# zbMATH — the first resource for mathematics

## Falk, Michael J.

Compute Distance To:
 Author ID: falk.michael-j Published as: Falk, Michael; Falk, Michael J.; Falk, M.
 Documents Indexed: 32 Publications since 1985, including 1 Book Reviewing Activity: 74 Reviews
all top 5

#### Co-Authors

 12 single-authored 7 Randell, Richard C. 5 Cohen, Daniel C. 4 Varchenko, Alexander Nikolaevich 2 Denham, Graham 2 Terao, Hiroaki 1 Brady, Thomas 1 Bruse, Florian 1 Delucchi, Emanuele 1 Eschenbrenner, Carrie J. 1 Lange, Martin 1 Proudfoot, Nicholas J. 1 Schechtman, Vadim 1 Watt, Colum 1 Yuzvinsky, Sergey
all top 5

#### Serials

 2 Inventiones Mathematicae 2 Proceedings of the American Mathematical Society 2 Transactions of the American Mathematical Society 2 European Journal of Combinatorics 2 Advances in Applied Mathematics 1 Advances in Mathematics 1 Canadian Journal of Mathematics 1 Compositio Mathematica 1 Topology 1 Topology and its Applications 1 IMRN. International Mathematics Research Notices 1 Journal of Algebraic Combinatorics 1 Annals of Combinatorics 1 Algebraic & Geometric Topology 1 Advanced Studies in Pure Mathematics 1 European Journal of Mathematics 1 Journal de l’École Polytechnique – Mathématiques
all top 5

#### Fields

 20 Convex and discrete geometry (52-XX) 16 Algebraic topology (55-XX) 10 Several complex variables and analytic spaces (32-XX) 9 Combinatorics (05-XX) 7 Group theory and generalizations (20-XX) 6 Algebraic geometry (14-XX) 6 Manifolds and cell complexes (57-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Special functions (33-XX) 1 General and overarching topics; collections (00-XX) 1 Commutative algebra (13-XX) 1 Nonassociative rings and algebras (17-XX) 1 Computer science (68-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)

#### Citations contained in zbMATH Open

26 Publications have been cited 346 times in 216 Documents Cited by Year
The lower central series of a fiber-type arrangement. Zbl 0574.55010
Falk, Michael; Randell, Richard
1985
Arrangements and cohomology. Zbl 0941.52022
Falk, Michael
1997
Multinets, resonance varieties, and pencils of plane curves. Zbl 1122.52009
Falk, Michael; Yuzvinsky, Sergey
2007
The minimal model of the complement of an arrangement of hyperplanes. Zbl 0707.57001
Falk, Michael
1988
Homotopy types of line arrangements. Zbl 0772.52011
Falk, Michael
1993
On the algebra associated with a geometric lattice. Zbl 0733.05026
Falk, Michael
1990
$$\beta\mathbf{nbc}$$-bases for cohomology of local systems on hyperplane complements. Zbl 0869.55005
Falk, Michael; Terao, Hiroaki
1997
On the homotopy theory of arrangements. II. Zbl 0990.32006
Falk, Michael; Randell, Richard
2000
Combinatorial and algebraic structure in Orlik-Solomon algebras. Zbl 0984.52008
Falk, Michael
2001
Orlik-Solomon algebras and Tutte polynomials. Zbl 0955.52010
Eschenbrenner, Carrie J.; Falk, Michael J.
1999
A note on discriminantal arrangements. Zbl 0815.52013
Falk, Michael
1994
The cohomology and fundamental group of a hyperplane complement. Zbl 0697.55013
Falk, Michael
1989
Parallel connections and bundles of arrangements. Zbl 1002.52017
Falk, Michael J.; Proudfoot, Nicholas J.
2002
Critical points and resonance of hyperplane arrangements. Zbl 1228.32028
Cohen, D.; Denham, G.; Falk, M.; Varchenko, A.
2011
On the homotopy theory of arrangements. Zbl 0636.14003
Falk, Michael; Randell, Richard
1987
$$K(\pi,1)$$ arrangements. Zbl 0815.57019
Falk, Michael
1995
Line-closed matroids, quadratic algebras, and formal arrangments. Zbl 1001.05039
Falk, Michael
2002
Resonance varieties over fields of positive characteristic. Zbl 1180.14054
Falk, Michael J.
2007
Pure braid groups and products of free groups. Zbl 0669.20028
Falk, Michael; Randell, Richard
1988
Pure braid groups are not residually free. Zbl 1282.20035
Cohen, Daniel C.; Falk, Michael; Randell, Richard
2012
BGG resolutions via configuration spaces. (Résolutions BGG via les espaces de configurations.) Zbl 1323.55013
Falk, Michael; Schechtman, Vadim; Varchenko, Alexander
2014
An equivariant discrete model for complexified arrangement complements. Zbl 1352.05044
Delucchi, Emanuele; Falk, Michael J.
2017
The lower central series of generalized pure braid groups. Zbl 0631.55005
Falk, Michael; Randell, Richard
1987
The contravariant form on singular vectors of a projective arrangement. Zbl 1400.14138
Falk, Michael J.; Varchenko, Alexander N.
2012
Geometry and combinatorics of resonant weights. Zbl 1281.32024
Falk, Michael
2010
Vanishing products of one-forms and critical points of master functions. Zbl 1260.32007
Cohen, Daniel C.; Denham, Graham; Falk, Michael; Varchenko, Alexander
2012
An equivariant discrete model for complexified arrangement complements. Zbl 1352.05044
Delucchi, Emanuele; Falk, Michael J.
2017
BGG resolutions via configuration spaces. (Résolutions BGG via les espaces de configurations.) Zbl 1323.55013
Falk, Michael; Schechtman, Vadim; Varchenko, Alexander
2014
Pure braid groups are not residually free. Zbl 1282.20035
Cohen, Daniel C.; Falk, Michael; Randell, Richard
2012
The contravariant form on singular vectors of a projective arrangement. Zbl 1400.14138
Falk, Michael J.; Varchenko, Alexander N.
2012
Vanishing products of one-forms and critical points of master functions. Zbl 1260.32007
Cohen, Daniel C.; Denham, Graham; Falk, Michael; Varchenko, Alexander
2012
Critical points and resonance of hyperplane arrangements. Zbl 1228.32028
Cohen, D.; Denham, G.; Falk, M.; Varchenko, A.
2011
Geometry and combinatorics of resonant weights. Zbl 1281.32024
Falk, Michael
2010
Multinets, resonance varieties, and pencils of plane curves. Zbl 1122.52009
Falk, Michael; Yuzvinsky, Sergey
2007
Resonance varieties over fields of positive characteristic. Zbl 1180.14054
Falk, Michael J.
2007
Parallel connections and bundles of arrangements. Zbl 1002.52017
Falk, Michael J.; Proudfoot, Nicholas J.
2002
Line-closed matroids, quadratic algebras, and formal arrangments. Zbl 1001.05039
Falk, Michael
2002
Combinatorial and algebraic structure in Orlik-Solomon algebras. Zbl 0984.52008
Falk, Michael
2001
On the homotopy theory of arrangements. II. Zbl 0990.32006
Falk, Michael; Randell, Richard
2000
Orlik-Solomon algebras and Tutte polynomials. Zbl 0955.52010
Eschenbrenner, Carrie J.; Falk, Michael J.
1999
Arrangements and cohomology. Zbl 0941.52022
Falk, Michael
1997
$$\beta\mathbf{nbc}$$-bases for cohomology of local systems on hyperplane complements. Zbl 0869.55005
Falk, Michael; Terao, Hiroaki
1997
$$K(\pi,1)$$ arrangements. Zbl 0815.57019
Falk, Michael
1995
A note on discriminantal arrangements. Zbl 0815.52013
Falk, Michael
1994
Homotopy types of line arrangements. Zbl 0772.52011
Falk, Michael
1993
On the algebra associated with a geometric lattice. Zbl 0733.05026
Falk, Michael
1990
The cohomology and fundamental group of a hyperplane complement. Zbl 0697.55013
Falk, Michael
1989
The minimal model of the complement of an arrangement of hyperplanes. Zbl 0707.57001
Falk, Michael
1988
Pure braid groups and products of free groups. Zbl 0669.20028
Falk, Michael; Randell, Richard
1988
On the homotopy theory of arrangements. Zbl 0636.14003
Falk, Michael; Randell, Richard
1987
The lower central series of generalized pure braid groups. Zbl 0631.55005
Falk, Michael; Randell, Richard
1987
The lower central series of a fiber-type arrangement. Zbl 0574.55010
Falk, Michael; Randell, Richard
1985
all top 5

#### Cited by 178 Authors

 24 Suciu, Alexander I. 16 Papadima, Ștefan 12 Cohen, Daniel C. 11 Falk, Michael J. 10 Denham, Graham 8 Guaschi, John 7 Dimca, Alexandru 7 Gonçalves, Daciberg Lima 6 Cohen, Frederick Ronald 6 Korchmáros, Gábor 6 Yoshinaga, Masahiko 5 Bardakov, Valeriĭ Georgievich 5 Nagy, Gábor Péter 5 Schenck, Hal 5 Settepanella, Simona 5 Yau, Stephen Shing-Toung 4 Cordovil, Raul 4 Guo, Weili 4 Măcinic, Daniela Anca 4 Röhrle, Gerhard E. 4 Salvetti, Mario 4 Terao, Hiroaki 4 Torielli, Michele 4 Wang, He 4 Yuzvinsky, Sergey 3 Amend, Nils 3 Artal Bartolo, Enrique 3 Cogolludo Agustín, José Ignacio 3 Guerville-Ballé, Benoît 3 Jambu, Michel 3 Jiang, Guangfeng 3 Jiang, Tan 3 Kawahara, Yukihito 3 Libgober, Anatoly S. 3 Marco-Buzunáriz, Miguel A. 3 Marin, Ivan 3 Ocampo Uribe, Oscar Eduardo 3 Orlik, Peter 3 Vershinin, Vladimir V. 3 Williams, Kristopher 3 Wu, Jie 2 Bartz, Jeremiah 2 Bellingeri, Paolo 2 Berceanu, Barbu Rudolf 2 Delucchi, Emanuele 2 Friedman, Michael 2 Gaiffi, Giovanni 2 Garrousian, Mehdi 2 Golubeva, Valentina Alekseevna 2 Guo, Qiumin 2 Huh, June 2 Kofinas, Constantinos E. 2 Kohno, Toshitake 2 Le, Dinh Van 2 Leksin, Vladimir Pavlovich 2 Mikhaĭlov, Roman Valer’evich 2 Nguyen Viet Dung 2 Pace, Nicola 2 Papistas, Athanassios I. 2 Paris, Luis 2 Peeva, Irena V. 2 Proudfoot, Nicholas J. 2 Schick, Thomas 2 Schulze, Mathias 2 Serventi, Matteo 2 Varchenko, Alexander Nikolaevich 2 Wakefield, Max D. 2 Walther, Uli 2 Xicoténcatl, Miguel A. 2 Ziegler, Günter Matthias 1 Adiprasito, Karim Alexander 1 Aguilar Aguilar, Rodolfo 1 Ardila Mantilla, Federico 1 Bailet, Pauline 1 Bayer, Margaret M. 1 Berrick, A. Jon 1 Billey, Sara C. 1 Blokhuis, Aart 1 Bogya, N. 1 Brandt, Keith A. 1 Brown, Francis C. S. 1 Chen, Beifang 1 Choudary, A. D. R. 1 Church, Thomas 1 Cong, Tran Quoc 1 Conner, Andrew 1 Damon, James Norman 1 de Miranda e Pereiro, Carolina 1 Deligne, Pierre René 1 Deshpande, Priyavrat 1 Douai, Antoine 1 Dunn, Corey M. 1 Dupont, Clément 1 Edelman, Paul H. 1 Eisenbud, David 1 Elduque, Eva 1 Eliyahu, Meital 1 Eschenbrenner, Carrie J. 1 Etienne, Gwihen 1 Farb, Benson ...and 78 more Authors
all top 5

#### Cited in 75 Serials

 21 Topology and its Applications 12 Advances in Mathematics 12 Proceedings of the American Mathematical Society 11 Journal of Algebra 11 Transactions of the American Mathematical Society 10 Advances in Applied Mathematics 7 Journal of Pure and Applied Algebra 6 Communications in Algebra 5 Compositio Mathematica 5 European Journal of Combinatorics 5 Algebraic & Geometric Topology 5 European Journal of Mathematics 4 Graphs and Combinatorics 4 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 4 Journal of Algebraic Combinatorics 4 Annals of Combinatorics 3 Annales de l’Institut Fourier 3 Geometriae Dedicata 3 Inventiones Mathematicae 3 Science in China. Series A 3 Journal of Knot Theory and its Ramifications 3 Journal of Singularities 2 Duke Mathematical Journal 2 Mathematische Annalen 2 Mathematische Zeitschrift 2 Journal of the American Mathematical Society 2 Bulletin of the American Mathematical Society. New Series 2 The Australasian Journal of Combinatorics 2 Geometry & Topology 2 Revista Matemática Complutense 2 Oberwolfach Reports 2 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 1 Communications in Mathematical Physics 1 Discrete Mathematics 1 Israel Journal of Mathematics 1 Mathematical Notes 1 Journal of Geometry and Physics 1 Acta Mathematica Vietnamica 1 Algebra and Logic 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Bulletin of the London Mathematical Society 1 Functional Analysis and its Applications 1 Journal of Combinatorial Theory. Series A 1 Journal of Computational and Applied Mathematics 1 Journal of the Korean Mathematical Society 1 Journal of Number Theory 1 Kodai Mathematical Journal 1 Michigan Mathematical Journal 1 Tokyo Journal of Mathematics 1 Combinatorica 1 Revista Matemática Iberoamericana 1 Forum Mathematicum 1 Sugaku Expositions 1 International Journal of Algebra and Computation 1 Designs, Codes and Cryptography 1 Linear Algebra and its Applications 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 1 Experimental Mathematics 1 Algebra Colloquium 1 Annales Mathématiques Blaise Pascal 1 Selecta Mathematica. New Series 1 Documenta Mathematica 1 Vietnam Journal of Mathematics 1 Journal of Group Theory 1 Communications in Contemporary Mathematics 1 Advances in Geometry 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Journal of the Institute of Mathematics of Jussieu 1 Journal of Algebra and its Applications 1 Journal of Topology 1 Journal of Commutative Algebra 1 Mathematics 1 Arnold Mathematical Journal
all top 5

#### Cited in 25 Fields

 98 Convex and discrete geometry (52-XX) 83 Group theory and generalizations (20-XX) 69 Algebraic geometry (14-XX) 68 Several complex variables and analytic spaces (32-XX) 56 Algebraic topology (55-XX) 50 Manifolds and cell complexes (57-XX) 38 Combinatorics (05-XX) 16 Commutative algebra (13-XX) 15 Associative rings and algebras (16-XX) 12 Nonassociative rings and algebras (17-XX) 9 Geometry (51-XX) 6 Special functions (33-XX) 4 Order, lattices, ordered algebraic structures (06-XX) 3 Number theory (11-XX) 3 $$K$$-theory (19-XX) 3 Differential geometry (53-XX) 3 Global analysis, analysis on manifolds (58-XX) 2 General and overarching topics; collections (00-XX) 2 Quantum theory (81-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Topological groups, Lie groups (22-XX) 1 Ordinary differential equations (34-XX) 1 Functional analysis (46-XX) 1 General topology (54-XX) 1 Information and communication theory, circuits (94-XX)