# Claudio Procesi

**Claudio Procesi** (March 31, 1941 in Rome) is an Italian mathematician, known for works in algebra and representation theory.

## Career

Procesi studied at the University of Rome, where he received his degree (Laurea) in 1963. In 1966 he graduated from the University of Chicago advised by Israel Herstein, with a study of the article called "On rings with polynomial identities". From 1966 he was Assistant Professor at the University of Rome, 1970 associate professor at the University of Lecce and 1971 at the Pisa University. From 1973 he was full professor in Pisa and in 1975 ordinary Professor at the University La Sapienza in Rome. He was a visiting scientist at the Columbia University (1969–1970), and UCLA (1973/74) at IMPA, the Massachusetts Institute of Technology (1991), in Grenoble, at the Brandeis University (1981/2), at the University of Texas at Austin (1984), the Institute for Advanced Study (1994), the MSRI (1992, etc.), at the ICTP in Trieste, at the École Normale Supérieure.

Procesi studies noncommutative algebra, algebraic groups, invariant theory, enumerative geometry, infinite dimensional algebras and quantum groups, polytopes, braid groups, cyclic homology, geometry of orbits of compact groups, arrangements of subspaces and tori.

Procesi^{[1]} proved that
the polynomial invariants of n x n matrices over a field *K* all come from the Hamilton-Cayley theorem, which says that a square matrix satisfies its own characteristic polynomial.^{[2]}

In 1981 he was awarded the Medal of the Accademia dei Mathematics Lincei, of which he is a member since 1987. In 1986 he received the Feltrinelli Prize in mathematics. In 1978 he was an invited speaker at the International Congress of Mathematicians (ICM) in Helsinki. From 2007 to 2010 he is a vice-president of the International Mathematical Union. He was an editor of the Duke Mathematical Journal, the Journal of Algebra, Communications in Algebra and of Advances in Mathematics. Finally, he was on the committee of the Abel Prize and the algebra committee for the ICM 1986-1994.

## Works

- 2010: (with Corrado de Concini)
*Topics in Hyperplane Arrangements, Polytopes and Box-Splines*, Springer MR 2722776 - 2006:
*Lie groups: An approach through invariants and representations*, Springer, Universitext^{[3]} - 1996: (with Haspeter Kraft) Classical Invariant Theory
- 1993: (with Corrado de Concini)
*Quantum groups*, Lecture notes in Mathematics, Springer MR 1288995 - 1993:
*Rings with polynomial identities*, Dekker MR 0366968 - 1983:
*A primer on invariant theory*, Brandeis University

## See also

## References

The original article was a translation (Google) of the corresponding German article.

- ↑ C. Procesi (1976) "Invariant theory of n x n matrices", Advances in Mathematics 19: 306-381
- ↑ Edward W. Formanek (1989) "Polynomial identities and the Cayley-Hamilton theorem", Mathematical Intelligencer 11(1): 37
- ↑ Varadarajan, V. S. (2008). "Review:
*Lie groups. An approach through invariants and representations*, by Claudio Procesi" (PDF).*Bull. Amer. Math. Soc. (N.S.)*.**45**(4): 661–674. doi:10.1090/s0273-0979-08-01201-9.