Lysenko, Sergey
Overview
Works:  8 works in 12 publications in 2 languages and 101 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Editor, Author, Thesis advisor 
Classifications:  QA353.A9, 516.35 
Publication Timeline
.
Most widely held works by
Sergey Lysenko
De la géométrie algébrique aux formes automorphes : une collection d'articles en l'honneur du soixantième anniversaire
de Gérard Laumon(
Book
)
2 editions published in 2015 in English and held by 88 WorldCat member libraries worldwide
" ... The range of subjects covered reflects the diversity and richness of the works and interests of Gérard Laumon: étale cohomology of schemes and stacks, adic sheaves and Fourier transform, character sheaves, classic and geometric Langlands correspondence, GrothendieckLefschetz trace formula, ArthurSelberg trace formula, Shimura varieties, Higgs fibre bundles and Hitchin fibration ..."
2 editions published in 2015 in English and held by 88 WorldCat member libraries worldwide
" ... The range of subjects covered reflects the diversity and richness of the works and interests of Gérard Laumon: étale cohomology of schemes and stacks, adic sheaves and Fourier transform, character sheaves, classic and geometric Langlands correspondence, GrothendieckLefschetz trace formula, ArthurSelberg trace formula, Shimura varieties, Higgs fibre bundles and Hitchin fibration ..."
RELATIONS D'ORTHOGONALITE ENTRE LES FAISCEAUX AUTOMORPHES ATTACHES AUX SYSTEMES LOCAUX IRREDUCTIBLES DE RANG 2 SUR UNE COURBE by
Sergey Lysenko(
Book
)
2 editions published in 1999 in French and held by 4 WorldCat member libraries worldwide
L'OBJET PRINCIPAL DE CETTE THESE EST DE DONNER UNE INTERPRETATION GEOMETRIQUE DES RESULTATS DE RANKIN ET SELBERG SUR LE PRODUIT SCALAIRE DE DEUX FORMES AUTOMORPHES (CUSPIDALES ET PARTOUT NON RAMIFIEES) POUR GL(2) SUR UN CORPS DE FONCTIONS. CETTE GEOMETRISATION FAIT PARTIE DU PROGRAMME DE LANGLANDS GEOMETRIQUE INITIE PAR V.DRINFELD, A.BEILINSON ET G.LAUMON. SOIT E 0 UN SYSTEME LOCAL LADIC IRREDUCTIBLE DE RANG 2 SUR UNE COURBE X. PAR LA CORRESPONDENCE DE LANGLANDS GEOMETRIQUE, A E 0 EST ASSOCIE UN FAISCEAU PERVERS IRREDUCTIBLE AUT N E 0 SUR LE CHAMP BUN N 2 DE MODULES DES FIBRES VECTORIELS DE RANK 2 ET DE DEGREE N SUR X, QUI EST UN VECTEUR PROPRE DES OPERATEURS DE HECKE. ON INTRODUIT UN CHAMP $BUN N 2, LE QUOTIENT DE BUN N 2 PAR 2ACTION DE G M PAR LES AUTOMORPHISMES SCALAIRES DES FIBRES VECTORIELS. ON DEMONTRE QUE AUT N E 0 EST L'IMAGE INVERSE D'UN FAISCEAU PERVERS $AUT N E 0 SUR $BUN N 2. ON CALCULE R C($BUN N 2,$AUT N E * 1 $ $AUT N E 2), OU E 1 ET E 2 SONT DEUX DEFORMATIONS UNIVERSELLES DE E 0 INDEPENDENTES L'UNE DE L'AUTRE. LE RESULTAT, CONSIDERE COMME UN FAISCEAU SUR LE SCHEMA FORMEL DES PARAMETRES, EST UN FAISCEAU CONSTANT SUR LE DIAGONAL. LA DEMONSTRATION EST BASEE SUR UN RESULTAT LOCAL QUI N'APPARAIT PAS DANS LA METHODE CLASSIQUE DE RANKINSELBERG POUR LES FORMES AUTOMORPHES CORRESPONDANTES
2 editions published in 1999 in French and held by 4 WorldCat member libraries worldwide
L'OBJET PRINCIPAL DE CETTE THESE EST DE DONNER UNE INTERPRETATION GEOMETRIQUE DES RESULTATS DE RANKIN ET SELBERG SUR LE PRODUIT SCALAIRE DE DEUX FORMES AUTOMORPHES (CUSPIDALES ET PARTOUT NON RAMIFIEES) POUR GL(2) SUR UN CORPS DE FONCTIONS. CETTE GEOMETRISATION FAIT PARTIE DU PROGRAMME DE LANGLANDS GEOMETRIQUE INITIE PAR V.DRINFELD, A.BEILINSON ET G.LAUMON. SOIT E 0 UN SYSTEME LOCAL LADIC IRREDUCTIBLE DE RANG 2 SUR UNE COURBE X. PAR LA CORRESPONDENCE DE LANGLANDS GEOMETRIQUE, A E 0 EST ASSOCIE UN FAISCEAU PERVERS IRREDUCTIBLE AUT N E 0 SUR LE CHAMP BUN N 2 DE MODULES DES FIBRES VECTORIELS DE RANK 2 ET DE DEGREE N SUR X, QUI EST UN VECTEUR PROPRE DES OPERATEURS DE HECKE. ON INTRODUIT UN CHAMP $BUN N 2, LE QUOTIENT DE BUN N 2 PAR 2ACTION DE G M PAR LES AUTOMORPHISMES SCALAIRES DES FIBRES VECTORIELS. ON DEMONTRE QUE AUT N E 0 EST L'IMAGE INVERSE D'UN FAISCEAU PERVERS $AUT N E 0 SUR $BUN N 2. ON CALCULE R C($BUN N 2,$AUT N E * 1 $ $AUT N E 2), OU E 1 ET E 2 SONT DEUX DEFORMATIONS UNIVERSELLES DE E 0 INDEPENDENTES L'UNE DE L'AUTRE. LE RESULTAT, CONSIDERE COMME UN FAISCEAU SUR LE SCHEMA FORMEL DES PARAMETRES, EST UN FAISCEAU CONSTANT SUR LE DIAGONAL. LA DEMONSTRATION EST BASEE SUR UN RESULTAT LOCAL QUI N'APPARAIT PAS DANS LA METHODE CLASSIQUE DE RANKINSELBERG POUR LES FORMES AUTOMORPHES CORRESPONDANTES
La correspondance de Howe géométrique modérément ramifiée pour les paires duales de type II dans le cadre du programme
de Langlands géométrique by
Banafsheh FarangHariri(
Book
)
2 editions published in 2012 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 2012 in English and held by 2 WorldCat member libraries worldwide
De la géométrie algébrique aux formes automorphes : une collection d'articles en l'honneur du soixantième anniversaire
de Gérard Laumon by
JeanBenoît Bost(
Book
)
2 editions published in 2015 in English and held by 2 WorldCat member libraries worldwide
"... The range of subjects covered reflects the diversity and richness of the works and interests of Gérard Laumon: étale cohomology of schemes and stacks, adic sheaves and Fourier transform, character sheaves, classic and geometric Langlands correspondence, GrothendieckLefschetz trace formula, ArthurSelberg trace formula, Shimura varieties, Higgs fibre bundles and Hitchin fibration, ..."
2 editions published in 2015 in English and held by 2 WorldCat member libraries worldwide
"... The range of subjects covered reflects the diversity and richness of the works and interests of Gérard Laumon: étale cohomology of schemes and stacks, adic sheaves and Fourier transform, character sheaves, classic and geometric Langlands correspondence, GrothendieckLefschetz trace formula, ArthurSelberg trace formula, Shimura varieties, Higgs fibre bundles and Hitchin fibration, ..."
Twisted Whittaker models for metaplectic groups by
Sergey Lysenko(
)
1 edition published in 2017 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2017 in English and held by 2 WorldCat member libraries worldwide
Geometrized RankinSelberg method for GL(n) by
Sergey Lysenko(
Book
)
1 edition published in 2000 in English and held by 1 WorldCat member library worldwide
1 edition published in 2000 in English and held by 1 WorldCat member library worldwide
Twisted Whittaker category on affine flags and category of representations of mixed quantum group by
Ruotao Yang(
)
1 edition published in 2020 in English and held by 1 WorldCat member library worldwide
Suppose that G is a reductive group. We have the geometric Satake equivalence which identifies Sph (G), the perverse G (O) equivalent Dmodules on affine grassmannin as the category of finite dimensional representation of H, the Langlands dual group of G. We note that: Whit(Gr) = Sph(G). Here, Whit (Gr) is the module category D (N (K), \ chi) equivalent on Gr. Now, the category of representation admits a deformation by the category of representations of quantum group. On the Whittaker side, we can consider the twisted Dmodules on affine grassmannin. This is the fundamental local equivalence: Whit_q (Gr) = Rep_q (H) . Recently, D. Gaitsgory proposed its ramified version. We consider the affine flags instead of the affine grassmannians. In this case, we have to replace the category of quantum group representations with another category, the category of mixed quantum group representations. Whit_q (Fl) = Rep_q ^ {mix} (H) . We prove that the category of twisted Whittaker Dmodules on the affine flags and the category of representations of the mixed quantum group are equivalent
1 edition published in 2020 in English and held by 1 WorldCat member library worldwide
Suppose that G is a reductive group. We have the geometric Satake equivalence which identifies Sph (G), the perverse G (O) equivalent Dmodules on affine grassmannin as the category of finite dimensional representation of H, the Langlands dual group of G. We note that: Whit(Gr) = Sph(G). Here, Whit (Gr) is the module category D (N (K), \ chi) equivalent on Gr. Now, the category of representation admits a deformation by the category of representations of quantum group. On the Whittaker side, we can consider the twisted Dmodules on affine grassmannin. This is the fundamental local equivalence: Whit_q (Gr) = Rep_q (H) . Recently, D. Gaitsgory proposed its ramified version. We consider the affine flags instead of the affine grassmannians. In this case, we have to replace the category of quantum group representations with another category, the category of mixed quantum group representations. Whit_q (Fl) = Rep_q ^ {mix} (H) . We prove that the category of twisted Whittaker Dmodules on the affine flags and the category of representations of the mixed quantum group are equivalent
Faisceau automorphe unipotent pour G₂, nombres de Franel, et stratification de ThomBoardman by
Lizao Ye(
)
1 edition published in 2019 in French and held by 1 WorldCat member library worldwide
In this thesis, on the one hand, we generalise to the equivariant case a result of J. Denef and F. Loeser about trigonometric sums on tori ; on the other hand, we study the ThomBoardman stratification associated to the multiplication of global sections of line bundles on a curve. We prove a subtle inequaliity about the dimensions of these strata. Our motivation comes from the geometric Langlands program. Based on works of W. T. Gan, N. Gurevich, D. Jiang and S. Lysenko, we propose, for the reductive group G of type G2, a conjectural construction of the automorphic sheaf whose Arthur parameter is unipotent and subregular. Using our two results above, we determine the generic ranks of all isotypic components of an S3equivaraint sheaf which appears in our conjecture, this S3 being the centraliser of the subregular SL2 inside the Langlands dual group of G
1 edition published in 2019 in French and held by 1 WorldCat member library worldwide
In this thesis, on the one hand, we generalise to the equivariant case a result of J. Denef and F. Loeser about trigonometric sums on tori ; on the other hand, we study the ThomBoardman stratification associated to the multiplication of global sections of line bundles on a curve. We prove a subtle inequaliity about the dimensions of these strata. Our motivation comes from the geometric Langlands program. Based on works of W. T. Gan, N. Gurevich, D. Jiang and S. Lysenko, we propose, for the reductive group G of type G2, a conjectural construction of the automorphic sheaf whose Arthur parameter is unipotent and subregular. Using our two results above, we determine the generic ranks of all isotypic components of an S3equivaraint sheaf which appears in our conjecture, this S3 being the centraliser of the subregular SL2 inside the Langlands dual group of G
Audience Level
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Related Identities
 Laumon, Gérard Opponent Thesis advisor
 Genestier, Alain Other Opponent Editor
 Boyer, Pascal 1970 Editor
 Bost, JeanBenoît 1961 Editor
 Lafforgue, Laurent Editor
 Morel, Sophie 1979 Editor
 Ngô, Báo Châu Editor
 Université ParisSud Centre d'Orsay
 Université ParisSud Degree grantor
 École doctorale IAEM Lorraine  Informatique, Automatique, Électronique  Électrotechnique, Mathématiques de Lorraine Other
Associated Subjects