Graham Denham

Research

Preprints and publications

• On Ziegler's conjectures for logarithmic derivations of arrangements, with Takuro Abe.
  arXiv:2307.08173 Comments welcome!
• Deletion-restriction for logarithmic forms on multiarrangements, with Takuro Abe.
  arXiv:2203.04816 Comments welcome!
• Geometry of logarithmic derivations of hyperplane arrangements, with Avi Steiner. Contemporary Mathematics, Compactifications, Configurations and Cohomology, (Peter Crooks and Alex Suciu, ed.) vol 790 (2023).
  arXiv:2112.13462
• Lagrangian combinatorics of matroids, with Federico Ardila and June Huh. Algebraic Combinatorics, Vol 6 (2023), 387-411.
  arXiv:2109.11565 | journal
• Configuration polynomials under contact equivalence, with Delphine Pol, Mathias Schulze and Uli Walther. Annales de l’Institut Henri Poincaré D, Vol 9 No 4 (2022), 793-812.
  arXiv:2005.08181 | journal
• Graph hypersurfaces with torus action and a conjecture of Aluffi, with Delphine Pol, Mathias Schulze and Uli Walther. Communications in Number Theory and Physics, 15 (2021), no. 3, 455-488.
  arXiv:2005.02673 | journal
• Lagrangian geometry of matroids, with Federico Ardila and June Huh. Journal of the American Mathematical Society (2023), 727-794.
  arXiv:2004.13116 | pdf | doi
• A Leray model for the Orlik-Solomon algebra, with Christin Bibby and Eva Maria Feichtner. International Mathematical Research Notices, rnab131 (online, 70 pages) 2021
  arXiv:1910.10001 | journal
• Matroid connectivity and singularities of configuration hypersurfaces, with Mathias Schulze and Uli Walther. Letters in Mathematical Physics 111 (2021), no. 1, Paper No. 11, 67pp.
  arXiv:1902.06507 | pdf | journal
• Local systems on complements of arrangements of smooth, complex algebraic hypersurfaces, with A. Suciu.  Forum of Mathematics, Sigma, vol. 6, 2018 e8 (online, 20 pages).
  arXiv:1706.00956 | pdf | journal
  
• Abelian duality and propagation of resonance, with A. Suciu and S. Yuzvinsky, Selecta Mathematica (N.S.) 23 no. 4 (2017), 2331--2367.
  arXiv:1512.07702 | pdf | Journal
  
• Higher resonance varieties of matroids.  Proceedings of the Conference on Configuration Spaces, Cortona 2014, Springer INdAM series 41--66, volume 14, 2016.
  arXiv:1503.05177 | pdf
  
• Combinatorial covers and vanishing cohomology, with A. Suciu and S. Yuzvinsky, Selecta Mathematica (N.S.) 22 no. 2 (2016), 561-594.
  arXiv:1411.7981 | pdf | Journal
  
• Toric and tropical compactifications of hyperplane complements, Ann. Fac. Sci. Toulouse Math. (6) 23 (2014), no. 2, 297–333.
  arXiv:1306.3519 | pdf | Journal
  
• Multinets, parallel connections, and Milnor fibrations of arrangements, with A. Suciu, Proceedings of the London Math. Society 108 (2014) no. 6, 1435-1470.
  arXiv:1209.3414 | pdf | Journal
  
• Modular decomposition of the Orlik-Terao algebra of a hyperplane arrangement, with M. Garrousian and Stefan Tohaneanu, Annals of Combinatorics, 18 (2014), no. 2, 289–312.
  arXiv:1211.4562 | Journal
  
• A geometric deletion-restriction formula, with M. Garrousian and M. Schulze. Advances in Mathematics, 230 (2012) no. 4-6, 1979-1994.
  arXiv:1110.2799 | Journal
  
• Local cohomology of logarithmic forms, with H. Schenck, M. Schulze, U. Walther, M. Wakefield.  Annales de l'institut Fourier, 63 no. 3 (2013), p. 1177-1203.
  arXiv:1103.2459 | Journal
  
• Vanishing products of one-forms and critical points of master functions, with D. Cohen, M. Falk, A. Varchenko, Arrangements of hyperplanes—Sapporo 2009, 75–107, Adv. Stud. Pure Math., 62, Math. Soc. Japan, Tokyo, 2012.
  arXiv:1010.3743
  
• Eigenvectors for a random walk on a hyperplane arrangement, Advances in Applied Mathematics, 48 (2012) no.2, 312–324.
  arXiv:1010.0232 | ps | pdf | Journal
  
• Complexes, duality and Chern classes of logarithmic forms along hyperplane arrangements, with Mathias Schulze, Arrangements of hyperplanes—Sapporo 2009, 27–57, Adv. Stud. Pure Math., 62, Math. Soc. Japan, Tokyo, 2012.
  arXiv:1004.4237 | ps | pdf
  
• Homological aspects of hyperplane arrangements, in Arrangements, Local Systems and Singularities,
  in Arrangements, Local Systems and Singularities, CIMPA Summer School, Galatasaray University, Istanbul, 2007, El Zein, F.; Suciu, A.I.; Tosun, M.; Uludag, M.; Yuzvinsky, S. (eds.), Progress in Mathematics vol. 283, 2010, Birkhäuser.
  pdf
  
• Critical points and resonance of hyperplane arrangements, with D. Cohen, M. Falk, A. Varchenko, Canadian Journal of Mathematics, 63 (2011) no. 5, 1038-1057.
  arXiv:0907.0896v2 | Journal
  
• A note on De Concini and Procesi's curious identity, Rendiconti Lincei 19 (2008), no. 1, 59--63.
  pdf | Journal
  
• Moment-angle complexes, monomial ideals, and Massey products, with A. Suciu, Pure and Applied Mathematics Quarterly 3 (2007), no. 1, part 3, 25--60.
  math.AT/0512497 | pdf
• On the homotopy Lie algebra of an arrangement, with A. Suciu, Michigan Math. Journal, 54 (2006) no. 2, 319--340.
  math.AT/0502417 | pdf | Journal
  
• Short Generating Functions for some Semigroup Algebras, Electronic Journal of Combinatorics, 10 (2003) #R36.
  Journal
• Torsion in Milnor fibre homology, with D. Cohen and A. Suciu, Algebraic and Geometric Topology, 3 (2003) 511--535.
  pdf | Journal
• Equivariant Euler characteristics of disciminants of reflection groups, with N. Lemire, Indagationes Mathematicae, N.S., 13 (2002) no. 4, 441--457.
  pdf | Journal
• Annihilators of ideals of exterior algebras, with S. Yuzvinsky, Advances in Applied Mathematics, 28 (2002) no. 2, 231--249.
  postscript | Journal
• The Orlik-Solomon complex and Milnor fibre homology, Topology and its Applications 118 (2002) 45-63.
  Journal
• The combinatorial Laplacian of the Tutte complex, Journal of Algebra 242, (2001) 160-175.
  pdf | Journal
• Hanlon and Stanley's conjecture and the Milnor fibre of the braid arrangement, Journal of Algebraic Combinatorics 11 (2000) 227-240.
  Journal
• Some algebraic properties of the Schechtman-Varchenko bilinear forms, with P. Hanlon, in New Perspectives in Algebraic Combinatorics, Billera, Bjorner, Greene, Simion, Stanley eds., MSRI publications 1999.

Manuscripts under construction

• Homology of subgroups of right-angled Artin groups, preprint, math.GR/0612748. Right now, here is a more recent version: ps | pdf

Postal Address

Department of Mathematics
Middlesex College
University of Western Ontario
London, ON N6A 5B7
Canada

Contact

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Phone:	+1 519 661 2111 x86527
Office:	MC 135

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