Edit Profile Goldberg, Paul W. Compute Distance To: Compute Author ID: goldberg.paul-w Published as: Goldberg, Paul; Goldberg, Paul W. External Links: MGP · Wikidata Documents Indexed: 61 Publications since 1995, including 1 Book all top 5 Co-Authors 9 single-authored 11 Goldberg, Leslie Ann 6 Papadimitriou, Christos Harilaos 6 Savani, Rahul 5 Deng, Xiao-Tie 5 Tang, Bo 5 Ventre, Carmine 5 Zhang, Jinshan 4 Berenbrink, Petra 4 Sørensen, Troels Bjerre 3 Fearnley, John 3 Friedetzky, Tom 3 Marmolejo Cossío, Francisco J. 3 Martin, Russell A. 3 Sahinalp, Suleyman Cenk 3 Sweedyk, Elizabeth 3 Turchetta, Stefano 2 Ackermann, Heiner 2 Daskalakis, Constantinos 2 Elkind, Edith 2 Ferraioli, Diodato 2 Filos-Ratsikas, Aris 2 Hu, Zengjian 2 McCabe, Antony 2 Mirrokni, Vahab S. 2 Palmer, Nick 2 Pastink, Arnoud 2 Paterson, Mike S. 2 Pevzner, Pavel A. 2 Phillips, Cynthia A. 2 Röglin, Heiko 2 Vöcking, Berthold 2 Wooldridge, Michael J. 2 Wu, Zhiwei Steven 1 Aziz, Haris 1 Bshouty, Nader H. 1 Chen, Ning 1 Colini-Baldeschi, Riccardo 1 Cryan, Mary 1 de Keijzer, Bart 1 Eichler, Evan 1 Ergun, Funda 1 Gairing, Martin 1 Gerstgrasser, Matthias 1 Goldman, Sally A. 1 Hollender, Alexandros 1 Jerrum, Mark R. 1 Koutsoupias, Elias 1 Krysta, Piotr 1 Leonardi, Stefano 1 Mathias, H. David 1 Sorkin, Gregory B. 1 Suksompong, Warut 1 Sun, Yang 1 Walsh, Toby 1 Warnow, Tandy J. all top 5 Serials 5 SIAM Journal on Computing 4 Theoretical Computer Science 2 Journal of Computer and System Sciences 2 Journal of Algorithms 2 Journal of Machine Learning Research (JMLR) 1 Discrete Applied Mathematics 1 International Journal of Game Theory 1 Algorithmica 1 Information and Computation 1 SIAM Journal on Discrete Mathematics 1 Machine Learning 1 Games and Economic Behavior 1 Mathematical Logic Quarterly (MLQ) 1 The Journal of Artificial Intelligence Research (JAIR) 1 Annals of Mathematics and Artificial Intelligence 1 Theory of Computing Systems 1 Journal of Combinatorial Optimization 1 Computational Intelligence 1 Journal of Discrete Algorithms 1 Internet Mathematics 1 Lecture Notes in Computer Science all top 5 Fields 43 Computer science (68-XX) 41 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Biology and other natural sciences (92-XX) 2 Combinatorics (05-XX) 2 Statistics (62-XX) 2 Operations research, mathematical programming (90-XX) 1 General and overarching topics; collections (00-XX) 1 Mathematical logic and foundations (03-XX) 1 Approximations and expansions (41-XX) 1 Convex and discrete geometry (52-XX) 1 Numerical analysis (65-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH 43 Publications have been cited 388 times in 318 Documents Cited by ▼ Year ▼ The complexity of computing a Nash equilibrium. Zbl 1185.91019Daskalakis, Constantinos; Goldberg, Paul W.; Papadimitriou, Christos H. 95 2009 The complexity of computing a Nash equilibrium. Zbl 1301.68142Daskalakis, Constantinos; Goldberg, Paul W.; Papadimitriou, Christos H. 64 2006 On the computational complexity of weighted voting games. Zbl 1185.91081Elkind, Edith; Goldberg, Leslie Ann; Goldberg, Paul W.; Wooldridge, Michael 30 2009 Bounding the Vapnik-Chervonenkis dimension of concept classes parameterized by real numbers. Zbl 0831.68087Goldberg, Paul W.; Jerrum, Mark R. 23 1995 Reducibility among equilibrium problems. Zbl 1301.68161Goldberg, Paul W.; Papadimitriou, Christos H. 16 2006 Uncoordinated two-sided matching markets. Zbl 1216.68200Ackermann, Heiner; Goldberg, Paul W.; Mirrokni, Vahab S.; Röglin, Heiko; Vöcking, Berthold 13 2011 Learning equilibria of games via payoff queries. Zbl 1351.91008Fearnley, John; Gairing, Martin; Goldberg, Paul W.; Savani, Rahul 11 2015 Approximate well-supported Nash equilibria below two-thirds. Zbl 1284.91018Fearnley, John; Goldberg, Paul W.; Savani, Rahul; Sørensen, Troels Bjerre 11 2012 Evolutionary trees can be learned in polynomial time in the two-state general Markov model. Zbl 1052.68061Cryan, Mary; Goldberg, Leslie Ann; Goldberg, Paul W. 11 2001 A tractable and expressive class of marginal contribution nets and its applications. Zbl 1175.91022Elkind, Edith; Goldberg, Leslie Ann; Goldberg, Paul W.; Wooldridge, Michael 10 2009 Bounds for the convergence rate of randomized local search in a multiplayer load-balancing game. Zbl 1321.68082Goldberg, Paul W. 8 2004 Exact learning of discretized geometric concepts. Zbl 0915.68087Bshouty, Nader H.; Goldberg, Paul W.; Goldman, Sally A.; Mathias, H. David 8 1998 Utilitarian resource assignment. Zbl 1124.91042Berenbrink, Petra; Goldberg, Leslie Ann; Goldberg, Paul W.; Martin, Russell 7 2006 Distributed selfish load balancing. Zbl 1141.68018Berenbrink, Petra; Friedetzky, Tom; Goldberg, Leslie Ann; Goldberg, Paul W.; Hu, Zengjian; Martin, Russell 6 2007 Minimizing phylogenetic number to find good evolutionary trees. Zbl 0880.92030Goldberg, Leslie Ann; Goldberg, Paul W.; Phillips, Cynthia A.; Sweedyk, Elizabeth; Warnow, Tandy 6 1996 Decentralized dynamics for finite opinion games. Zbl 1414.91072Ferraioli, Diodato; Goldberg, Paul W.; Ventre, Carmine 5 2016 Distributed selfish load balancing. Zbl 1192.68094Berenbrink, Petra; Friedetzky, Tom; Goldberg, Leslie Ann; Goldberg, Paul; Hu, Zengjian; Martin, Russell 5 2006 Consensus halving is PPA-complete. Zbl 1428.68162Filos-Ratsikas, Aris; Goldberg, Paul W. 4 2018 Decentralized dynamics for finite opinion games. Zbl 1284.91019Ferraioli, Diodato; Goldberg, Paul W.; Ventre, Carmine 4 2012 A bound on the precision required to estimate a Boolean perceptron from its average satisfying assignment. Zbl 1115.68092Goldberg, Paul W. 4 2006 Construction computer virus phylogenies. Zbl 0891.68045Goldberg, Leslie Ann; Goldberg, Paul W.; Phillips, Cynthia A.; Sorkin, Gregory B. 4 1998 Towards a unified complexity theory of total functions. Zbl 1393.68053Goldberg, Paul W.; Papadimitriou, Christos H. 3 2018 Query complexity of approximate equilibria in anonymous games. Zbl 1404.91009Goldberg, Paul W.; Turchetta, Stefano 3 2015 On the communication complexity of approximate Nash equilibria. Zbl 1290.91017Goldberg, Paul W.; Pastink, Arnoud 3 2014 On the approximation performance of fictitious play in finite games. Zbl 1300.91004Goldberg, Paul W.; Savani, Rahul; Sørensen, Troels Bjerre; Ventre, Carmine 3 2013 Pricing ad slots with consecutive multi-unit demand. Zbl 1319.91080Deng, Xiaotie; Goldberg, Paul; Sun, Yang; Tang, Bo; Zhang, Jinshan 3 2013 The complexity of the homotopy method, equilibrium selection and Lemke-Howson solutions. Zbl 1292.91013Goldberg, Paul W.; Papadimitriou, Christos H.; Savani, Rahul 3 2011 A unified approach to congestion games and two-sided markets. Zbl 1194.91030Ackermann, Heiner; Goldberg, Paul W.; Mirrokni, Vahab S.; Röglin, Heiko; Vöcking, Berthold 3 2008 PAC-learnability of probabilistic deterministic finite state automata in terms of variation distance. Zbl 1143.68024Palmer, Nick; Goldberg, Paul W. 3 2007 Some discriminant-based PAC algorithms. Zbl 1222.68097Goldberg, Paul W. 3 2006 Contiguous cake cutting: hardness results and approximation algorithms. Zbl 07269303Goldberg, Paul W.; Hollender, Alexandros; Suksompong, Warut 2 2020 On revenue maximization with sharp multi-unit demands. Zbl 1341.91101Chen, Ning; Deng, Xiaotie; Goldberg, Paul W.; Zhang, Jinshan 2 2016 PAC-learnability of probabilistic deterministic finite state automata in terms of variation distance. Zbl 1143.68421Palmer, Nick; Goldberg, Paul W. 2 2005 The complexity of splitting necklaces and bisecting ham sandwiches. Zbl 1433.68157Filos-Ratsikas, Aris; Goldberg, Paul W. 1 2019 Query complexity of approximate equilibria in anonymous games. Zbl 1376.91018Goldberg, Paul W.; Turchetta, Stefano 1 2017 TFNP: an update. Zbl 06751046Goldberg, Paul W.; Papadimitriou, Christos H. 1 2017 Approximate well-supported Nash equilibria below two-thirds. Zbl 1347.91008Fearnley, John; Goldberg, Paul W.; Savani, Rahul; Sørensen, Troels Bjerre 1 2016 Logarithmic query complexity for approximate Nash computation in large games. Zbl 1403.91032Goldberg, Paul W.; Marmolejo Cossío, Francisco J.; Wu, Zhiwei Steven 1 2016 Revenue maximization in a Bayesian double auction market. Zbl 1360.91093Deng, Xiaotie; Goldberg, Paul; Tang, Bo; Zhang, Jinshan 1 2014 Shortest paths with bundles and non-additive weights is hard. Zbl 1382.68091Goldberg, Paul W.; McCabe, Antony 1 2013 On the communication complexity of approximate Nash equilibria. Zbl 1284.91021Goldberg, Paul W.; Pastink, Arnoud 1 2012 A survey of PPAD-completeness for computing Nash equilibria. Zbl 1223.91017Goldberg, Paul W. 1 2011 When can two unsupervised learners achieve PAC separation? Zbl 0992.68112Goldberg, Paul W. 1 2001 Contiguous cake cutting: hardness results and approximation algorithms. Zbl 07269303Goldberg, Paul W.; Hollender, Alexandros; Suksompong, Warut 2 2020 The complexity of splitting necklaces and bisecting ham sandwiches. Zbl 1433.68157Filos-Ratsikas, Aris; Goldberg, Paul W. 1 2019 Consensus halving is PPA-complete. Zbl 1428.68162Filos-Ratsikas, Aris; Goldberg, Paul W. 4 2018 Towards a unified complexity theory of total functions. Zbl 1393.68053Goldberg, Paul W.; Papadimitriou, Christos H. 3 2018 Query complexity of approximate equilibria in anonymous games. Zbl 1376.91018Goldberg, Paul W.; Turchetta, Stefano 1 2017 TFNP: an update. Zbl 06751046Goldberg, Paul W.; Papadimitriou, Christos H. 1 2017 Decentralized dynamics for finite opinion games. Zbl 1414.91072Ferraioli, Diodato; Goldberg, Paul W.; Ventre, Carmine 5 2016 On revenue maximization with sharp multi-unit demands. Zbl 1341.91101Chen, Ning; Deng, Xiaotie; Goldberg, Paul W.; Zhang, Jinshan 2 2016 Approximate well-supported Nash equilibria below two-thirds. Zbl 1347.91008Fearnley, John; Goldberg, Paul W.; Savani, Rahul; Sørensen, Troels Bjerre 1 2016 Logarithmic query complexity for approximate Nash computation in large games. Zbl 1403.91032Goldberg, Paul W.; Marmolejo Cossío, Francisco J.; Wu, Zhiwei Steven 1 2016 Learning equilibria of games via payoff queries. Zbl 1351.91008Fearnley, John; Gairing, Martin; Goldberg, Paul W.; Savani, Rahul 11 2015 Query complexity of approximate equilibria in anonymous games. Zbl 1404.91009Goldberg, Paul W.; Turchetta, Stefano 3 2015 On the communication complexity of approximate Nash equilibria. Zbl 1290.91017Goldberg, Paul W.; Pastink, Arnoud 3 2014 Revenue maximization in a Bayesian double auction market. Zbl 1360.91093Deng, Xiaotie; Goldberg, Paul; Tang, Bo; Zhang, Jinshan 1 2014 On the approximation performance of fictitious play in finite games. Zbl 1300.91004Goldberg, Paul W.; Savani, Rahul; Sørensen, Troels Bjerre; Ventre, Carmine 3 2013 Pricing ad slots with consecutive multi-unit demand. Zbl 1319.91080Deng, Xiaotie; Goldberg, Paul; Sun, Yang; Tang, Bo; Zhang, Jinshan 3 2013 Shortest paths with bundles and non-additive weights is hard. Zbl 1382.68091Goldberg, Paul W.; McCabe, Antony 1 2013 Approximate well-supported Nash equilibria below two-thirds. Zbl 1284.91018Fearnley, John; Goldberg, Paul W.; Savani, Rahul; Sørensen, Troels Bjerre 11 2012 Decentralized dynamics for finite opinion games. Zbl 1284.91019Ferraioli, Diodato; Goldberg, Paul W.; Ventre, Carmine 4 2012 On the communication complexity of approximate Nash equilibria. Zbl 1284.91021Goldberg, Paul W.; Pastink, Arnoud 1 2012 Uncoordinated two-sided matching markets. Zbl 1216.68200Ackermann, Heiner; Goldberg, Paul W.; Mirrokni, Vahab S.; Röglin, Heiko; Vöcking, Berthold 13 2011 The complexity of the homotopy method, equilibrium selection and Lemke-Howson solutions. Zbl 1292.91013Goldberg, Paul W.; Papadimitriou, Christos H.; Savani, Rahul 3 2011 A survey of PPAD-completeness for computing Nash equilibria. Zbl 1223.91017Goldberg, Paul W. 1 2011 The complexity of computing a Nash equilibrium. Zbl 1185.91019Daskalakis, Constantinos; Goldberg, Paul W.; Papadimitriou, Christos H. 95 2009 On the computational complexity of weighted voting games. Zbl 1185.91081Elkind, Edith; Goldberg, Leslie Ann; Goldberg, Paul W.; Wooldridge, Michael 30 2009 A tractable and expressive class of marginal contribution nets and its applications. Zbl 1175.91022Elkind, Edith; Goldberg, Leslie Ann; Goldberg, Paul W.; Wooldridge, Michael 10 2009 A unified approach to congestion games and two-sided markets. Zbl 1194.91030Ackermann, Heiner; Goldberg, Paul W.; Mirrokni, Vahab S.; Röglin, Heiko; Vöcking, Berthold 3 2008 Distributed selfish load balancing. Zbl 1141.68018Berenbrink, Petra; Friedetzky, Tom; Goldberg, Leslie Ann; Goldberg, Paul W.; Hu, Zengjian; Martin, Russell 6 2007 PAC-learnability of probabilistic deterministic finite state automata in terms of variation distance. Zbl 1143.68024Palmer, Nick; Goldberg, Paul W. 3 2007 The complexity of computing a Nash equilibrium. Zbl 1301.68142Daskalakis, Constantinos; Goldberg, Paul W.; Papadimitriou, Christos H. 64 2006 Reducibility among equilibrium problems. Zbl 1301.68161Goldberg, Paul W.; Papadimitriou, Christos H. 16 2006 Utilitarian resource assignment. Zbl 1124.91042Berenbrink, Petra; Goldberg, Leslie Ann; Goldberg, Paul W.; Martin, Russell 7 2006 Distributed selfish load balancing. Zbl 1192.68094Berenbrink, Petra; Friedetzky, Tom; Goldberg, Leslie Ann; Goldberg, Paul; Hu, Zengjian; Martin, Russell 5 2006 A bound on the precision required to estimate a Boolean perceptron from its average satisfying assignment. Zbl 1115.68092Goldberg, Paul W. 4 2006 Some discriminant-based PAC algorithms. Zbl 1222.68097Goldberg, Paul W. 3 2006 PAC-learnability of probabilistic deterministic finite state automata in terms of variation distance. Zbl 1143.68421Palmer, Nick; Goldberg, Paul W. 2 2005 Bounds for the convergence rate of randomized local search in a multiplayer load-balancing game. Zbl 1321.68082Goldberg, Paul W. 8 2004 Evolutionary trees can be learned in polynomial time in the two-state general Markov model. Zbl 1052.68061Cryan, Mary; Goldberg, Leslie Ann; Goldberg, Paul W. 11 2001 When can two unsupervised learners achieve PAC separation? Zbl 0992.68112Goldberg, Paul W. 1 2001 Exact learning of discretized geometric concepts. Zbl 0915.68087Bshouty, Nader H.; Goldberg, Paul W.; Goldman, Sally A.; Mathias, H. David 8 1998 Construction computer virus phylogenies. Zbl 0891.68045Goldberg, Leslie Ann; Goldberg, Paul W.; Phillips, Cynthia A.; Sorkin, Gregory B. 4 1998 Minimizing phylogenetic number to find good evolutionary trees. Zbl 0880.92030Goldberg, Leslie Ann; Goldberg, Paul W.; Phillips, Cynthia A.; Sweedyk, Elizabeth; Warnow, Tandy 6 1996 Bounding the Vapnik-Chervonenkis dimension of concept classes parameterized by real numbers. Zbl 0831.68087Goldberg, Paul W.; Jerrum, Mark R. 23 1995 all cited Publications top 5 cited Publications all top 5 Cited by 549 Authors 19 Goldberg, Paul W. 10 Fearnley, John 10 Hoefer, Martin 10 Spirakis, Paul G. 9 Savani, Rahul 8 Papadimitriou, Christos Harilaos 7 Deligkas, Argyrios 7 Ferraioli, Diodato 7 Wooldridge, Michael J. 6 Bachrach, Yoram 6 Brandt, Felix 6 Deng, Xiao-Tie 6 Greco, Gianluigi 6 Mehta, Ruta 6 Serna, Maria José 5 Auletta, Vincenzo 5 Bilò, Vittorio 5 Fischer, Felix 5 Persiano, Giuseppe 5 Servedio, Rocco A. 4 Anshelevich, Elliot 4 Anthony, Martin H. G. 4 Chen, Xi 4 Conitzer, Vincent 4 Dang, Chuangyin 4 Daskalakis, Constantinos 4 Diakonikolas, Ilias 4 Fischer, Simon 4 Fotakis, Dimitris A. 4 Kontogiannis, Spyros C. 4 Molinero, Xavier 4 Pasquale, Francesco 4 Rosenschein, Jeffrey S. 4 Scarcello, Francesco 4 Ye, Yinyu 3 Berenbrink, Petra 3 Elkind, Edith 3 Harrenstein, Paul 3 Huang, Chien-Chung 3 Jiang, Albert Xin 3 Leyton-Brown, Kevin 3 Markakis, Evangelos 3 Marmolejo Cossío, Francisco J. 3 Mavronicolas, Marios 3 Monien, Burkhard 3 Moran, Shlomo 3 Ortiz, Luis E. 3 Snir, Sagi 3 Sontag, Eduardo D. 3 Sørensen, Troels Bjerre 3 Suksompong, Warut 3 Vazirani, Vijay V. 3 Ventre, Carmine 3 Wagner, Lisa Sabine 3 Wojtczak, Dominik 3 Zick, Yair 2 Ackermann, Heiner 2 Ågotnes, Thomas 2 Balle, Borja 2 Barman, Siddharth 2 Bartlett, Peter L. 2 Ben-David, Shai 2 Bi, Dianjie 2 Blum, Avrim L. 2 Bshouty, Nader H. 2 Buss, Sam 2 Castro, Jorge E. 2 Chalkiadakis, Georgios 2 Chan, Hau 2 Chen, Ning 2 Corley, H. W. jun. 2 Czumaj, Artur 2 De, Anindya K. 2 Della Vedova, Gianluca 2 Du, Ye 2 Endriss, Ulle 2 Fanelli, Angelo 2 Fasoulakis, Michail 2 Filmus, Yuval 2 Gabarró, Joaquim 2 Gairing, Martin 2 Garg, Jugal 2 Gavaldà, Ricard 2 Goldberg, Leslie Ann 2 Goldman, Sally A. 2 Hansen, Kristoffer Arnsfelt 2 Hermelin, Danny 2 Hollender, Alexandros 2 Holzer, Markus 2 Hubáček, Pavel 2 Hui, Pan 2 Jurdziński, Marcin 2 Kar, Koushik 2 Kleinberg, Jon Michael 2 Kleinberg, Robert D. 2 Koiran, Pascal 2 Komargodski, Ilan 2 Koutsoupias, Elias 2 Kratsch, Stefan 2 Kurz, Sascha ...and 449 more Authors all top 5 Cited in 76 Serials 28 Theoretical Computer Science 20 Journal of Computer and System Sciences 17 Theory of Computing Systems 15 Algorithmica 15 Games and Economic Behavior 14 Artificial Intelligence 6 Distributed Computing 6 Mathematical Programming. Series A. Series B 5 Discrete Applied Mathematics 5 International Journal of Game Theory 5 SIAM Journal on Computing 5 Information and Computation 5 European Journal of Operational Research 5 Games 4 Information Processing Letters 4 Mathematics of Operations Research 4 Mathematical Social Sciences 4 Annals of Pure and Applied Logic 4 Machine Learning 4 Annals of Mathematics and Artificial Intelligence 4 Computer Science Review 3 Discrete Mathematics 3 Applied Mathematics and Computation 3 Journal of Economic Theory 3 Journal of Mathematical Economics 3 Mathematical Logic Quarterly (MLQ) 2 Synthese 2 Systems & Control Letters 2 Operations Research Letters 2 Social Choice and Welfare 2 SIAM Journal on Discrete Mathematics 2 Annals of Operations Research 2 The Journal of Artificial Intelligence Research (JAIR) 2 Mathematical Problems in Engineering 2 Journal of Combinatorial Optimization 2 International Game Theory Review 2 Journal of Machine Learning Research (JMLR) 2 Game Theory 1 American Mathematical Monthly 1 Information Sciences 1 Naval Research Logistics 1 Results in Mathematics 1 Transactions of the American Mathematical Society 1 Probability Theory and Related Fields 1 Journal of Cryptology 1 Queueing Systems 1 Neural Networks 1 Random Structures & Algorithms 1 The Annals of Applied Probability 1 Applied Mathematical Modelling 1 Automation and Remote Control 1 Bulletin of the American Mathematical Society. New Series 1 Computational Complexity 1 Computational Optimization and Applications 1 Formal Methods in System Design 1 Economic Theory 1 ETNA. Electronic Transactions on Numerical Analysis 1 Constraints 1 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 1 Journal of Scheduling 1 Journal of the ACM 1 Annals of Combinatorics 1 International Journal of Applied Mathematics and Computer Science 1 CEJOR. Central European Journal of Operations Research 1 RAIRO. Operations Research 1 OR Spectrum 1 ACM Transactions on Computational Logic 1 Journal of Discrete Algorithms 1 Advances in Difference Equations 1 Networks and Spatial Economics 1 Optimization Letters 1 Logical Methods in Computer Science 1 Electronic Journal of Statistics 1 Theoretical Economics 1 ACM Transactions on Algorithms 1 ACM Transactions on Computation Theory all top 5 Cited in 29 Fields 223 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 181 Computer science (68-XX) 46 Operations research, mathematical programming (90-XX) 24 Combinatorics (05-XX) 15 Biology and other natural sciences (92-XX) 13 Mathematical logic and foundations (03-XX) 9 Probability theory and stochastic processes (60-XX) 9 Statistics (62-XX) 4 History and biography (01-XX) 3 Order, lattices, ordered algebraic structures (06-XX) 3 Convex and discrete geometry (52-XX) 3 Systems theory; control (93-XX) 3 Information and communication theory, circuits (94-XX) 2 Ordinary differential equations (34-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Approximations and expansions (41-XX) 2 Global analysis, analysis on manifolds (58-XX) 1 General and overarching topics; collections (00-XX) 1 Algebraic geometry (14-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Measure and integration (28-XX) 1 Operator theory (47-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 General topology (54-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) 1 Numerical analysis (65-XX) 1 Quantum theory (81-XX) 1 Statistical mechanics, structure of matter (82-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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