Sergey Yuzvinsky
University of Oregon, Mathematics, Emeritus
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Page 1. COMMUNICATIONS IN ALGEBRA, 11 (9), 973-1009 (1983) THE VARIETY OF PRIMITIVE REPRESENTATIONS OF A QUIVER WITH NORMAL RELATIONS Sergey Yuzvinsky University of Ore on Eugene, Oregon 97&03 INTRODUCTION ...
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Research Interests: Robotics, Mathematics, Geometry And Topology, Computer Science, Robotics (Computer Science), and 12 moreMotion Planning, Knots and Quandles: (mathematics Algebraic Topology), Pure Mathematics(Differential Geometry), Three Dimensional, Euclidean space, Obstacle, COL, Hyperplane, Topological Complexity, arXiv, Configuration space, and Planar
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The theory of transformations with invariant measure or the metric theory of dynamical systems or ergodic theory is extensively related to various branches of mathematics — to the theory of classical dynamical systems, i.e., to classical... more
The theory of transformations with invariant measure or the metric theory of dynamical systems or ergodic theory is extensively related to various branches of mathematics — to the theory of classical dynamical systems, i.e., to classical mechanics, to probability theory, to functional analysis, to algebra, to number theory, to topology, etc. These diverse and steadfast relationships are rooted in the following two factors: first, the basic object of study, namely, a transformation with invariant measure (in other words, an automorphism of a space with measure), frequently encountered in mathematics, has proved to be a topic which is very meaningful and which lends itself to profound study; second, ergodic theory itself has repeatedly turned out to be an area in which there have been applied and verified new powerful general mathematical ideas and methods such as operator theory, general measure theory, and quite recently, information theory and probability theory, etc.
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Conjectures of J. Igusa for p-adic local zeta functions and of J. Denef and F. Loeser for topological local zeta functions assert that (the real part of) the poles of these local zeta functions are roots of the Bernstein-Sato polynomials... more
Conjectures of J. Igusa for p-adic local zeta functions and of J. Denef and F. Loeser for topological local zeta functions assert that (the real part of) the poles of these local zeta functions are roots of the Bernstein-Sato polynomials (i.e. the b-functions). We prove these conjectures for certain hyperplane arrangements, including the case of reduced hyperplane arrangements in three-dimensional affine space.
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Page 1. Progress in Mathematics, Vol. 283, 83110 c© 2009 Birkhäuser Verlag Basel/Switzerland Lectures on Orlik-Solomon Algebras Alexandru Dimca and Sergey Yuzvinsky Abstract. The first part of this survey is an elementary introduction... more
Page 1. Progress in Mathematics, Vol. 283, 83110 c© 2009 Birkhäuser Verlag Basel/Switzerland Lectures on Orlik-Solomon Algebras Alexandru Dimca and Sergey Yuzvinsky Abstract. The first part of this survey is an elementary introduction into Orlik-Solomon algebras. ...
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ABSTRACT this paper contains some of highlights of Deligne's theory [7] and several examples from the theory of Alexander invariants developed mostly by the first author in the series of papers [17] - [22]. We also included... more
ABSTRACT this paper contains some of highlights of Deligne's theory [7] and several examples from the theory of Alexander invariants developed mostly by the first author in the series of papers [17] - [22]. We also included several problems indicating possible further development. The second author uses the opportunity to thank M.Oka and H.Terao for the hard labor of organizing the Arrangement Workshop. 2 Cohomology of local systems Local systems. A local system of rank n on a topological space X is a homomorphism ß 1 (X) ! GL(n; C). Such a homomorphism defines a vector bundle on X with discrete structure group or a locally constant bundle (cf. [7], I.1). Indeed, if ~
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Multinets are certain configurations of lines and points with multiplicities in the complex projective plane P2. They are used in the studies of resonance and characteristic varieties of complex hyperplane arrangement complements and... more
Multinets are certain configurations of lines and points with multiplicities in the complex projective plane P2. They are used in the studies of resonance and characteristic varieties of complex hyperplane arrangement complements and cohomology of Milnor fibers. From combinatorics viewpoint they can be considered as generalizations of Latin squares. Very few exam- ples of multinets with non-trivial multiplicities are known. In this paper, we present new examples of multinets. These are obtained by using an analogue of nets in P3 and intersecting them by planes.
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This is a survey of Orlik-Solomon algebras of hyperplane arrangements. These algebras first appeared in theorems due to Arnol'd, Brieskorn, and Orlik and Solomon as the cohomology algebras of the complements of complex hyperplane... more
This is a survey of Orlik-Solomon algebras of hyperplane arrangements. These algebras first appeared in theorems due to Arnol'd, Brieskorn, and Orlik and Solomon as the cohomology algebras of the complements of complex hyperplane arrangements. Numerous applications of these algebras have subsequently been found. This survey is confined to studying Orlik-Solomon algebras per se and some of their applications to
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... Kouider Djerfi Kursat Hakan Oral Le Dung Trang Mamuka Shubladze Maria Pe Pereira Masaaki Yoshida Masahiko Yoshinaga Meral Tosun Mesut Arslandok Michael Falk Mikhail Mazin Mohammed Salim Jbara Mohan Bhupal Muhammed Uludag Mustafa... more
... Kouider Djerfi Kursat Hakan Oral Le Dung Trang Mamuka Shubladze Maria Pe Pereira Masaaki Yoshida Masahiko Yoshinaga Meral Tosun Mesut Arslandok Michael Falk Mikhail Mazin Mohammed Salim Jbara Mohan Bhupal Muhammed Uludag Mustafa Topkara Mutsuo Oka ...
We give a necessary and sufficient condition on a homogeneous polynomial ideal for its Taylor complex to be exact. Then we give a combinatorial construction of a minimal resolution for ideals satisfying the above condition (in particular... more
We give a necessary and sufficient condition on a homogeneous polynomial ideal for its Taylor complex to be exact. Then we give a combinatorial construction of a minimal resolution for ideals satisfying the above condition (in particular for monomial ideals).
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In the paper, we study special configurations of lines and points in the complex projective plane, so called k-nets. We describe the role of these configurations in studies of cohomology on arrangement complements. Our most general result... more
In the paper, we study special configurations of lines and points in the complex projective plane, so called k-nets. We describe the role of these configurations in studies of cohomology on arrangement complements. Our most general result is the restriction on k - it can be only 3,4, or 5. The most interesting class of nets is formed by 3-nets
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ABSTRACT We apply cohomology of sheaves to arrangements of hyperplanes. In particular we prove an inequality for the depth of cohomology modules of local sheaves on the intersection lattice of an arrangement. This generalizes a result of... more
ABSTRACT We apply cohomology of sheaves to arrangements of hyperplanes. In particular we prove an inequality for the depth of cohomology modules of local sheaves on the intersection lattice of an arrangement. This generalizes a result of Solomon-Terao about the commulative property of local functors. We also prove a characterization of free arrangements by certain properties of the cohomology of a sheaf of derivation modules. This gives a condition on the Möbius function of the intersection lattice of a free arrangement. Using this condition we prove that certain geometric lattices cannot afford free arrangements although their Poincaré polynomials factor.
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ABSTRACT Without Abstract