Edit Profile (opens in new tab) Tsygan, Boris Co-Author Distance Author ID: tsygan.boris Published as: Tsygan, Boris; Tsygan, B. External Links: MGP · Wikidata · GND · IdRef · theses.fr Documents Indexed: 44 Publications since 1991, including 1 Book and 5 Additional arXiv Preprints 2 Contributions as Editor Co-Authors: 23 Co-Authors with 38 Joint Publications 564 Co-Co-Authors all top 5 Co-Authors 7 single-authored 26 Nest, Ryszard 17 Bressler, Paul 11 Gorokhovsky, Alexander 6 Tamarkin, Dmitry E. 3 Dolgushev, Vasily A. 1 Bismut, Jean-Michel 1 Brylinski, Jean-Luc 1 Brylinski, Ranee Kathryn 1 Cuntz, Joachim 1 Feng, Ping 1 Hitrik, Michael 1 Kapranov, Mikhail M. 1 Kolyada, Sergiǐ Fedorovych 1 Leichtnam, Eric 1 Malikov, Fyodor 1 Nistor, Victor 1 Reznikova, Ida 1 Schechtman, Vadim 1 Skandalis, Georges 1 Soibelman, Yan S. 1 Vasserot, Eric 1 Xu, Ping 1 Zelditch, Steve all top 5 Serials 6 Advances in Mathematics 3 Letters in Mathematical Physics 2 Communications in Mathematical Physics 2 IMRN. International Mathematics Research Notices 2 Methods of Functional Analysis and Topology 1 Compositio Mathematica 1 Journal of Differential Geometry 1 Journal für die Reine und Angewandte Mathematik 1 Selecta Mathematica 1 Theory and Applications of Categories 1 The Asian Journal of Mathematics 1 Moscow Mathematical Journal 1 Encyclopaedia of Mathematical Sciences 1 Progress in Mathematics 1 Journal of Noncommutative Geometry 1 Springer Proceedings in Mathematics & Statistics all top 5 Fields 24 Differential geometry (53-XX) 21 Global analysis, analysis on manifolds (58-XX) 14 Category theory; homological algebra (18-XX) 13 Associative rings and algebras (16-XX) 8 Nonassociative rings and algebras (17-XX) 7 Algebraic geometry (14-XX) 6 \(K\)-theory (19-XX) 4 Several complex variables and analytic spaces (32-XX) 3 Partial differential equations (35-XX) 3 Algebraic topology (55-XX) 2 General and overarching topics; collections (00-XX) 2 Functional analysis (46-XX) 2 Manifolds and cell complexes (57-XX) 1 History and biography (01-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Quantum theory (81-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 36 Publications have been cited 456 times in 311 Documents Cited by ▼ Year ▼ Algebraic index theorem. Zbl 0887.58050 Nest, Ryszard; Tsygan, Boris 79 1995 Noncommutative differential calculus, homotopy BV algebras and formality conjectures. Zbl 0965.58010 Tamarkin, D.; Tsygan, B. 46 2000 Deformations of symplectic Lie algebroids, deformations of holomorphic symplectic structures, and index theorems. Zbl 1023.53060 Nest, Ryszard; Tsygan, Boris 41 2001 Algebraic index theorem for families. Zbl 0837.58029 Nest, Ryszard; Tsygan, Boris 40 1995 The homotopy Gerstenhaber algebra of Hochschild cochains of a regular algebra is formal. Zbl 1144.18007 Dolgushev, Vasiliy A.; Tamarkin, Dmitry; Tsygan, Boris 31 2007 Formality conjectures for chains. Zbl 0962.18008 Tsygan, B. 27 1999 Hochschild and cyclic homology of quantum groups. Zbl 0743.17020 Feng, Ping; Tsygan, Boris 27 1991 Deformation quantization of gerbes. Zbl 1125.53069 Bressler, Paul; Gorokhovsky, Alexander; Nest, Ryszard; Tsygan, Boris 23 2007 Riemann-Roch theorems via deformation quantization. I. Zbl 1021.53064 Bressler, P.; Nest, R.; Tsygan, B. 21 2002 Formal deformations of symplectic manifolds with boundary. Zbl 0866.58038 Nest, Ryszard; Tsygan, Boris 21 1996 The ring of differential operators on forms in noncommutative calculus. Zbl 1150.16011 Tamarkin, Dmitri; Tsygan, Boris 20 2005 Cyclic formality and index theorem. Zbl 1008.19002 Tamarkin, Dmitry; Tsygan, Boris 16 2001 Cyclic homology in non-commutative geometry. Zbl 1045.46043 Cuntz, Joachim; Skandalis, Georges; Tsygan, Boris 15 2004 On the cohomology ring of an algebra. Zbl 0919.57019 Nest, Ryszard; Tsygan, Boris 14 1999 Formality theorems for Hochschild complexes and their applications. Zbl 1193.19002 Dolgushev, Vasiliy; Tamarkin, Dmitry; Tsygan, Boris 11 2009 Remarks on modules over deformation quantization algebras. Zbl 1116.53052 Nest, Ryszard; Tsygan, Boris 11 2004 Formal versus analytic index theorems. Zbl 0871.58076 Nest, Ryszard; Tsygan, Boris 9 1996 Noncommutative calculus and operads. Zbl 1316.18001 Tsygan, Boris 9 2012 On the Gauss-Manin connection in cyclic homology. Zbl 1116.18010 Tsygan, Boris 8 2007 Deformations of gerbes on smooth manifolds. Zbl 1157.53051 Bressler, Paul; Gorokhovsky, Alexander; Nest, Ryszard; Tsygan, Boris 8 2008 Local formula for the index of a Fourier integral operator. Zbl 1030.58015 Leichtnam, Eric; Nest, Ryszard; Tsygan, Boris 8 2001 Deformations of algebroid stacks. Zbl 1209.53062 Bressler, Paul; Gorokhovsky, Alexander; Nest, Ryszard; Tsygan, Boris 6 2011 Oscillatory modules. Zbl 1214.53069 Tsygan, Boris 6 2009 Formality theorem for gerbes. Zbl 1311.53023 Bressler, Paul; Gorokhovsky, Alexander; Nest, Ryszard; Tsygan, Boris 5 2015 A microlocal category associated to a symplectic manifold. Zbl 1417.53097 Tsygan, Boris 5 2018 Riemann-Roch for real varieties. Zbl 1230.14010 Bressler, Paul; Kapranov, Mikhail; Tsygan, Boris; Vasserot, Eric 4 2009 Riemann-Roch theorems via deformation quantization. II. Zbl 1021.53065 Bressler, P.; Nest, R.; Tsygan, B. 3 2002 Notes on differential forms on quantum groups. Zbl 1013.58501 Tsygan, Boris 3 1993 Deligne groupoid revisited. Zbl 1330.18022 Bressler, Paul; Gorokhovsky, Alexander; Nest, Ryszard; Tsygan, Boris 3 2015 Deformations of Azumaya algebras. Zbl 1204.53078 Bressler, Paul; Gorokhovsky, Alexander; Nest, Ryszard; Tsygan, Boris 2 2007 Product structures in (cyclic)homology and their applications. Zbl 0926.58018 Nest, Ryszard; Tsygan, Boris 2 1997 Chern character for twisted complexes. Zbl 1146.19003 Bressler, Paul; Gorokhovsky, Alexander; Nest, Ryszard; Tsygan, Boris 1 2008 Algebraic index theorem for symplectic deformations of gerbes. Zbl 1235.53094 Bressler, Paul; Gorokhovsky, Alexander; Nest, Ryszard; Tsygan, Boris 1 2011 A Riemann-Roch type formula for the microlocal Euler class. Zbl 0915.32001 Bressler, P.; Nest, R.; Tsygan, B. 1 1997 The Fukaya type categories for associative algebras. Zbl 1167.18303 Nest, Ryszard; Tsygan, Boris 1 1997 On quasi-classical limits of DQ-algebroids. Zbl 1373.53125 Bressler, Paul; Gorokhovsky, Alexander; Nest, Ryszard; Tsygan, Boris 1 2017 A microlocal category associated to a symplectic manifold. Zbl 1417.53097 Tsygan, Boris 5 2018 On quasi-classical limits of DQ-algebroids. Zbl 1373.53125 Bressler, Paul; Gorokhovsky, Alexander; Nest, Ryszard; Tsygan, Boris 1 2017 Formality theorem for gerbes. Zbl 1311.53023 Bressler, Paul; Gorokhovsky, Alexander; Nest, Ryszard; Tsygan, Boris 5 2015 Deligne groupoid revisited. Zbl 1330.18022 Bressler, Paul; Gorokhovsky, Alexander; Nest, Ryszard; Tsygan, Boris 3 2015 Noncommutative calculus and operads. Zbl 1316.18001 Tsygan, Boris 9 2012 Deformations of algebroid stacks. Zbl 1209.53062 Bressler, Paul; Gorokhovsky, Alexander; Nest, Ryszard; Tsygan, Boris 6 2011 Algebraic index theorem for symplectic deformations of gerbes. Zbl 1235.53094 Bressler, Paul; Gorokhovsky, Alexander; Nest, Ryszard; Tsygan, Boris 1 2011 Formality theorems for Hochschild complexes and their applications. Zbl 1193.19002 Dolgushev, Vasiliy; Tamarkin, Dmitry; Tsygan, Boris 11 2009 Oscillatory modules. Zbl 1214.53069 Tsygan, Boris 6 2009 Riemann-Roch for real varieties. Zbl 1230.14010 Bressler, Paul; Kapranov, Mikhail; Tsygan, Boris; Vasserot, Eric 4 2009 Deformations of gerbes on smooth manifolds. Zbl 1157.53051 Bressler, Paul; Gorokhovsky, Alexander; Nest, Ryszard; Tsygan, Boris 8 2008 Chern character for twisted complexes. Zbl 1146.19003 Bressler, Paul; Gorokhovsky, Alexander; Nest, Ryszard; Tsygan, Boris 1 2008 The homotopy Gerstenhaber algebra of Hochschild cochains of a regular algebra is formal. Zbl 1144.18007 Dolgushev, Vasiliy A.; Tamarkin, Dmitry; Tsygan, Boris 31 2007 Deformation quantization of gerbes. Zbl 1125.53069 Bressler, Paul; Gorokhovsky, Alexander; Nest, Ryszard; Tsygan, Boris 23 2007 On the Gauss-Manin connection in cyclic homology. Zbl 1116.18010 Tsygan, Boris 8 2007 Deformations of Azumaya algebras. Zbl 1204.53078 Bressler, Paul; Gorokhovsky, Alexander; Nest, Ryszard; Tsygan, Boris 2 2007 The ring of differential operators on forms in noncommutative calculus. Zbl 1150.16011 Tamarkin, Dmitri; Tsygan, Boris 20 2005 Cyclic homology in non-commutative geometry. Zbl 1045.46043 Cuntz, Joachim; Skandalis, Georges; Tsygan, Boris 15 2004 Remarks on modules over deformation quantization algebras. Zbl 1116.53052 Nest, Ryszard; Tsygan, Boris 11 2004 Riemann-Roch theorems via deformation quantization. I. Zbl 1021.53064 Bressler, P.; Nest, R.; Tsygan, B. 21 2002 Riemann-Roch theorems via deformation quantization. II. Zbl 1021.53065 Bressler, P.; Nest, R.; Tsygan, B. 3 2002 Deformations of symplectic Lie algebroids, deformations of holomorphic symplectic structures, and index theorems. Zbl 1023.53060 Nest, Ryszard; Tsygan, Boris 41 2001 Cyclic formality and index theorem. Zbl 1008.19002 Tamarkin, Dmitry; Tsygan, Boris 16 2001 Local formula for the index of a Fourier integral operator. Zbl 1030.58015 Leichtnam, Eric; Nest, Ryszard; Tsygan, Boris 8 2001 Noncommutative differential calculus, homotopy BV algebras and formality conjectures. Zbl 0965.58010 Tamarkin, D.; Tsygan, B. 46 2000 Formality conjectures for chains. Zbl 0962.18008 Tsygan, B. 27 1999 On the cohomology ring of an algebra. Zbl 0919.57019 Nest, Ryszard; Tsygan, Boris 14 1999 Product structures in (cyclic)homology and their applications. Zbl 0926.58018 Nest, Ryszard; Tsygan, Boris 2 1997 A Riemann-Roch type formula for the microlocal Euler class. Zbl 0915.32001 Bressler, P.; Nest, R.; Tsygan, B. 1 1997 The Fukaya type categories for associative algebras. Zbl 1167.18303 Nest, Ryszard; Tsygan, Boris 1 1997 Formal deformations of symplectic manifolds with boundary. Zbl 0866.58038 Nest, Ryszard; Tsygan, Boris 21 1996 Formal versus analytic index theorems. Zbl 0871.58076 Nest, Ryszard; Tsygan, Boris 9 1996 Algebraic index theorem. Zbl 0887.58050 Nest, Ryszard; Tsygan, Boris 79 1995 Algebraic index theorem for families. Zbl 0837.58029 Nest, Ryszard; Tsygan, Boris 40 1995 Notes on differential forms on quantum groups. Zbl 1013.58501 Tsygan, Boris 3 1993 Hochschild and cyclic homology of quantum groups. Zbl 0743.17020 Feng, Ping; Tsygan, Boris 27 1991 all cited Publications top 5 cited Publications all top 5 Cited by 335 Authors 16 Waldmann, Stefan 15 Miranda, Eva 11 Tang, Xiang 10 Gorokhovsky, Alexander 10 Tsygan, Boris 10 Xu, Ping 9 Bressler, Paul 9 Nest, Ryszard 8 Calaque, Damien 8 Dolgushev, Vasily A. 8 Karabegov, Alexander V. 8 Stiénon, Mathieu 6 Pflaum, Markus J. 6 Posthuma, Hessel Bouke 6 Willwacher, Thomas Hans 6 Yekutieli, Amnon 5 Gutt, Simone 5 Hadfield, Tom 5 Krähmer, Ulrich 5 Neumaier, Nikolai 5 Ramadoss, Ajay C. 5 Schedler, Travis 5 Schrohe, Elmar 5 Van den Bergh, Michel 4 Chen, Zhuo 4 Grady, Ryan E. 4 Kiesenhofer, Anna 4 Leung, Naichung Conan 3 Berger, Roland 3 Bieliavsky, Pierre 3 Bordemann, Martin 3 Bursztyn, Henrique 3 Chen, Xiaojun 3 D’Agnolo, Andrea 3 Etingof, Pavel Il’ich 3 Felder, Giovanni 3 Ginzburg, Victor 3 Halbout, Gilles 3 Kashiwara, Masaki 3 Li, Qin 3 Liao, Hsuan-Yi 3 Markl, Martin 3 Mir, Pau 3 Polesello, Pietro 3 Rubtsov, Vladimir Nikolaevich 3 Savin, Anton Yur’evich 3 Schapira, Pierre 3 Schmitt, Philipp 3 Sharapov, Alexey A. 3 Skvortsov, Evgeny D. 3 Tseng, Hsian-Hua 3 Yu, Shilin 2 Bai, Chengming 2 Behrend, Kai A. 2 Braddell, Roisin 2 Bruzzo, Ugo 2 Cattaneo, Alberto Sergio 2 Chan, Kwokwai 2 Chen, Youming 2 Das, Apurba 2 Delshams, Amadeu 2 Eshmatov, Farkhod 2 Esposito, Chiara 2 Eu, Ching-Hwa 2 Grensing, Martin 2 Gwilliam, Owen 2 Kaledin, Dmitry B. 2 Kapranov, Mikhail M. 2 Klaasse, Ralph L. 2 Kowalzig, Niels 2 La Fuente Gravy, Laurent 2 Leichtnam, Eric 2 Li, Si 2 Liu, Jiefeng 2 Liu, Leilei 2 Menichi, Luc 2 Oms, Cédric 2 Planas, Arnau 2 Rawnsley, John H. 2 Reichert, Thorsten 2 Rogers, Christopher Lee 2 Römer, Hartmann 2 Rossi, Carlo Antonio 2 Schötz, Matthias 2 Scott, Geoffrey 2 Sheng, Yunhe 2 Shoikhet, Boris B. 2 Solotar, Andrea Leonor 2 Sternin, Boris Yur’evich 2 Tonks, Andrew 2 Tortella, Pietro 2 van Erp, Erik 2 Vasserot, Eric 2 Wei, Zhaoting George 2 Weinstein, Alan David 2 Yang, Song 2 Yao, Yijun 2 Zeng, Jieheng 1 Aastrup, Johannes 1 Abbaspour, Hossein ...and 235 more Authors all top 5 Cited in 90 Serials 42 Advances in Mathematics 26 Journal of Geometry and Physics 24 Communications in Mathematical Physics 19 Letters in Mathematical Physics 15 Journal of Noncommutative Geometry 11 Journal of Algebra 9 Journal of Functional Analysis 7 Duke Mathematical Journal 6 Journal of Mathematical Physics 6 Reviews in Mathematical Physics 6 Journal für die Reine und Angewandte Mathematik 5 Compositio Mathematica 4 Israel Journal of Mathematics 4 \(K\)-Theory 4 Journal of High Energy Physics 4 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 3 Communications in Algebra 3 Journal of Pure and Applied Algebra 3 Mathematische Annalen 3 Publications of the Research Institute for Mathematical Sciences, Kyoto University 3 Transactions of the American Mathematical Society 3 International Journal of Mathematics 3 Applied Categorical Structures 3 Journal of the Institute of Mathematics of Jussieu 2 Bulletin of the London Mathematical Society 2 Proceedings of the American Mathematical Society 2 Proceedings of the London Mathematical Society. Third Series 2 Annals of Global Analysis and Geometry 2 Journal de Mathématiques Pures et Appliquées. Neuvième Série 2 Selecta Mathematica. New Series 2 Theory and Applications of Categories 2 Documenta Mathematica 2 Annals of Mathematics. Second Series 2 Regular and Chaotic Dynamics 2 Algebraic & Geometric Topology 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Central European Journal of Mathematics 2 International Journal of Geometric Methods in Modern Physics 2 Journal of Physics A: Mathematical and Theoretical 2 Journal of Homotopy and Related Structures 2 Journal of \(K\)-Theory 1 International Journal of Modern Physics A 1 Reports on Mathematical Physics 1 Rocky Mountain Journal of Mathematics 1 Theoretical and Mathematical Physics 1 American Journal of Mathematics 1 Annales de l’Institut Fourier 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Archivum Mathematicum 1 Bulletin de la Société Mathématique de France 1 Czechoslovak Mathematical Journal 1 Glasgow Mathematical Journal 1 Inventiones Mathematicae 1 Journal of Differential Geometry 1 Journal of the London Mathematical Society. Second Series 1 Mathematische Zeitschrift 1 Pacific Journal of Mathematics 1 Physica D 1 Revista Matemática Iberoamericana 1 Journal of the American Mathematical Society 1 Asymptotic Analysis 1 Forum Mathematicum 1 Differential Geometry and its Applications 1 The Journal of Geometric Analysis 1 Geometric and Functional Analysis. GAFA 1 Journal of Knot Theory and its Ramifications 1 Nuclear Physics. B. Proceedings Supplements 1 Journal of Mathematical Sciences (New York) 1 Bulletin des Sciences Mathématiques 1 Transformation Groups 1 Abstract and Applied Analysis 1 Mathematical Physics, Analysis and Geometry 1 Geometry & Topology 1 Algebras and Representation Theory 1 Acta Mathematica Sinica. English Series 1 Annales Henri Poincaré 1 La Gaceta de la Real Sociedad Matemática Española 1 Journal of Nonlinear Mathematical Physics 1 Journal of the Australian Mathematical Society 1 Journal of Algebra and its Applications 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 Proceedings of the Steklov Institute of Mathematics 1 São Paulo Journal of Mathematical Sciences 1 Advances in Mathematical Physics 1 Iranian Journal of Mathematical Sciences and Informatics 1 EMS Surveys in Mathematical Sciences 1 European Journal of Mathematics 1 Annals of \(K\)-Theory 1 Electronic Research Archive 1 Frontiers of Mathematics all top 5 Cited in 28 Fields 171 Differential geometry (53-XX) 78 Associative rings and algebras (16-XX) 64 Global analysis, analysis on manifolds (58-XX) 60 Quantum theory (81-XX) 59 Nonassociative rings and algebras (17-XX) 51 Category theory; homological algebra (18-XX) 46 Algebraic geometry (14-XX) 45 Functional analysis (46-XX) 41 \(K\)-theory (19-XX) 33 Several complex variables and analytic spaces (32-XX) 18 Topological groups, Lie groups (22-XX) 18 Algebraic topology (55-XX) 16 Manifolds and cell complexes (57-XX) 15 Dynamical systems and ergodic theory (37-XX) 11 Partial differential equations (35-XX) 9 Commutative algebra (13-XX) 7 Operator theory (47-XX) 6 Relativity and gravitational theory (83-XX) 5 Mechanics of particles and systems (70-XX) 3 Group theory and generalizations (20-XX) 2 Number theory (11-XX) 1 Combinatorics (05-XX) 1 Functions of a complex variable (30-XX) 1 Ordinary differential equations (34-XX) 1 Sequences, series, summability (40-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Fluid mechanics (76-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.