Joachim Cuntz (born 28 September 1948 in

Mannheim Mannheim (; Palatine German: or ), officially the University City of Mannheim (german: Universitätsstadt Mannheim), is the second-largest city in the German state of Baden-Württemberg after the state capital of Stuttgart, and Germany's 2 ...

) is a German

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

, currently a professor at the

University of Münster The University of Münster (german: Westfälische Wilhelms-Universität Münster, WWU) is a public university, public research university located in the city of Münster, North Rhine-Westphalia in Germany. With more than 43,000 students and over ...

Work

Joachim Cuntz has made fundamental contributions to the area of

C*-algebras In mathematics, specifically in functional analysis, a C∗-algebra (pronounced "C-star") is a Banach algebra together with an involution satisfying the properties of the adjoint. A particular case is that of a complex algebra ''A'' of continuous ...

and to the field of

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 ge ...

in the sense of

Alain Connes Alain Connes (; born 1 April 1947) is a French mathematician, and a theoretical physicist, known for his contributions to the study of operator algebras and noncommutative geometry. He is a professor at the , , Ohio State University and Vande ...

. He initiated the analysis of the structure of simple C*-algebras and introduced new methods and examples, including the Cuntz algebras and the Cuntz semigroup. He was one of the first to apply

K-theory In mathematics, K-theory is, roughly speaking, the study of a ring generated by vector bundles over a topological space or scheme. In algebraic topology, it is a cohomology theory known as topological K-theory. In algebra and algebraic geometry, ...

to noncommutative operator algebras and contributed to the development of that theory. In collaboration with

Daniel Quillen Daniel Gray "Dan" Quillen (June 22, 1940 – April 30, 2011) was an American mathematician. He is known for being the "prime architect" of higher algebraic ''K''-theory, for which he was awarded the Cole Prize in 1975 and the Fields Medal in 197 ...

, he developed a new approach to

cyclic cohomology In noncommutative geometry and related branches of mathematics, cyclic homology and cyclic cohomology are certain (co)homology theories for associative algebras which generalize the de Rham (co)homology of manifolds. These notions were independent ...

and proved the excision property of periodic cyclic theory. In recent years, he has been working mainly on C*-algebras that are related to structures from

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777� ...

. Joachim Cuntz had dozens of PhD students and research assistants, many of which are professors in mathematics today. Among them are: * Xin Li (PhD 2010, professor of mathematics at the

University of Glasgow , image = UofG Coat of Arms.png , image_size = 150px , caption = Coat of arms Flag , latin_name = Universitas Glasguensis , motto = la, Via, Veritas, Vita , ...

) * Ralf Meyer (PhD 1999, professor of mathematics at the

University of Göttingen The University of Göttingen, officially the Georg August University of Göttingen, (german: Georg-August-Universität Göttingen, known informally as Georgia Augusta) is a public research university in the city of Göttingen, Germany. Founded ...

) *

Andreas Thom Andreas Thom (born 7 September 1965) is a German former professional footballer who played as a forward for BFC Dynamo, Bayer Leverkusen, Celtic and Hertha BSC. He played 51 times for East Germany throughout the 1980s and played ten times for ...

(PhD 2003, professor of geometry at the

TU Dresden TU Dresden (for german: Technische Universität Dresden, abbreviated as TUD and often wrongly translated as "Dresden University of Technology") is a public research university, the largest institute of higher education in the city of Dresden, th ...

) * Christian Voigt (PhD 2003, professor of mathematics at the

University of Glasgow , image = UofG Coat of Arms.png , image_size = 150px , caption = Coat of arms Flag , latin_name = Universitas Glasguensis , motto = la, Via, Veritas, Vita , ...

) * Moritz Weber (PhD 2011, junior professor of mathematics at

Saarland University Saarland University (german: Universität des Saarlandes, ) is a public research university located in Saarbrücken, the capital of the German state of Saarland. It was founded in 1948 in Homburg in co-operation with France and is organized in si ...

) * Wilhelm Winter (PhD 2000, professor of mathematics at the

) * Joachim Zacharias (PhD 1996, professor of mathematics at the

University of Glasgow , image = UofG Coat of Arms.png , image_size = 150px , caption = Coat of arms Flag , latin_name = Universitas Glasguensis , motto = la, Via, Veritas, Vita , ...

)

Awards and honors

* 1990

Invited speaker at the International Congress of Mathematicians This is a list of International Congresses of Mathematicians Plenary and Invited Speakers. Being invited to talk at an International Congress of Mathematicians has been called "the equivalent, in this community, of an induction to a hall of fame." ...

in Kyoto (Cyclic Cohomology and K-homology). * Max Planck Research Award (together with G. Kasparov), 1993 * Medal of the Collège de France, 1997 *

Gottfried Wilhelm Leibniz Prize The Gottfried Wilhelm Leibniz Prize (german: link=no, Förderpreis für deutsche Wissenschaftler im Gottfried Wilhelm Leibniz-Programm der Deutschen Forschungsgemeinschaft), in short Leibniz Prize, is awarded by the German Research Foundation to ...

of the DFG 1999, *

Honorary doctorate An honorary degree is an academic degree for which a university (or other degree-awarding institution) has waived all of the usual requirements. It is also known by the Latin phrases ''honoris causa'' ("for the sake of the honour") or ''ad hon ...

from the

University of Copenhagen The University of Copenhagen ( da, Københavns Universitet, KU) is a prestigious public university, public research university in Copenhagen, Copenhagen, Denmark. Founded in 1479, the University of Copenhagen is the second-oldest university in ...

* ERC Advanced Investigators Grant, 2010 * 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, ...

, 2012List of Fellows of the American Mathematical Society
retrieved 2013-02-16.

Work

Awards and honors

References

Further reading