The Max Planck Institute for Mathematics (, MPIM) is a research institute located in

Bonn Bonn () is a federal city in the German state of North Rhine-Westphalia, located on the banks of the Rhine. With a population exceeding 300,000, it lies about south-southeast of Cologne, in the southernmost part of the Rhine-Ruhr region. This ...

Germany Germany, officially the Federal Republic of Germany, is a country in Central Europe. It lies between the Baltic Sea and the North Sea to the north and the Alps to the south. Its sixteen States of Germany, constituent states have a total popu ...

. It is named in honor of the

German German(s) may refer to: * Germany, the country of the Germans and German things **Germania (Roman era) * Germans, citizens of Germany, people of German ancestry, or native speakers of the German language ** For citizenship in Germany, see also Ge ...

physicist A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists generally are interested in the root or ultimate cau ...

Max Planck Max Karl Ernst Ludwig Planck (; ; 23 April 1858 – 4 October 1947) was a German Theoretical physics, theoretical physicist whose discovery of energy quantum, quanta won him the Nobel Prize in Physics in 1918. Planck made many substantial con ...

and forms part of the

Max Planck Society The Max Planck Society for the Advancement of Science (; abbreviated MPG) is a formally independent non-governmental and non-profit association of German research institutes. Founded in 1911 as the Kaiser Wilhelm Society, it was renamed to the M ...

(''Max-Planck-Gesellschaft''), an association of 84 institutes engaging in fundamental research in the arts and the sciences. The MPIM is the only Max Planck institute specializing in

pure mathematics Pure mathematics is the study of mathematical concepts independently of any application outside mathematics. These concepts may originate in real-world concerns, and the results obtained may later turn out to be useful for practical applications ...

. The Institute was founded by

Friedrich Hirzebruch Friedrich Ernst Peter Hirzebruch ForMemRS (17 October 1927 – 27 May 2012) was a German mathematician, working in the fields of topology, complex manifolds and algebraic geometry, and a leading figure in his generation. He has been described as ...

in 1980, having emerged from the collaborative research center "Theoretical Mathematics" ( Sonderforschungsbereich "Theoretische Mathematik"). Hirzebruch shaped the institute as its director until his retirement in 1995. Currently, the institute is managed by a board of three directors consisting of Peter Teichner (managing director), Peter Scholze and Dennis Gaitsgory.

and

Yuri Manin Yuri Ivanovich Manin (; 16 February 1937 – 7 January 2023) was a Russian mathematician, known for work in algebraic geometry and diophantine geometry, and many expository works ranging from mathematical logic to theoretical physics. Life an ...

were, and Günter Harder, Werner Ballmann,

Gerd Faltings Gerd Faltings (; born 28 July 1954) is a German mathematician known for his work in arithmetic geometry. Education From 1972 to 1978, Faltings studied mathematics and physics at the University of Münster. Interrupted by 15 months of obligatory ...

and

Don Zagier Don Bernard Zagier (born 29 June 1951) is an American-German mathematician whose main area of work is number theory. He is currently one of the directors of the Max Planck Institute for Mathematics in Bonn, Germany. He was a professor at the ''Co ...

are, acting as emeriti.

Research

The Max Planck Institute for Mathematics offers mathematicians from around the world the opportunity to visit Bonn and engage in

sabbatical A sabbatical (from the Hebrew: (i.e., Sabbath); in Latin ; Greek: ) is a rest or break from work; "an extended period of time intentionally spent on something that’s not your routine job." The concept of the sabbatical is based on the Bi ...

work lasting from weeks to several months. This guest program distinguishes the MPIM from other Max Planck institutes, and results in only a limit number of permanent positions and the absence of separate departments within the institute. The research of the members and guests of the institute can be classified into the following areas: *

Algebraic Geometry Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; th ...

and

Complex Geometry In mathematics, complex geometry is the study of geometry, geometric structures and constructions arising out of, or described by, the complex numbers. In particular, complex geometry is concerned with the study of space (mathematics), spaces su ...

Algebraic Groups In mathematics, an algebraic group is an algebraic variety endowed with a group structure that is compatible with its structure as an algebraic variety. Thus the study of algebraic groups belongs both to algebraic geometry and group theory. Many ...

Algebraic Topology Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariant (mathematics), invariants that classification theorem, classify topological spaces up t ...

Arithmetic Geometry In mathematics, arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. Arithmetic geometry is centered around Diophantine geometry, the study of rational points of algebraic varieties. ...

Differential Geometry Differential geometry is a Mathematics, mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of Calculus, single variable calculus, vector calculus, lin ...

and

Topology Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...

Dynamical Systems In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in an ambient space, such as in a parametric curve. Examples include the mathematical models ...

* Global Analysis *

Mathematical Physics Mathematical physics is the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and the de ...

Noncommutative Geometry Noncommutative geometry (NCG) is a branch of mathematics concerned with a geometric approach to noncommutative algebras, and with the construction of ''spaces'' that are locally presented by noncommutative algebras of functions, possibly in some g ...

Number Theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

Representation Theory Representation theory is a branch of mathematics that studies abstract algebra, abstract algebraic structures by ''representing'' their element (set theory), elements as linear transformations of vector spaces, and studies Module (mathematics), ...

References

External links

* * Research institutes established in 1980 Mathematical institutes

Mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

Max-Planck-Institut fur Mathematik Max-Planck-Institut fur Mathematik Mathematics in Germany {{Math-org-stub