A.Morozov
Resultant as Determinant of Koszul Complex.
Tue, 12/01/2009 - 16:01 — SomNambulAuthors: A.Morozov, Sh.Shakirov, A.Anokhina
Subjects: Mathematical Physics
AbstractA linear map between two vector spaces has a very important characteristic: a
determinant. In modern theory two generalizations of linear maps are
intensively used: to linear complexes (the nilpotent chains of linear maps) and
to non-linear mappings. Accordingly, determinant of a linear map has two
generalizations: to determinants of complexes and to resultants. These
quantities are in fact related: resultant of a non-linear map is determinant of
the corresponding Koszul complex.New and Old Results in Resultant Theory.
Mon, 11/30/2009 - 16:01 — SomNambulAuthors: A.Morozov, Sh.Shakirov
Subjects: Mathematical Physics
AbstractResultants are getting increasingly important in modern theoretical physics:
they appear whenever one deals with non-linear (polynomial) equations, with
non-quadratic forms or with non-Gaussian integrals. Being a subject of more
than three-hundred-year research, resultants are of course rather well studied:
a lot of explicit formulas, beautiful properties and intriguing relationships
are known in this field. We present a brief overview of these results,
including both recent and already classical.Universal Algebras of Hurwitz Numbers.
Tue, 09/08/2009 - 12:16 — SomNambulAuthors: A.Mironov, A.Morozov, S.Natanzon
Subjects: Geometric Topology
AbstractInfinite-dimensional universal Cardy-Frobenius algebra is constructed, which
unifies all particular algebras of closed and open Hurwitz numbers and is
closely related to the algebra of differential operators, familiar from the
theory of Generalized Kontsevich Model.
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