemáticas, Madrid, Spain by International Research Workshop Periods and Motives  a Modern Perspective on Renormalization(
Book
)
9 editions published between 2012 and 2015 in English and held by 133 WorldCat member libraries worldwide
This volume contains the proceedings of the International Research Workshop on Periods and MotivesA Modern Perspective on Renormalization, held from July 26, 2012, at the Instituto de Ciencias Matemáticas, Madrid, Spain. Feynman amplitudes are integrals attached to Feynman diagrams by means of Feynman rules. They form a central part of perturbative quantum field theory, where they appear as coefficients of power series expansions of probability amplitudes for physical processes. The efficient computation of Feynman amplitudes is pivotal for theoretical predictions in particle physics. Periods are numbers computed as integrals of algebraic differential forms over topological cycles on algebraic varieties. The term originated from the period of a periodic elliptic function, which can be computed as an elliptic integral. Motives emerged from Grothendieck's "universal cohomology theory", where they describe an intermediate step between algebraic varieties and their linear invariants (cohomology). The theory of motives provides a conceptual framework for the study of periods. In recent work, a beautiful relation between Feynman amplitudes, motives and periods has emerged. The articles provide an exciting panoramic view on recent developments in this fascinating and fruitful interaction between pure mathematics and modern theoretical physics
9 editions published between 2012 and 2015 in English and held by 133 WorldCat member libraries worldwide
This volume contains the proceedings of the International Research Workshop on Periods and MotivesA Modern Perspective on Renormalization, held from July 26, 2012, at the Instituto de Ciencias Matemáticas, Madrid, Spain. Feynman amplitudes are integrals attached to Feynman diagrams by means of Feynman rules. They form a central part of perturbative quantum field theory, where they appear as coefficients of power series expansions of probability amplitudes for physical processes. The efficient computation of Feynman amplitudes is pivotal for theoretical predictions in particle physics. Periods are numbers computed as integrals of algebraic differential forms over topological cycles on algebraic varieties. The term originated from the period of a periodic elliptic function, which can be computed as an elliptic integral. Motives emerged from Grothendieck's "universal cohomology theory", where they describe an intermediate step between algebraic varieties and their linear invariants (cohomology). The theory of motives provides a conceptual framework for the study of periods. In recent work, a beautiful relation between Feynman amplitudes, motives and periods has emerged. The articles provide an exciting panoramic view on recent developments in this fascinating and fruitful interaction between pure mathematics and modern theoretical physics
The regulators of Beilinson and Borel by
José I Burgos Gil(
)
10 editions published between 2001 and 2002 in 3 languages and held by 33 WorldCat member libraries worldwide
This book contains a complete proof of the fact that Borel's regulator map is twice Beilinson's regulator map. The strategy of the proof follows the argument sketched in Beilinson's original paper and relies on very similar descriptions of the ChernWeil morphisms and the van Est isomorphism. The book has two different parts. The first one reviews the material from algebraic topology and Lie group theory needed for the comparison theorem. Topics such as simplicial objects, Hopf algebras, characteristic classes, the Weil algebra, Bott's Periodicity theorem, Lie algebra cohomology, continuous gr
10 editions published between 2001 and 2002 in 3 languages and held by 33 WorldCat member libraries worldwide
This book contains a complete proof of the fact that Borel's regulator map is twice Beilinson's regulator map. The strategy of the proof follows the argument sketched in Beilinson's original paper and relies on very similar descriptions of the ChernWeil morphisms and the van Est isomorphism. The book has two different parts. The first one reviews the material from algebraic topology and Lie group theory needed for the comparison theorem. Topics such as simplicial objects, Hopf algebras, characteristic classes, the Weil algebra, Bott's Periodicity theorem, Lie algebra cohomology, continuous gr
The regulators of Beilinson and Borel by
José I Burgos Gil(
Book
)
2 editions published in 2002 in English and held by 32 WorldCat member libraries worldwide
2 editions published in 2002 in English and held by 32 WorldCat member libraries worldwide
Feynman Amplitudes, Periods and Motives by
Luis ÁlvarezCónsul(
)
1 edition published in 2015 in English and held by 13 WorldCat member libraries worldwide
This volume contains the proceedings of the International Research Workshop on Periods and MotivesA Modern Perspective on Renormalization, held from July 26, 2012, at the Instituto de Ciencias Matemáticas, Madrid, Spain. Feynman amplitudes are integrals attached to Feynman diagrams by means of Feynman rules. They form a central part of perturbative quantum field theory, where they appear as coefficients of power series expansions of probability amplitudes for physical processes. The efficient computation of Feynman amplitudes is pivotal for theoretical predictions in particle physics. Period
1 edition published in 2015 in English and held by 13 WorldCat member libraries worldwide
This volume contains the proceedings of the International Research Workshop on Periods and MotivesA Modern Perspective on Renormalization, held from July 26, 2012, at the Instituto de Ciencias Matemáticas, Madrid, Spain. Feynman amplitudes are integrals attached to Feynman diagrams by means of Feynman rules. They form a central part of perturbative quantum field theory, where they appear as coefficients of power series expansions of probability amplitudes for physical processes. The efficient computation of Feynman amplitudes is pivotal for theoretical predictions in particle physics. Period
Regulators(
Book
)
1 edition published in 2012 in English and held by 4 WorldCat member libraries worldwide
1 edition published in 2012 in English and held by 4 WorldCat member libraries worldwide
Anillos de Chow aritméticos by
José I Burgos Gil(
Book
)
3 editions published between 1994 and 1995 in Spanish and English and held by 3 WorldCat member libraries worldwide
3 editions published between 1994 and 1995 in Spanish and English and held by 3 WorldCat member libraries worldwide
On higher arithmetic intersection theory by
Elisenda Feliu i Trijueque(
)
2 editions published between 2007 and 2008 in English and held by 2 WorldCat member libraries worldwide
2 editions published between 2007 and 2008 in English and held by 2 WorldCat member libraries worldwide
Regulators : regulators 3. conference, July 1222, 2012, Barcelona, Spain by *Regulators(
Book
)
1 edition published in 2012 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2012 in English and held by 2 WorldCat member libraries worldwide
The RiemannRoch theorem and Gysin morphism in arithmetic geometry El teroema de RiemannRoch y el morfismo de Gysin en geometría
aritmética by Alberto Navarro Garmendia(
Book
)
1 edition published in 2016 in English and held by 1 WorldCat member library worldwide
The original Grothendieck's RiemannRoch theorem states that for any proper morphism f : Y ! X, between nonsingular quasiprojective irreducible varieties over a eld, and any element a 2 K0(Y ) of the Grothendieck group of vector bundles the relation ch(f!(a)) = f {u100000}Td(Tf ) ch(a) holds (cf. [BS58]). Recall that ch denotes the Chern character, Td(Tf ) the Todd class of the relative tangent bundle and f and f! the direct image in the Chow ring and K0 respectively. Later Baum, Fulton and MacPherson proved in [BFM75] the RiemannRoch theorem for locally complete intersection morphisms between singular projective algebraic schemes (i.e., locally of nite type separated schemes over a eld). In [FG83] Fulton and Gillet proved the theorem without projective assumptions on the schemes. The remarkable extension to higher Ktheory and schemes over a regular base was proved by Gillet in [Gil81]. The RiemannRoch theorem proved there is for projective morphisms between smooth quasiprojective schemes. However, note that in the case over a eld Gillet's theorem does not recover the result of [BFM75]. The furthest generalization of the RiemannRoch theorem I know is [D eg14] and [HS15] where D eglise and HolmstromScholbach independently obtained the RiemannRoch theorem for higher Ktheory and projective lci morphisms between regular schemes over a nite dimensional noetherian base
1 edition published in 2016 in English and held by 1 WorldCat member library worldwide
The original Grothendieck's RiemannRoch theorem states that for any proper morphism f : Y ! X, between nonsingular quasiprojective irreducible varieties over a eld, and any element a 2 K0(Y ) of the Grothendieck group of vector bundles the relation ch(f!(a)) = f {u100000}Td(Tf ) ch(a) holds (cf. [BS58]). Recall that ch denotes the Chern character, Td(Tf ) the Todd class of the relative tangent bundle and f and f! the direct image in the Chow ring and K0 respectively. Later Baum, Fulton and MacPherson proved in [BFM75] the RiemannRoch theorem for locally complete intersection morphisms between singular projective algebraic schemes (i.e., locally of nite type separated schemes over a eld). In [FG83] Fulton and Gillet proved the theorem without projective assumptions on the schemes. The remarkable extension to higher Ktheory and schemes over a regular base was proved by Gillet in [Gil81]. The RiemannRoch theorem proved there is for projective morphisms between smooth quasiprojective schemes. However, note that in the case over a eld Gillet's theorem does not recover the result of [BFM75]. The furthest generalization of the RiemannRoch theorem I know is [D eg14] and [HS15] where D eglise and HolmstromScholbach independently obtained the RiemannRoch theorem for higher Ktheory and projective lci morphisms between regular schemes over a nite dimensional noetherian base
Selfcalibration of projective and generic central cameras by Ferran Espuny i Pujol(
)
1 edition published in 2009 in English and held by 1 WorldCat member library worldwide
1 edition published in 2009 in English and held by 1 WorldCat member library worldwide
Cálculo de la representación de los estados y de los coeficientes de acoplamiento para múltiples atómicos by
José I Burgos Gil(
)
1 edition published in 1986 in Spanish and held by 1 WorldCat member library worldwide
1 edition published in 1986 in Spanish and held by 1 WorldCat member library worldwide
Feynman Amplitudes, Periods and Motives by
Luis ÁlvarezCónsul(
Book
)
1 edition published in 2015 in English and held by 1 WorldCat member library worldwide
This volume contains the proceedings of the International Research Workshop on Periods and MotivesA Modern Perspective on Renormalization, held from July 26, 2012, at the Instituto de Ciencias Matemáticas, Madrid, Spain. Feynman amplitudes are integrals attached to Feynman diagrams by means of Feynman rules. They form a central part of perturbative quantum field theory, where they appear as coefficients of power series expansions of probability amplitudes for physical processes. The efficient computation of Feynman amplitudes is pivotal for theoretical predictions in particle physics. Periods are numbers computed as integrals of algebraic differential forms over topological cycles on algebraic varieties. The term originated from the period of a periodic elliptic function, which can be computed as an elliptic integral. Motives emerged from Grothendieck's "universal cohomology theory", where they describe an intermediate step between algebraic varieties and their linear invariants (cohomology). The theory of motives provides a conceptual framework for the study of periods. In recent work, a beautiful relation between Feynman amplitudes, motives and periods has emerged. The articles provide an exciting panoramic view on recent developments in this fascinating and fruitful interaction between pure mathematics and modern theoretical physics
1 edition published in 2015 in English and held by 1 WorldCat member library worldwide
This volume contains the proceedings of the International Research Workshop on Periods and MotivesA Modern Perspective on Renormalization, held from July 26, 2012, at the Instituto de Ciencias Matemáticas, Madrid, Spain. Feynman amplitudes are integrals attached to Feynman diagrams by means of Feynman rules. They form a central part of perturbative quantum field theory, where they appear as coefficients of power series expansions of probability amplitudes for physical processes. The efficient computation of Feynman amplitudes is pivotal for theoretical predictions in particle physics. Periods are numbers computed as integrals of algebraic differential forms over topological cycles on algebraic varieties. The term originated from the period of a periodic elliptic function, which can be computed as an elliptic integral. Motives emerged from Grothendieck's "universal cohomology theory", where they describe an intermediate step between algebraic varieties and their linear invariants (cohomology). The theory of motives provides a conceptual framework for the study of periods. In recent work, a beautiful relation between Feynman amplitudes, motives and periods has emerged. The articles provide an exciting panoramic view on recent developments in this fascinating and fruitful interaction between pure mathematics and modern theoretical physics
Applets interactius de restauració d'imatges by Ning Li(
)
1 edition published in 2008 in Spanish and held by 1 WorldCat member library worldwide
1 edition published in 2008 in Spanish and held by 1 WorldCat member library worldwide
Regulators : regulators IIIconference, July 1222, 2010, Barcelona, Spain(
Book
)
1 edition published in 2012 in English and held by 1 WorldCat member library worldwide
1 edition published in 2012 in English and held by 1 WorldCat member library worldwide
Approximation diophantienne sur les variétés projectives et les groupes algébriques commutatifs by
François Ballaÿ(
)
1 edition published in 2017 in French and held by 1 WorldCat member library worldwide
In this thesis, we study diophantine geometry problems on projective varieties and commutative algebraic groups, by means of tools from Arakelov theory. A central notion in this work is the slope theory for hermitian vector bundles, introduced by Bost in the 1990s. More precisely, we work with its generalization in an adelic setting, inspired by Zhang and developed by Gaudron. This dissertation contains two major lines. The first one is devoted to the study of a remarkable theorem due to Faltings and Wüstholz, which generalizes Schmidt's subspace theorem. We first reformulate the proof of Faltings and Wüstholz using the formalism of adelic vector bundles and the adelic slope method. We then establish some effective variants of the theorem, and we deduce an effective generalization of Liouville's theorem for closed points on a projective variety defined over a number field. In particular, we give an explicit upper bound for the height of the points satisying a Liouvilletype inequality. In the second part, we establish new measures of linear independence of logarithms over a commutative algebraic group. We focus our study on the rational case. Our approach combines Baker's method (revisited by Philippon and Waldschmidt) with arguments from the slope theory. More importantly, we introduce a new argument to deal with the periodic case, inspired by previous works of Bertrand and Philippon. This method does not require the use of an extrapolation on derivations in the sense of PhilipponWaldschmidt. In this way, we are able to remove an important hypothesis in several theorems of Gaudron establishing lower bounds for linear forms in logarithms
1 edition published in 2017 in French and held by 1 WorldCat member library worldwide
In this thesis, we study diophantine geometry problems on projective varieties and commutative algebraic groups, by means of tools from Arakelov theory. A central notion in this work is the slope theory for hermitian vector bundles, introduced by Bost in the 1990s. More precisely, we work with its generalization in an adelic setting, inspired by Zhang and developed by Gaudron. This dissertation contains two major lines. The first one is devoted to the study of a remarkable theorem due to Faltings and Wüstholz, which generalizes Schmidt's subspace theorem. We first reformulate the proof of Faltings and Wüstholz using the formalism of adelic vector bundles and the adelic slope method. We then establish some effective variants of the theorem, and we deduce an effective generalization of Liouville's theorem for closed points on a projective variety defined over a number field. In particular, we give an explicit upper bound for the height of the points satisying a Liouvilletype inequality. In the second part, we establish new measures of linear independence of logarithms over a commutative algebraic group. We focus our study on the rational case. Our approach combines Baker's method (revisited by Philippon and Waldschmidt) with arguments from the slope theory. More importantly, we introduce a new argument to deal with the periodic case, inspired by previous works of Bertrand and Philippon. This method does not require the use of an extrapolation on derivations in the sense of PhilipponWaldschmidt. In this way, we are able to remove an important hypothesis in several theorems of Gaudron establishing lower bounds for linear forms in logarithms
Regulators by
José I Burgos Gil(
)
1 edition published in 2012 in English and held by 1 WorldCat member library worldwide
1 edition published in 2012 in English and held by 1 WorldCat member library worldwide
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Related Identities
 Sombra, Martín 1970
 Philippon, Patrice 1954
 ÁlvarezCónsul, Luis 1970 Author Editor
 EbrahimiFard, Kurusch 1973 Editor
 Université de Montréal Centre de recherches mathématiques
 American Mathematical Society Publisher
 Sombra, Martín
 Philippon, Patrice
 Universitat de Barcelona Departament d'Àlgebra i Geometria
 Feliu i Trijueque, Elisenda Author
Covers
Alternative Names
Burgos Gil, J. I.
BurgosGil, José Burgos
BurgosGil, José I
BurgosGil, José I. 1962
Burgos Gil, José Ignacio.
BurgosGil, José Ignacio 1962
Gil, José I. 1962
Gil, José I. Burgos.
Gil, José I. Burgos 1962
Gil, José I. Burgos (José Ignacio Burgos), 1962
Gil, José Ignacio Burgos.
Gil José Ignacio Burgos 1962....
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