nLab Peter Orlik

Peter Orlik is a professor emeritus at the Departement of Mathematics of the University of Wisconsin at Madison.

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Selected writings

On the (holomorphic) de Rham cohomology of configuration spaces of points (whose “twisted” generalization leads to the hypergeometric construction of KZ solutions):

• Peter Orlik, Louis Solomon, Combinatorics and topology of complements of hyperplanes, Invent Math 56 (1980) 167–189 [doi:10.1007/BF01392549]

On local system-twisted de Rham cohomology over configuration spaces of points (such as for the hypergeometric integral construction of solutions to the Knizhnik-Zamolodchikov equation):

• Peter Orlik, Hypergeometric integrals and arrangements, Journal of Computational and Applied Mathematics 105 (1999) 417–424 [doi:10.1016/S0377-0427(99)00036-9, pdf]

• Daniel C. Cohen, Peter Orlik, Arrangements and local systems, Math. Res. Lett. 7 (2000) 299-316 $[$arXiv:math/9907117, doi:10.4310/MRL.2000.v7.n3.a5$]$

On Gauss-Manin connections over configuration spaces of points:

• Daniel C. Cohen, Peter Orlik, Gauss-Manin connections for arrangements, I Eigenvalues, Compositio Math. 136 (2003) 299-316 $[$arXiv:math/0105063, doi:10.1023/A:1023262022279$]$

• Daniel C. Cohen, Peter Orlik, Gauss-Manin connections for arrangements, II Nonresonant weights, Amer. J. Math. 127 (2005) 569-594 $[$arXiv:math/0207114, jstor:40067930$]$

• Daniel C. Cohen, Peter Orlik, Gauss-Manin connections for arrangements, III Formal connections, Trans. Amer. Math. Soc. 357 (2005) 3031-3050 $[$arXiv:math/0307210, doi:10.1090/S0002-9947-04-03621-9$]$

category: people