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Cohomology in algebra, geometry, physicsand statistics
Koszul algebras and one-dependent random 0-1 sequences
Speaker’s name:
Leonid Positselski
Speaker’s affiliation:
IM, CAS
Place:
https://cesnet.zoom.us/j/239249755
Meeting ID 239-249-755
Date:
Wednesday, 1. April 2020 - 11:30 to 12:30
Abstract:
Koszul algebras are a natural class of graded algebras with
quadratic relations, defined by a series of homological conditions.
To a Koszul algebra over a field with finite-dimensional components,
one can assign a one-dependent stochastic 0-1 sequence, which carries
information about the dimensions of the algebra's grading components.
This construction allows to show that the Hilbert series of a Koszul
algebra can be extended meromorphically to the circle of double radius.
Conjecturally, such Hilbert series are meromorphic in the whole
complex plane (and consequently, rational).
quadratic relations, defined by a series of homological conditions.
To a Koszul algebra over a field with finite-dimensional components,
one can assign a one-dependent stochastic 0-1 sequence, which carries
information about the dimensions of the algebra's grading components.
This construction allows to show that the Hilbert series of a Koszul
algebra can be extended meromorphically to the circle of double radius.
Conjecturally, such Hilbert series are meromorphic in the whole
complex plane (and consequently, rational).