Homological algebra and representation theory form a powerful confluence in modern mathematics. Homological algebra provides a framework for analysing algebraic structures via chain complexes, ...

We study the complexity of the problem to describe, up to unitary equivalence, representations of *-algebras by unbounded operators on a Hilbert space. A number of examples are developed in detail.

Transactions of the American Mathematical Society, Vol. 149, No. 2 (Jun., 1970), pp. 503-537 (35 pages) We construct a general class of Banach algebras which include as special cases the group algebra ...

Current Projects • EXC 2044 - T01: K-Groups and cohomology K-groups and cohomology groups are important invariants in different areas of mathematics, from arithmetic geometry to geometric topology to ...

University of Chicago mathematicians Alexander Beilinson and Vladimir Drinfeld have been awarded the prestigious Wolf Prize for Mathematics “for their groundbreaking work in algebraic geometry, ...

Masaki Kashiwara has won the 2025 Abel prize, sometimes called the Nobel prize of mathematics, for his work on algebraic analysis. Kashiwara, a professor at Kyoto University, Japan, received the award ...

Current Projects • EXC 2044 - T04: Groups and actions The study of symmetry and space through the medium of groups and their actions has long been a central theme in modern mathematics, indeed one ...

“Mathematics is the art of reducing any problem to linear algebra.” This is a quote often attributed to William Stein, a former mathematics professor at the University of Washington, now the lead ...