Sergei Gelfand
Country:
Russia
Company:
Science
The son of Israel Gelfand. Gelfand came to the American Mathematics Society from Moscow in 1990 as the Manager of the Russian Translation Program. Sergei becameDirector of Acquisitions in 1997 and Associate Publisher for
Acquisitions in 2002. Sergei Gelfand was appointed Publisher of the AMS in October
2007. Author of the books: "Factorizations of Polynomials over Noncommutative Algebras and Sufficient Sets of Edges in Directed Graphs" (2005) - To directed graphs with unique sink and source we associate a noncommutative associative algebra and
a polynomial over this algebra. Edges of the graph correspond to pseudo-roots of
the polynomial. We give a sufficient condition when coefficients of the polynomi- al can be rationally expressed via elements of a given set of pseudo-roots (edges); Ouasideterminants (2002)- The determinant is a main organizing tool in commuta- tive linear algebra. In this review he present atheory of the quasideterminants defined for matrices over a division ring, Hilbert series of quadratic algebras associated with pseudo-roots of noncommutative polynomials -The quadratic algebras Q_n are asso- ciated with pseudo-roots ofnoncommutative polynomials. He compute the Hilbert se- ries of the algebras Q_n and ofthe dual quadratic algebras Q_n^!; Quantum Schubert Polynomials (2001)- he compute Gromov-Witten invariants of the flagmanifold us- ing a new combinatorial construction for its quantum cohomology ring.