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## Mukai, Shigeru

Compute Distance To:
 Author ID: mukai.shigeru Published as: Mukai, S.; Mukai, Shigeru External Links: MGP · Wikidata · GND
 Documents Indexed: 54 Publications since 1978, including 7 Books Biographic References: 2 Publications
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#### Co-Authors

 36 single-authored 6 Mori, Shigefumi 2 Mabuchi, Toshiki 2 Ohashi, Hisanori 1 Fujino, Osamu 1 Green, Mark Lee 1 Ide, Manabu 1 Illusie, Luc 1 Kato, Kazuya 1 Kawaguchi, Shu 1 Kollár, János 1 Looijenga, Eduard J. N. 1 Miyaoka, Yoichi 1 Moriwaki, Atsushi 1 Nakayama, Noboru 1 Namikawa, Yukihiko 1 Nasu, Hirokazu 1 Nkamura, Iku 1 Saito, Shuji 1 Sakai, Fumio 1 Umemura, Hiroshi 1 Usui, Sampei 1 Yoshikawa, Ken-Ichi
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#### Serials

 3 Inventiones Mathematicae 3 Advanced Studies in Pure Mathematics 2 American Journal of Mathematics 2 Manuscripta Mathematica 2 Proceedings of the Japan Academy. Series A 2 Sūgaku 2 Kyoto Journal of Mathematics 1 Journal of Mathematics of Kyoto University 1 Journal of the Mathematical Society of Japan 1 Nagoya Mathematical Journal 1 Sugaku Expositions 1 Proceedings of the National Academy of Sciences of the United States of America 1 Journal of Algebraic Geometry 1 Annals of Mathematics. Second Series 1 Cambridge Studies in Advanced Mathematics 1 Cambridge Tracts in Mathematics 1 Lecture Notes in Pure and Applied Mathematics 1 RIMS Kôkyûroku Bessatsu
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#### Fields

 53 Algebraic geometry (14-XX) 5 General and overarching topics; collections (00-XX) 5 Differential geometry (53-XX) 3 History and biography (01-XX) 3 Commutative algebra (13-XX) 3 Several complex variables and analytic spaces (32-XX) 2 Number theory (11-XX) 1 Nonassociative rings and algebras (17-XX) 1 Group theory and generalizations (20-XX) 1 Abstract harmonic analysis (43-XX) 1 Global analysis, analysis on manifolds (58-XX)

#### Citations contained in zbMATH

47 Publications have been cited 1,335 times in 1,014 Documents Cited by Year
Duality between $$D(X)$$ and $$D(\hat X)$$ with its application to Picard sheaves. Zbl 0417.14036
Mukai, Shigeru
1981
Symplectic structure of the moduli space of sheaves on an abelian or K 3 surface. Zbl 0565.14002
Mukai, Shigeru
1984
Classification of Fano 3-folds with $$B_ 2 \geq 2$$. Zbl 0478.14033
Mori, Shigefumi; Mukai, Shigeru
1981
Finite groups of automorphisms of K3 surfaces and the Mathieu group. Zbl 0705.14045
Mukai, Shigeru
1988
Biregular classification of Fano 3-folds and Fano manifolds of coindex 3. Zbl 0679.14020
Mukai, Shigeru
1989
On the moduli space of bundles on $$K3$$ surfaces. I. Zbl 0674.14023
Mukai, S.
1987
Fano 3-folds. Zbl 0774.14037
Mukai, Shigeru
1992
An introduction to invariants and moduli. Transl. by W. M. Oxbury. Zbl 1033.14008
Mukai, Shigeru
2003
Semi-homogeneous vector bundles on an abelian variety. Zbl 0417.14029
Mukai, Shigeru
1978
The uniruledness of the moduli space of curves of genus 11. Zbl 0557.14015
Mori, Shigefumi; Mukai, Shigeru
1983
Curves and symmetric spaces. I. Zbl 0871.14025
Mukai, Shigeru
1995
Curves, K3 surfaces and Fano 3-folds of genus $$\leq 10$$. Zbl 0701.14044
Mukai, Shigeru
1988
Maximal subbundles of vector bundles on a curve. Zbl 0572.14008
Mukai, Shigeru; Sakai, Fumio
1985
Curves and Grassmannians. Zbl 0846.14030
Mukai, Shigeru
1993
Polarized K3 surfaces of genus 18 and 20. Zbl 0774.14035
Mukai, Shigeru
1992
Minimal rational threefolds. Zbl 0526.14006
Mukai, Shigeru; Umemura, Hiroshi
1983
Classification of Fano $$3$$-folds with $$B_ 2\geq 2$$. I. Zbl 0800.14021
Mori, Shigefumi; Mukai, Shigeru
1986
Automorphisms of Enriques surfaces which act trivially on the cohomology groups. Zbl 0559.14038
Mukai, Shigeru; Namikawa, Yukihiko
1984
Moduli of vector bundles on K3 surfaces, and symplectic manifolds. Zbl 0685.14021
Mukai, Shigeru
1987
On Fano 3-folds with $$B_ 2\geq 2$$. Zbl 0537.14026
Mori, Shigefumi; Mukai, Shigeru
1983
Geometric realization of $$T$$-shaped root systems and counterexamples to Hilbert’s fourteenth problem. Zbl 1108.13300
Mukai, Shigeru
2004
Duality of polarized K3 surfaces. Zbl 0948.14032
Mukai, Shigeru
1999
Curves and K3 surfaces of genus eleven. Zbl 0884.14010
Mukai, Shigeru
1996
Curves and symmetric spaces. Zbl 0768.14014
Mukai, Shigeru
1992
New developments of Fano varieties – on vector bundles and moduli problems. Zbl 0889.14020
Mukai, Shigeru
1995
Numerically trivial involutions of Kummer type of an Enriques surface. Zbl 1207.14038
Mukai, Shigeru
2010
Counterexamples to Kodaira’s vanishing and Yau’s inequality in positive characteristics. Zbl 1291.14038
Mukai, Shigeru
2013
Curves and symmetric spaces. II. Zbl 1210.14034
Mukai, Shigeru
2010
Vector bundles and Brill-Noether theory. Zbl 0866.14024
Mukai, Shigeru
1995
Plane quartics and Fano threefolds of genus twelve. Zbl 1068.14050
Mukai, Shigeru
2004
Polarized $$K3$$ surfaces of genus thirteen. Zbl 1117.14040
Mukai, Shigeru
2006
Stability and Einstein-Kähler metric of a quartic del Pezzo surface. Zbl 0809.53070
Mabuchi, Toshiki; Mukai, Shigeru
1993
Vector bundles on a $$K3$$ surface. Zbl 1046.14016
Mukai, Shigeru
2002
Fourier functor and its application to the moduli of bundles on an abelian variety. Zbl 0672.14025
Mukai, Shigeru
1987
Obstructions to deforming curves on a 3-fold, I: A generalization of Mumford’s example and an application to $$\operatorname{Hom}$$ schemes. Zbl 1181.14031
Mukai, Shigeru; Nasu, Hirokazu
2009
Extremal rays and Fano 3-folds. Zbl 1070.14018
Mori, Shigefumi; Mukai, Shigeru
2004
Noncommutativizability of Brill-Noether theory and 3-dimensional Fano variety. Zbl 0929.14021
Mukai, Shigeru
1997
Moduli of vector bundles on K3 surfaces and symplectic manifolds. Zbl 0651.14003
Mukai, Shigeru
1987
Kummer’s quartics and numerically reflective involutions of Enriques surfaces. Zbl 1237.14046
Mukai, Shigeru
2012
$$K3$$ surfaces of genus sixteen. Zbl 1369.14049
Mukai, Shigeru
2016
The automorphism group of Enriques surfaces covered by symmetric quartic surfaces. Zbl 1326.14097
Mukai, Shigeru; Ohashi, Hisanori
2014
Igusa quartic and Steiner surfaces. Zbl 1256.14045
Mukai, Shigeru
2012
Resultants and the Borcherds $$\Phi$$-function. Zbl 1425.14033
Kawaguchi, Shu; Mukai, Shigeru; Yoshikawa, Ken-Ichi
2018
Enriques surfaces of Hutchinson-Göpel type and Mathieu automorphisms. Zbl 1302.14031
Mukai, Shigeru; Ohashi, Hisanori
2013
An introduction to invariants and moduli. Transl. from the Japanese by W. M. Oxbury. Reprint of the 2003 hardback ed. Zbl 1257.14006
Mukai, Shigeru
2012
Canonical curves of genus eight. Zbl 1051.14034
Ide, Manabu; Mukai, Shigeru
2003
Algebraic geometry 2000, Azumino. Proceedings of the symposium, Nagano, Japan, July 20–30, 2000. Zbl 1007.00031
Usui, Sampei (ed.); Green, Mark (ed.); Illusie, Luc (ed.); Kato, Kazuya (ed.); Looijenga, Eduard (ed.); Mukai, Shigeru (ed.); Saito, Shuji (ed.)
2002
Resultants and the Borcherds $$\Phi$$-function. Zbl 1425.14033
Kawaguchi, Shu; Mukai, Shigeru; Yoshikawa, Ken-Ichi
2018
$$K3$$ surfaces of genus sixteen. Zbl 1369.14049
Mukai, Shigeru
2016
The automorphism group of Enriques surfaces covered by symmetric quartic surfaces. Zbl 1326.14097
Mukai, Shigeru; Ohashi, Hisanori
2014
Counterexamples to Kodaira’s vanishing and Yau’s inequality in positive characteristics. Zbl 1291.14038
Mukai, Shigeru
2013
Enriques surfaces of Hutchinson-Göpel type and Mathieu automorphisms. Zbl 1302.14031
Mukai, Shigeru; Ohashi, Hisanori
2013
Kummer’s quartics and numerically reflective involutions of Enriques surfaces. Zbl 1237.14046
Mukai, Shigeru
2012
Igusa quartic and Steiner surfaces. Zbl 1256.14045
Mukai, Shigeru
2012
An introduction to invariants and moduli. Transl. from the Japanese by W. M. Oxbury. Reprint of the 2003 hardback ed. Zbl 1257.14006
Mukai, Shigeru
2012
Numerically trivial involutions of Kummer type of an Enriques surface. Zbl 1207.14038
Mukai, Shigeru
2010
Curves and symmetric spaces. II. Zbl 1210.14034
Mukai, Shigeru
2010
Obstructions to deforming curves on a 3-fold, I: A generalization of Mumford’s example and an application to $$\operatorname{Hom}$$ schemes. Zbl 1181.14031
Mukai, Shigeru; Nasu, Hirokazu
2009
Polarized $$K3$$ surfaces of genus thirteen. Zbl 1117.14040
Mukai, Shigeru
2006
Geometric realization of $$T$$-shaped root systems and counterexamples to Hilbert’s fourteenth problem. Zbl 1108.13300
Mukai, Shigeru
2004
Plane quartics and Fano threefolds of genus twelve. Zbl 1068.14050
Mukai, Shigeru
2004
Extremal rays and Fano 3-folds. Zbl 1070.14018
Mori, Shigefumi; Mukai, Shigeru
2004
An introduction to invariants and moduli. Transl. by W. M. Oxbury. Zbl 1033.14008
Mukai, Shigeru
2003
Canonical curves of genus eight. Zbl 1051.14034
Ide, Manabu; Mukai, Shigeru
2003
Vector bundles on a $$K3$$ surface. Zbl 1046.14016
Mukai, Shigeru
2002
Algebraic geometry 2000, Azumino. Proceedings of the symposium, Nagano, Japan, July 20–30, 2000. Zbl 1007.00031
Usui, Sampei (ed.); Green, Mark (ed.); Illusie, Luc (ed.); Kato, Kazuya (ed.); Looijenga, Eduard (ed.); Mukai, Shigeru (ed.); Saito, Shuji (ed.)
2002
Duality of polarized K3 surfaces. Zbl 0948.14032
Mukai, Shigeru
1999
Noncommutativizability of Brill-Noether theory and 3-dimensional Fano variety. Zbl 0929.14021
Mukai, Shigeru
1997
Curves and K3 surfaces of genus eleven. Zbl 0884.14010
Mukai, Shigeru
1996
Curves and symmetric spaces. I. Zbl 0871.14025
Mukai, Shigeru
1995
New developments of Fano varieties – on vector bundles and moduli problems. Zbl 0889.14020
Mukai, Shigeru
1995
Vector bundles and Brill-Noether theory. Zbl 0866.14024
Mukai, Shigeru
1995
Curves and Grassmannians. Zbl 0846.14030
Mukai, Shigeru
1993
Stability and Einstein-Kähler metric of a quartic del Pezzo surface. Zbl 0809.53070
Mabuchi, Toshiki; Mukai, Shigeru
1993
Fano 3-folds. Zbl 0774.14037
Mukai, Shigeru
1992
Polarized K3 surfaces of genus 18 and 20. Zbl 0774.14035
Mukai, Shigeru
1992
Curves and symmetric spaces. Zbl 0768.14014
Mukai, Shigeru
1992
Biregular classification of Fano 3-folds and Fano manifolds of coindex 3. Zbl 0679.14020
Mukai, Shigeru
1989
Finite groups of automorphisms of K3 surfaces and the Mathieu group. Zbl 0705.14045
Mukai, Shigeru
1988
Curves, K3 surfaces and Fano 3-folds of genus $$\leq 10$$. Zbl 0701.14044
Mukai, Shigeru
1988
On the moduli space of bundles on $$K3$$ surfaces. I. Zbl 0674.14023
Mukai, S.
1987
Moduli of vector bundles on K3 surfaces, and symplectic manifolds. Zbl 0685.14021
Mukai, Shigeru
1987
Fourier functor and its application to the moduli of bundles on an abelian variety. Zbl 0672.14025
Mukai, Shigeru
1987
Moduli of vector bundles on K3 surfaces and symplectic manifolds. Zbl 0651.14003
Mukai, Shigeru
1987
Classification of Fano $$3$$-folds with $$B_ 2\geq 2$$. I. Zbl 0800.14021
Mori, Shigefumi; Mukai, Shigeru
1986
Maximal subbundles of vector bundles on a curve. Zbl 0572.14008
Mukai, Shigeru; Sakai, Fumio
1985
Symplectic structure of the moduli space of sheaves on an abelian or K 3 surface. Zbl 0565.14002
Mukai, Shigeru
1984
Automorphisms of Enriques surfaces which act trivially on the cohomology groups. Zbl 0559.14038
Mukai, Shigeru; Namikawa, Yukihiko
1984
The uniruledness of the moduli space of curves of genus 11. Zbl 0557.14015
Mori, Shigefumi; Mukai, Shigeru
1983
Minimal rational threefolds. Zbl 0526.14006
Mukai, Shigeru; Umemura, Hiroshi
1983
On Fano 3-folds with $$B_ 2\geq 2$$. Zbl 0537.14026
Mori, Shigefumi; Mukai, Shigeru
1983
Duality between $$D(X)$$ and $$D(\hat X)$$ with its application to Picard sheaves. Zbl 0417.14036
Mukai, Shigeru
1981
Classification of Fano 3-folds with $$B_ 2 \geq 2$$. Zbl 0478.14033
Mori, Shigefumi; Mukai, Shigeru
1981
Semi-homogeneous vector bundles on an abelian variety. Zbl 0417.14029
Mukai, Shigeru
1978
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#### Cited by 945 Authors

 12 Ciliberto, Ciro 12 Yoshioka, Kōta 11 Farkas, Gavril 10 Iliev, Atanas Iliev 10 Kuznetsov, Aleksandr Gennad’evich 9 Biswas, Indranil 9 Chen, Jungkai Alfred 9 Garbagnati, Alice 9 Hacon, Christopher Derek 9 Hassett, Brendan 9 Knutsen, Andreas Leopold 9 Maciocia, Antony 9 Pareschi, Giuseppe 9 Ranestad, Kristian 9 Stellari, Paolo 8 Ballico, Edoardo 8 Kondō, Shigeyuki 8 Markman, Eyal 8 Oguiso, Keiji 8 Popa, Mihnea 8 Takagi, Hiromichi 8 Tschinkel, Yuri 8 Yau, Shing-Tung 8 Zhang, De-Qi 7 Bruzzo, Ugo 7 Cheltsov, Ivan Anatol’evich 7 Faenzi, Daniele 7 Fujita, Kento 7 Macrì, Emanuele 7 Markushevich, Dimitri Genrikhovich 7 Mukai, Shigeru 7 Nakashima, Tohru 7 Prokhorov, Yuriĭ Gennad’evich 7 Shramov, Konstantin Aleksandrovich 6 Dolgachev, Igor’ Vladimirovich 6 Hernández Ruipérez, Daniel 6 Keum, Jonghae 6 Lange, Herbert 6 Lopez, Angelo Felice 6 Massarenti, Alex 6 Mongardi, Giovanni 6 Newstead, Peter E. 6 O’Grady, Kieran G. 6 Polishchuk, Alexander Evgen’evich 6 Schreyer, Frank-Olaf 6 Süss, Hendrik 6 Verra, Alessandro 5 Eisenbud, David 5 Flamini, Flaminio 5 Huybrechts, Daniel 5 Li, Jun 5 López Martín, Ana Cristina 5 Manivel, Laurent 5 Miura, Makoto 5 Muñoz, Roberto 5 Nikulin, Vyacheslav Valentinovich 5 Occhetta, Gianluca 5 Peternell, Thomas Martin 5 Rapagnetta, Antonio 5 Sarti, Alessandra 5 Sawon, Justin 5 Staglianò, Giovanni 5 Tsukioka, Toru 5 Voisin, Claire 5 Zhang, Lei 5 Zucconi, Francesco 4 Aprodu, Marian 4 Bridgeland, Tom 4 Casagrande, Cinzia 4 Dedieu, Thomas 4 Furushima, Mikio 4 Galati, Concettina 4 Govindarajan, Suresh 4 Harrison, Sarah M. 4 Hosono, Shinobu 4 Hurtubise, Jacques C. 4 Ilten, Nathan Owen 4 Ito, Atsushi M. 4 Jiang, Zhi 4 Klemm, Albrecht 4 Laface, Antonio 4 Lahoz, Martí 4 Lanteri, Antonio 4 Laza, Radu 4 Lian, Bong H. 4 Mella, Massimiliano 4 Michałek, Mateusz 4 Muñoz Porras, José María 4 Ohashi, Hisanori 4 Oprea, Dragos 4 Ottaviani, Giorgio Maria 4 Pioli, Fabio 4 Saccà, Giulia 4 Tejero Prieto, Carlos 4 Ueda, Kazushi 4 Wendland, Katrin 4 Whitcher, Ursula A. 3 Addington, Nicolas M. 3 Araujo, Carolina 3 Banlaki, Andreas ...and 845 more Authors
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#### Cited in 146 Serials

 50 Mathematische Annalen 49 Advances in Mathematics 48 Mathematische Zeitschrift 40 Journal of Algebraic Geometry 39 Duke Mathematical Journal 36 International Journal of Mathematics 35 Journal of Algebra 35 Transactions of the American Mathematical Society 27 Journal of Geometry and Physics 27 Manuscripta Mathematica 26 Compositio Mathematica 23 Proceedings of the American Mathematical Society 23 Journal of High Energy Physics 22 Journal für die Reine und Angewandte Mathematik 21 Nagoya Mathematical Journal 19 Communications in Algebra 19 Nuclear Physics. B 19 Inventiones Mathematicae 18 Annales de l’Institut Fourier 16 Journal of Pure and Applied Algebra 14 Geometriae Dedicata 13 Kyoto Journal of Mathematics 12 Michigan Mathematical Journal 11 Communications in Mathematical Physics 11 Proceedings of the Japan Academy. Series A 10 Mathematical Proceedings of the Cambridge Philosophical Society 10 Journal of the American Mathematical Society 10 European Journal of Mathematics 8 Mathematische Nachrichten 8 Selecta Mathematica. New Series 7 Rendiconti del Circolo Matemàtico di Palermo. Serie II 7 Izvestiya: Mathematics 7 Geometry & Topology 7 Central European Journal of Mathematics 6 Journal of Mathematical Physics 6 Collectanea Mathematica 6 Journal de Mathématiques Pures et Appliquées. Neuvième Série 6 Documenta Mathematica 6 Communications in Contemporary Mathematics 5 Mathematical Notes 5 Archiv der Mathematik 5 Publications of the Research Institute for Mathematical Sciences, Kyoto University 5 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 5 Annals of Mathematics. Second Series 5 Comptes Rendus. Mathématique. Académie des Sciences, Paris 4 Israel Journal of Mathematics 4 Annali di Matematica Pura ed Applicata. Serie Quarta 4 Bulletin de la Société Mathématique de France 4 Journal of the London Mathematical Society. Second Series 4 Osaka Journal of Mathematics 4 Tohoku Mathematical Journal. Second Series 4 Tokyo Journal of Mathematics 4 Indagationes Mathematicae. New Series 4 Experimental Mathematics 4 Journal of Mathematical Sciences (New York) 4 Journal of the European Mathematical Society (JEMS) 4 Advances in Geometry 4 Proceedings of the Steklov Institute of Mathematics 4 Annali dell’Università di Ferrara. Sezione VII. Scienze Matematiche 4 Japanese Journal of Mathematics. 3rd Series 4 Journal de l’École Polytechnique – Mathématiques 4 Bollettino dell’Unione Matematica Italiana 3 Rocky Mountain Journal of Mathematics 3 Canadian Journal of Mathematics 3 Rendiconti del Seminario Matematico della Università di Padova 3 Differential Geometry and its Applications 3 The Journal of Geometric Analysis 3 Linear Algebra and its Applications 3 Transformation Groups 3 Revista Matemática Complutense 3 Forum of Mathematics, Sigma 2 Physics Letters. B 2 Russian Mathematical Surveys 2 Arkiv för Matematik 2 Reviews in Mathematical Physics 2 Beiträge zur Algebra und Geometrie 2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 2 Illinois Journal of Mathematics 2 Publications Mathématiques 2 Journal of the Mathematical Society of Japan 2 Kodai Mathematical Journal 2 Monatshefte für Mathematik 2 Proceedings of the Edinburgh Mathematical Society. Series II 2 Proceedings of the London Mathematical Society. Third Series 2 Topology and its Applications 2 Journal of Symbolic Computation 2 Geometric and Functional Analysis. GAFA 2 Bulletin of the American Mathematical Society. New Series 2 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 2 Bulletin des Sciences Mathématiques 2 Representation Theory 2 Algebras and Representation Theory 2 Bulletin of the Brazilian Mathematical Society. New Series 2 Milan Journal of Mathematics 2 Journal of the Institute of Mathematics of Jussieu 2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 2 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 2 Algebra & Number Theory 2 Science China. Mathematics 2 Research in the Mathematical Sciences ...and 46 more Serials
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#### Cited in 34 Fields

 929 Algebraic geometry (14-XX) 105 Differential geometry (53-XX) 93 Several complex variables and analytic spaces (32-XX) 77 Quantum theory (81-XX) 62 Category theory; homological algebra (18-XX) 44 Number theory (11-XX) 39 Commutative algebra (13-XX) 29 Group theory and generalizations (20-XX) 27 Global analysis, analysis on manifolds (58-XX) 22 Manifolds and cell complexes (57-XX) 19 Dynamical systems and ergodic theory (37-XX) 17 Nonassociative rings and algebras (17-XX) 17 Relativity and gravitational theory (83-XX) 14 Associative rings and algebras (16-XX) 12 Linear and multilinear algebra; matrix theory (15-XX) 11 Algebraic topology (55-XX) 10 $$K$$-theory (19-XX) 9 Topological groups, Lie groups (22-XX) 7 Combinatorics (05-XX) 5 Convex and discrete geometry (52-XX) 4 Functional analysis (46-XX) 4 Geometry (51-XX) 4 Mechanics of particles and systems (70-XX) 3 Numerical analysis (65-XX) 3 Computer science (68-XX) 2 Field theory and polynomials (12-XX) 2 Functions of a complex variable (30-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Partial differential equations (35-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Biology and other natural sciences (92-XX) 1 Information and communication theory, circuits (94-XX)

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