Max Planck Institute for Mathematics in the Sciences

Encyclopedia

The

was founded on March 1, 1996.

At the institute scientists (mainly mathematicians) work on projects which apply mathematics

in various areas of natural science

s, in particular physics

, biology

, chemistry

and material science.

Main research areas are

The institute has an extensive visitors programme which had made Leipzig

a main place for research in applied mathematics

.

**Max Planck Institute for Mathematics**

in the Sciences(MPI-MIS) in LeipzigMathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

in the Sciences

Leipzig

Leipzig Leipzig has always been a trade city, situated during the time of the Holy Roman Empire at the intersection of the Via Regia and Via Imperii, two important trade routes. At one time, Leipzig was one of the major European centres of learning and culture in fields such as music and publishing...

was founded on March 1, 1996.

At the institute scientists (mainly mathematicians) work on projects which apply mathematics

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

in various areas of natural science

Natural science

The natural sciences are branches of science that seek to elucidate the rules that govern the natural world by using empirical and scientific methods...

s, in particular physics

Physics

Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

, biology

Biology

Biology is a natural science concerned with the study of life and living organisms, including their structure, function, growth, origin, evolution, distribution, and taxonomy. Biology is a vast subject containing many subdivisions, topics, and disciplines...

, chemistry

Chemistry

Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry is concerned with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds....

and material science.

Main research areas are

- Scientific computing (group of Wolfgang HackbuschWolfgang HackbuschWolfgang Hackbusch is a German mathematician, known for his pioneering research in multigrid methods and later hierarchical matrices, a concept generalizing the fast multipole method...

), - Nonlinear AnalysisMathematical analysisMathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions...

, in particular partial differential equationPartial differential equationIn mathematics, partial differential equations are a type of differential equation, i.e., a relation involving an unknown function of several independent variables and their partial derivatives with respect to those variables...

s and calculus of variationsCalculus of variationsCalculus of variations is a field of mathematics that deals with extremizing functionals, as opposed to ordinary calculus which deals with functions. A functional is usually a mapping from a set of functions to the real numbers. Functionals are often formed as definite integrals involving unknown...

with applications, e.g., on microstructureMicrostructureMicrostructure is defined as the structure of a prepared surface or thin foil of material as revealed by a microscope above 25× magnification...

s, micromagnetismMicromagnetismMicromagnetics deals with the interactions between magnetic moments on sub-micrometre length scales. These are governed by several competing energy terms. Dipolar energy is the energy which causes magnets to align north to south pole...

and material science (group of Stefan MüllerStefan Müller (mathematician)Stefan Müller is a German mathematician and currently a professor at the University of Bonn. He has been one of the founding directors of the Max Planck Institute for Mathematics in the Sciences in 1996 and was acting there until 2008.He his well known for his research in analysis and the calculus...

), - RiemannianRiemannian geometryRiemannian geometry is the branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a Riemannian metric, i.e. with an inner product on the tangent space at each point which varies smoothly from point to point. This gives, in particular, local notions of angle, length...

, KählerKahlerKahler may refer to:Places*Kahler, Luxembourg, a small town in the commune of Garnich*Kahler Asten,a German mountain rangePeople*Art Kahler , American football and basketball player and coach...

ian and algebraic geometryAlgebraic geometryAlgebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...

(group of Jürgen Jost), - neuronal networks (group of Jürgen Jost),
- Mathematical physicsMathematical physicsMathematical physics refers to development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines this area as: "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and...

(group of Eberhard Zeidler), - Mathematical biologyMathematical biologyMathematical and theoretical biology is an interdisciplinary scientific research field with a range of applications in biology, medicine and biotechnology...

(group of Angela Stevens).

The institute has an extensive visitors programme which had made Leipzig

Leipzig

Leipzig Leipzig has always been a trade city, situated during the time of the Holy Roman Empire at the intersection of the Via Regia and Via Imperii, two important trade routes. At one time, Leipzig was one of the major European centres of learning and culture in fields such as music and publishing...

a main place for research in applied mathematics

Applied mathematics

Applied mathematics is a branch of mathematics that concerns itself with mathematical methods that are typically used in science, engineering, business, and industry. Thus, "applied mathematics" is a mathematical science with specialized knowledge...

.