Dr. Alexandru I. Suciu

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Northeastern University
Mathematics
ProfessorAppointed: 2000
Professional Headshot of Alexandru I. Suciu

Mailing Address

360 Huntington Avenue
Boston, Massachusetts 02115-5096
United States

Contact Information

Phone: (617) 373-4456
Fax: (617) 373-5658
alexsuciu@neu.edu
http://www.math.neu.edu/~suciu/

Qualifications

Ph.D., Columbia University, Mathematics, 1984.
M.A., Columbia University, Mathematics, 1980.
M.S., University of Bucharest, Mathematics, 1976.
B.S., University of Bucharest, Mathematics, 1975.

Expertise and Research Interests

This project is centered around a topological study of complex hyperplane arrangements, with a view towards finding effectively computable invariants of their complements. The goal is to decide whether a given invariant is combinatorially determined, and, if it is, to express it explicitly in terms of the intersection lattice of the arrangement. An important role is played by the jumping loci for cohomology with coefficients in local systems, and the related resonance varieties. These varieties have emerged as a central object of study. They provide deep information about the homotopy theory of the complement of an arrangement, as well as a bridge relating various invariants, in often unexpected ways. Another key role is played by the rational-homotopy notion of formality, which provides the underlying explanation for many of the encountered phenomena. Whenever possible, the study is done in a more general setting, which includes certain types of subspace arrangements, both real and complex, as well as certain links in the 3-sphere. Such a point of view enlarges the range of applicability of the results, and helps explain what is really peculiar to complex hyperplane arrangements.

In its simplest manifestation, an arrangement is a finite collection of lines in the plane. These lines cut the plane into components, and understanding the topology of the complement amounts to counting those components. In the case of lines in the complex plane (or, for that matter, hyperplanes in complex n-space), the complement is connected, and its topology (as reflected, for example, in its homotopy groups) is much more interesting. The theory of arrangements is a relatively new branch of mathematics, started in the 1960's with a study of the classifying space for thepure braid group. The theory has developed at the interface between topology, algebra, algebraic geometry, and combinatorics. Hyperplane arrangements, and the closely related configuration spaces, are used in numerous areas, including robotics, multi-dimensional billiards, graphics, molecular biology, computer vision, and databases for representing the space of all possible states of a system characterized by many degrees of freedom. There are also deep connections between hyperplane arrangements, knot theory, hypergeometric functions, conformal field theory, and quantum cohomology.

Keywords

COS Keywords:

Mathematics, Topology.

Additional Terms:

Mathematics, Topology.

Languages

(Reading, Writing, Speaking)

French: (Fluent, Fluent, Fluent)
Romanian: (Fluent, Fluent, Fluent)

Previous Positions

2007-2007, Visiting Fellow, Institute of Mathematics of the Romanian Academy, Bucharest
2007-2007, Visiting Professor, University of Nice, Mathematics
2006-2006, General Member, Mathematical Sciences Research Institute, Berkeley
2006-2006, Visiting Fellow, Mathematics Institute, Oberwolfach, Research in Pairs
2004-2004, General Member, Mathematical Sciences Research Institute, Berkeley
2003-2003, Visiting Fellow, Institute of Mathematics of the Romanian Academy, Bucharest
1999-1999, Visiting Fellow, Mathematics Institute, Oberwolfach, Research in Pairs
1999-2000, Visiting Fellow, Brandeis University, College of Arts and Sciences, Department of Mathematics
1997-1997, Visiting Professor, University Henri Poincare, Nancy, France, Mathematics
1992-2000, Associate Professor, Northeastern University, Mathematics
1986-1992, Assistant Professor, Northeastern University, Mathematics
1984-1986, J. W. Gibbs Instructor, Yale University, Mathematics

Funding Received

  • National Science Foundation (NSF): 9504833, Mathematical Sciences: Topology of Complex Hyperplane Arrangements, $52,200, July 15, 1995 to June 30, 1997.
  • National Science Foundation (NSF): 9103556, Mathematical Sciences: Knots, Framed Manifolds, $47,800, July 1, 1991 to December 31, 1993 (E.
  • National Science Foundation (NSF): 0105342, Mathematical Sciences: Topology of Hyperplane Arrangements, $67,172, Jul 15, 2001 to Jul 31, 2003.
  • National Science Foundation (NSF): 9816607, Mathematical Sciences: Conference on Hyperplane Arrangements, $5,000, Jul 15, 1999 to Jun 30, 2000.
  • National Science Foundation (NSF): 0311142, Mathematical Sciences: Collaborative Research: Symbolic Computations in Algebra and Topology, $141,475, 2003 to 2006.

Publications

  • A. Dimca, A.I. Suciu (2009) Which 3-manifold groups are Kähler groups?, Journal of the European Mathematical Society, In Press
  • S. Papadima, A.I. Suciu (2009) Toric complexes and Artin kernels, Advances in Mathematics, 220 (2), 441-477
  • S. Papadima, A.I. Suciu (2008) Bieri-Neumann-Strebel-Renz invariants and homology jumping loc, arXiv:0812.2660, Submitted
  • A. Dimca, S. Papadima, A.I. Suciu (2008) Non-finiteness properties of fundamental groups of smooth projective varieties, Journal für die reine und angewandte Mathematik, In Press
  • A. Dimca, S. Papadima, A.I. Suciu (2008) Quasi-Kähler groups, 3-manifold groups, and formality, arXiv:0810.2158, Submitted
  • A. Dimca, S. Papadima, A.I. Suciu (2008) Quasi-K\"ahler Bestvina-Brady groups, Journal of Algebraic Geometry, 17 (1), 185-197
  • D.C. Cohen, A.I. Suciu (2008) The boundary manifold of a complex line arrangement, Geometry & Topology Monographs, 13, 105-146
  • M. Kreck, A. I. Suciu (2008) Free abelian covers, short loops, stable lengths, and systolic inequalities, Mathematische Annalen, 340 (3), 709-729
  • A. Dimca, S. Papadima, A.I. Suciu (15 Jan 2008) Alexander polynomials: Essential variables and multiplicities, International Mathematics Research Notices, 2008, rnm119, 36 pages
  • S. Papadima, A.I. Suciu (2007) The spectral sequence of an equivariant chain complex and homology with local coefficients, arXiv:0708.4262, Submitted
  • S. Papadima, A.I. Suciu (2007) Algebraic invariants for Bestvina-Brady groups, Journal of the London Mathematical Society, 76 (2), 273-292
  • G. Denham, A.I. Suciu (2007) Moment angle complexes, monomial ideals, and Massey products, Pure and Applied Mathematics Quarterly, 3 (1), 25-60
  • D.C. Cohen, A.I. Suciu (10 Nov 2006) Boundary manifolds of projective hypersurfaces, Advances in Mathematics, 206 (2), 538-566
  • S. Papadima, A.I. Suciu (11 Sept 2006) When does the associated graded Lie algebra of an arrangement group decompose?, Commentarii Mathematici Helvetici, 81 (4), 859-875
  • G. Denham, A.I. Suciu (23 Aug 2006) On the homotopy Lie algebra of an arrangement, Michigan Mathematical Journal, 54 (2), 319-340
  • S. Papadima, A.I. Suciu (2006) Algebraic invariants for right-angled Artin groups, Mathematische Annalen, 334 (3), 533-555
  • H.K. Schenck, A.I. Suciu (2006) Resonance, linear syzygies, Chen groups, and the Bernstein-Gelfand-Gelfand correspondence, Transactions American Mathematical Society, 358 (5), 2269-2289
  • A. Dimca, S. Papadima, A.I. Suciu (2005) Formality, Alexander invariants, and a question of Serre, arXiv:math/0512480, Submitted
  • M. Falk, A. Suciu, Complex Hyperplane Arrangements, Emissary, Berkeley, CA, Mathematical Sciences Research Institute, Spring 2005, 4-6, May 2005
  • D. Matei, A.I. Suciu (1 Apr 2005) Counting homomorphisms onto finite solvable groups, Journal of Algebra, 286 (1), 161-186
  • S. Papadima, A.I. Suciu (22 Aug 2004) Homotopy Lie algebras, lower central series, and the Koszul property, Geometry and Topology, 8, 1079-1125
  • S. Papadima, A.I. Suciu (2004) Chen Lie algebras, International Mathematics Research Notices, 2004 (21), 1057-1086
  • D. C. Cohen, G. Denham, A. I. Suciu (15 Jun 2003) Torsion in Milnor fiber homology, Algebraic and Geometric Topology, 3, 511-535
  • H. K. Schenck, A.I. Suciu, Lower central series and free resolutions of hyperplane arrangements, Transactions American Mathematical Society, 354(9), 3409-3433, 01 Sep 2002
  • D.C.Cohen, A.I. Suciu (28 Feb 2002) Editorial, Topology and Its Applications, 118 (1-2), 1-2
  • A. I. Suciu (28 Feb 2002) Translated tori in the characteristic varieties of complex hyperplane arrangements, Topology and its Applications, 118 (1-2), 209-223
  • S. Papadima, A.I. Suciu (15 Jan 2002) Higher homotopy groups of complements of hyperplane arrangements, Advances in Mathematics, 165 (1), 71-100
  • D. Matei, A.I. Suciu, Hall invariants, homology of subgroups, and characteristic varieties, International Mathematics Research Notices, 2002(9), 465-503, 01 Jan 2002
  • S. Papadima, A.I. Suciu (2002) Rational homotopy groups and Koszul algebras, Comptes Rendus Mathematique, 335 (1), 53-58
  • A. I. Suciu, Fundamental groups of line arrangements: Enumerative aspects, Contemporary Mathematics, 276, 43-79, 2001
  • M. G. Katz, A. I. Suciu (2001) Systolic freedom of loop space, Geometric and Functional Analysis, 11 (1), 60-73
  • D. Matei, A. I. Suciu, Cohomology rings and nilpotent quotients of real and complex arrangements, Advanced Studies in Pure Mathematics, 27, 185-215, 2000
  • D. Matei, A. I. Suciu (2000) Homotopy types of complements of 2-arrangements in R^4, Topology, 39 (1), 61-88
  • D. C. Cohen, A. I. Suciu, Alexander invariants of complex hyperplane arrangements, Transactions of the American Mathematical Society, 351(10), 4043-4067, 1999
  • M. G. Katz, A. I. Suciu, Volume of Riemannian manifolds, geometric inequalities, and homotopy theory, Contemporary Mathematics, 231, 113-136, 1999
  • D. C. Cohen, A. I. Suciu, Characteristic varieties of arrangements, Mathematical Proceedings of the Cambridge Philosophical Society, 127(1), 33-53, 1999
  • I. K. Babenko, M. G. Katz, A. I. Suciu, Volumes, middle-dimensional systoles, and Whitehead products, Mathematical Research Letters, 5(4), 461-471, 1998
  • D. C. Cohen, A. I. Suciu (1998) Homology of iterated semidirect products of free groups, Journal of Pure and Applied Algebra, 126 (1-3), 87-120
  • D. C. Cohen, A. I. Suciu, The braid monodromy of plane algebraic curves and hyperplane arrangements, Commentarii Mathematici Helvetici, 72(2), 285-315, 1997
  • D. C. Cohen, A. I. Suciu, On Milnor fibrations of arrangements, Journal of the London Mathematical Society, 51(1), 105-119, 1995
  • D. C. Cohen, A. I. Suciu, The Chen groups of the pure braid group, Contemporary Mathematics, 181, 45-64, 1995
  • E. D. Farjoun, S. M. Jekel, A. I. Suciu (1995) Homology of jet groups, Journal of Pure and Applied Algebra, 102 (1), 17-24
  • W. G. Dwyer, S. M. Jekel, A. I. Suciu, Homology isomorphisms between algebraic groups made discrete, Bulletin of the London Mathematical Society, 25(2), 145-149, 1993
  • A. I. Suciu, Inequivalent frame-spun knots with the same complement, Commentarii Matematici Helvetici, 67(1), 47-63, 1992
  • J. R. Klein, A. I. Suciu, Inequivalent fibred knots whose homotopy Seifert pairings are isometric, Mathematische Annalen, 289(4), 683-701, 1991
  • A. I. Suciu, Iterated spinning and homology spheres, Transactions of the American Mathematical Society, 321(1), 145-157, 1990
  • A. I. Suciu, The oriented homotopy type of spun 3-manifolds, Pacific Journal of Mathematics, 131(2), 393-399, 1988
  • S. P. Plotnick, A. I. Suciu, Fibered knots and spherical space forms, Journal of the London Mathematical Society, 35(3), 514-526, 1987
  • A. I. Suciu, Homology 4-spheres with distinct k-invariants, Topology and Its Applications, 25(1), 103-110, 1987
  • A. I. Suciu, Immersed spheres in CP^2 and S^2 x S^2, Mathematische Zeitschrift, 196(1), 51-57, 1987
  • S. P. Plotnick, A. I. Suciu, k-Invariants of knotted 2-spheres, Commentarii Mathematici Helvetici, 60(1), 54-84, 1985
  • A. I. Suciu, Infinitely many ribbon knots with the same fundamental group, Mathematical Proceedings of the Cambridge Philosophical Society, 98(3), 481--492, 1985
  • A. I. Suciu, Homotopy type invariants of four-dimensional knot complements, Ph. D. Thesis, Columbia University, 97 pp., 1984
  • Suciu-Foca N, Susinno E, Godfrey M, McKiernan P, Rohowsky C, Sankel M, Suciu A, HLA-Antigens in the Romanian population, Transplantation Proceedings, 11(4), 1732-4, December 1979
  • Suciu A, Suciu-Foca N, The genetics of LD2. I. Gene frequency: an estimation, Transplantation Proceedings, 11(2), 1323-6, June 1979

Profile Details

Last Updated: 12/27/2008

COS Expertise ID #514274
Reference this profile directly: http://myprofile.cos.com/suciu