Peter Paul Nikolas Orlik (born 12 November 1938, Budapest) is an American mathematician, known for his research on topology, algebra, and combinatorics.
Orlik earned in 1961 his bachelor's degree from the Norwegian Institute of Technology in Trondheim and in 1966 his Ph.D. from the University of Michigan under Frank Raymond with thesis Necessary conditions for the homeomorphism of Seifert manifolds. He became in 1966 an assistant professor and in 1973 a full professor at the University of Wisconsin-Madison.
Orlik was in the academic year 1971/72 a visiting professor in Oslo. From 1967 to 1969 he was a visiting scholar at the Institute for Advanced Study.
Orlik is the author of over 70 publications. He works on Seifert manifolds, singularity theory, braid theory, reflection groups, invariant theory, and hypergeometric integrals. He was, with Hiroaki Terao and Louis Solomon, a pioneer of the theory of arrangements of hyperplanes.
In 2012 he was elected a Fellow of the American Mathematical Society.
Seifert Manifolds, Lecture Notes in Mathematics 291, Springer Verlag 1972as editor: Singularities, 2 vols., AMS 1983Introduction to Arrangements, CBMS Regional Conference Series, AMS 1989with Hiroaki Terao: Arrangement of Hyperplanes, Grundlehren der mathematischen Wissenschaften, Springer Verlag 1992with Hiroaki Terao: Arrangements and hypergeometric integrals, Mathematical Society of Japan 2001, 2nd edition 2007with Volkmar Welker: Algebraic Combinatorics. Lectures at a Summer School in Nordfjordeid, Norway, June 2003, Universitext, Springer Verlag 2007Articles
with C. P. Rourke: "Free involutions on homotopy (4k+3)-spheres". Bull. Amer. Math. Soc. 74: 949–953. 1968. MR 0229245. doi:10.1090/s0002-9904-1968-12101-9. with John Milnor: "Isolated singularities defined by weighted homogeneous polynomials". Topology. 9: 385–393. 1970. doi:10.1016/0040-9383(70)90061-3. with Frank Raymond: "Actions of the torus on 4-manifolds. I". Trans. Amer. Math. Soc. 152: 531–559. 1970. MR 0268911. doi:10.1090/s0002-9947-1970-0268911-3. with P. Wagreich: "Isolated singularities of algebraic surfaces with C*-action". Annals of Mathematics. 93: 205–228. 1971. doi:10.2307/1970772. The multiplicity of a holomorphic map at an isolated critical point, in Real and complex singularities, Oslo: Sijthoff and Noordhoff, 1977, 405-474"Singularities and group actions". Bull. Amer. Math. Soc. (N.S.). 1: 703–720. 1979. MR 537624. doi:10.1090/s0273-0979-1979-14643-3. with Louis Solomon: "Combinatorics and topology of complements of hyperplanes". Invent. Math. 56 (2): 167–189. 1980. doi:10.1007/bf01392549. with Daniel C. Cohen: "Gauss-Manin connections for arrangements, III Formal connections". Trans. Amer. Math. Soc. 357: 3031–3050. 2005. MR 2135734. doi:10.1090/s0002-9947-04-03621-9. 