Peter Paul Nikolas Orlik (born 12 November 1938, in

Budapest Budapest is the Capital city, capital and List of cities and towns of Hungary, most populous city of Hungary. It is the List of cities in the European Union by population within city limits, tenth-largest city in the European Union by popul ...

) is an American mathematician, known for his research on topology, algebra, and combinatorics.Conference in honour of Peter Orlik, Fields Institute, August 2008
/ref> Orlik earned in 1961 his bachelor's degree from the

Norwegian Institute of Technology The Norwegian Institute of Technology ( Norwegian: ''Norges tekniske høgskole'', NTH) was a science institute in Trondheim, Norway. It was established in 1910, and existed as an independent technical university for 58 years, after which it was ...

Trondheim Trondheim ( , , ; ), historically Kaupangen, Nidaros, and Trondhjem (), is a city and municipality in Trøndelag county, Norway. As of 2022, it had a population of 212,660. Trondheim is the third most populous municipality in Norway, and is ...

and in 1966 his Ph.D. from the

University of Michigan The University of Michigan (U-M, U of M, or Michigan) is a public university, public research university in Ann Arbor, Michigan, United States. Founded in 1817, it is the oldest institution of higher education in the state. The University of Mi ...

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 The University of Wisconsin–Madison (University of Wisconsin, Wisconsin, UW, UW–Madison, or simply Madison) is a public land-grant research university in Madison, Wisconsin, United States. It was founded in 1848 when Wisconsin achieved st ...

. Orlik was in the academic year 1971/72 a visiting professor in

Oslo Oslo ( or ; ) is the capital and most populous city of Norway. It constitutes both a county and a municipality. The municipality of Oslo had a population of in 2022, while the city's greater urban area had a population of 1,064,235 in 2022 ...

. From 1967 to 1969 he was a visiting scholar at the

Institute for Advanced Study The Institute for Advanced Study (IAS) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey. It has served as the academic home of internationally preeminent scholars, including Albert Ein ...

. Orlik is the author of over 70 publications. He works on

Seifert manifold A Seifert fiber space is a 3-manifold together with a decomposition as a disjoint union of circles. In other words, it is a S^1-bundle (circle bundle) over a 2-dimensional orbifold. Many 3-manifolds are Seifert fiber spaces, and they account for al ...

singularity theory In mathematics, singularity theory studies spaces that are almost manifolds, but not quite. A string can serve as an example of a one-dimensional manifold, if one neglects its thickness. A singularity can be made by balling it up, dropping it ...

braid theory In mathematics, the braid group on strands (denoted B_n), also known as the Artin braid group, is the group whose elements are equivalence classes of -braids (e.g. under ambient isotopy), and whose group operation is composition of braids (see ...

reflection group In group theory and geometry, a reflection group is a discrete group which is generated by a set of reflections of a finite-dimensional Euclidean space. The symmetry group of a regular polytope or of a tiling of the Euclidean space by congruent co ...

invariant theory Invariant theory is a branch of abstract algebra dealing with actions of groups on algebraic varieties, such as vector spaces, from the point of view of their effect on functions. Classically, the theory dealt with the question of explicit descr ...

, and hypergeometric integrals. He was, with Louis Solomon and

Hiroaki Terao is a Japanese mathematician, known as, with Peter Orlik and Louis Solomon, a pioneer of the theory of arrangements of hyperplanes. He was awarded a Mathematical Society of Japan Algebra Prize in 2010. Education Terao started his studies at the U ...

, a pioneer of the theory of arrangements of hyperplanes in complex space. In 2012 he was elected a Fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

.List of Fellows of the American Mathematical Society
/ref>

Selected publications

Books

*''Seifert Manifolds'', Lecture Notes in Mathematics 291, Springer Verlag, 1972 *as editor: ''Singularities'', 2 vols., American Mathematical Society, 1983
''Introduction to Arrangements''
CBMS Regional Conference Series, American Mathematical Society, 1989 * * *with Volkmar Welker

Universitext, Springer Verlag, 2007

Articles

*with Colin P. Rourke: *with

John Milnor John Willard Milnor (born February 20, 1931) is an American mathematician known for his work in differential topology, algebraic K-theory and low-dimensional holomorphic dynamical systems. Milnor is a distinguished professor at Stony Brook Uni ...

: *with Frank Raymond: *with Philip Wagreich: *''The multiplicity of a holomorphic map at an isolated critical point'', in ''Real and complex singularities'', Oslo: Sijthoff and Noordhoff, 1977, 405–474 * *with Louis Solomon: *with Daniel C. Cohen:

References

{{DEFAULTSORT:Orlik, Peter 20th-century American mathematicians 21st-century American mathematicians American topologists Norwegian Institute of Technology alumni University of Michigan alumni University of Wisconsin–Madison faculty Fellows of the American Mathematical Society Institute for Advanced Study visiting scholars 1938 births Living people Hungarian emigrants to the United States Mathematicians from Budapest