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Complete moduli in the presence of semiabelian group action
 Ann. of Math
"... Abstract. I prove the existence, and describe the structure, of moduli space of pairs (P, Θ) consisting of a projective variety P with semiabelian group action and an ample Cartier divisor on it satisfying a few simple conditions. Every connected component of this moduli space is proper. A component ..."
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Cited by 103 (7 self)
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Abstract. I prove the existence, and describe the structure, of moduli space of pairs (P, Θ) consisting of a projective variety P with semiabelian group action and an ample Cartier divisor on it satisfying a few simple conditions. Every connected component of this moduli space is proper. A component containing a projective toric variety is described by a configuration of several polytopes the main of which is the secondary polytope. On the other hand, the component containing a principally polarized abelian variety provides a moduli compactification of Ag. The main irreducible component of this compactification is described by an ”infinite periodic ” analog of secondary polytope and coincides with the
Root polytopes and growth series of root lattices
 SIAM J. Discrete Math
"... Abstract. The convex hull of the roots of a classical root lattice is called a root polytope. We determine explicit unimodular triangulations of the boundaries of the root polytopes associated to the root lattices An, Cn and Dn, and compute their fand hvectors. This leads us to recover formulae fo ..."
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Cited by 18 (1 self)
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Abstract. The convex hull of the roots of a classical root lattice is called a root polytope. We determine explicit unimodular triangulations of the boundaries of the root polytopes associated to the root lattices An, Cn and Dn, and compute their fand hvectors. This leads us to recover formulae for the growth series of these root lattices, which were first conjectured by Conway–Mallows–Sloane and Baake–Grimm and proved by Conway–Sloane and Bacher–de la Harpe–Venkov. 1.
Skeletons in N dimensions using shape primitives
 Pattern Recognition Letters
, 2002
"... This paper describes the generation of shape primitive dimitive masks and their application in measurements on shapes as well as in conditions for topology preservation as used in skeletonization. The formalism is expanded from twoto fourdimensional images and elaborates on the extension of 3D ske ..."
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Cited by 5 (1 self)
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This paper describes the generation of shape primitive dimitive masks and their application in measurements on shapes as well as in conditions for topology preservation as used in skeletonization. The formalism is expanded from twoto fourdimensional images and elaborates on the extension of 3D skeletonization to 4D skeletonization.
Spectral distributions and isospectral sets of tridiagonal matrices
"... Abstract. We analyze the correspondence between finite sequences of finitely supported probability distributions and finitedimensional, real, symmetric, tridiagonal matrices. In particular, we give an intrinsic description of the topology induced on sequences of distributions by the usual Euclidean ..."
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Cited by 3 (0 self)
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Abstract. We analyze the correspondence between finite sequences of finitely supported probability distributions and finitedimensional, real, symmetric, tridiagonal matrices. In particular, we give an intrinsic description of the topology induced on sequences of distributions by the usual Euclidean structure on matrices. Our results provide an analytical tool with which to study ensembles of tridiagonal matrices, important in certain inverse problems and integrable systems. As an application, we prove that the Euler characteristic of any generic isospectral set of symmetric, tridiagonal matrices is a tangent number. Contents
Exceptional Points in the EllipticHyperelliptic Locus
, 2008
"... An exceptional point in moduli space is a unique surface class whose full group of conformal automorphisms acts with a triangular signature. In this paper we determine, up to topological conjugacy, the full group of conformal and anticonformal automorphisms of a symmetric exceptional point in the el ..."
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Cited by 3 (1 self)
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An exceptional point in moduli space is a unique surface class whose full group of conformal automorphisms acts with a triangular signature. In this paper we determine, up to topological conjugacy, the full group of conformal and anticonformal automorphisms of a symmetric exceptional point in the elliptichyperelliptic locus in moduli space. We determine the number of ovals of any symmetry of such a surface. We show that while the elliptichyperelliptic locus in moduli space can contain an arbitrarily large number of exceptional points, no more than four are also symmetric.
CONVEX HULLS OF ORBITS AND ORIENTATIONS OF A MOVING PROTEIN DOMAIN
, 2007
"... We study the facial structure and Carathéodory number of the convex hull of an orbit of the group of rotations in R³ acting on the space of pairs of anisotropic symmetric 3 × 3 tensors. This is motivated by the problem of determining the structure of some proteins in aqueous solution. ..."
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Cited by 3 (1 self)
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We study the facial structure and Carathéodory number of the convex hull of an orbit of the group of rotations in R³ acting on the space of pairs of anisotropic symmetric 3 × 3 tensors. This is motivated by the problem of determining the structure of some proteins in aqueous solution.
Sculptures in S3
"... We construct a number of sculptures, each based on a geometric design native to the threedimensional sphere. Using stereographic projection we transfer the design from the threesphere to ordinary Euclidean space. All of the sculptures are then fabricated by the 3D printing service Shapeways. 1 ..."
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Cited by 1 (1 self)
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We construct a number of sculptures, each based on a geometric design native to the threedimensional sphere. Using stereographic projection we transfer the design from the threesphere to ordinary Euclidean space. All of the sculptures are then fabricated by the 3D printing service Shapeways. 1
BETWEEN LOWER AND HIGHER DIMENSIONS (in the work of Terry Lawson)
"... There are several approaches to summarizing a mathematician’s research accomplishments, and each has its advantages and disadvantages. This article is based upon a talk given at Tulane that was aimed at a fairly general audience, including faculty members in other areas and graduate students who had ..."
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There are several approaches to summarizing a mathematician’s research accomplishments, and each has its advantages and disadvantages. This article is based upon a talk given at Tulane that was aimed at a fairly general audience, including faculty members in other areas and graduate students who had taken the usual entry level courses. As such, it is meant to be relatively nontechnical and to emphasize qualitative rather than quantitative issues; in keeping with this aim, references will be given for some standard topological notions that are not normally treated in entry level graduate courses. Since this was an hour talk, it was also not feasible to describe every single piece of published mathematical work that Terry Lawson has ever written; in particular, some papers like [42] and [50] would require lengthy digressions that are not easily related to the central themes in his main lines of research. Instead, we shall focus on some ways in which Terry’s work relates to an important thread in geometric topology; namely, the passage from studying problems in a given dimension to studying problems in the next dimensions. Qualitatively speaking, there are fairly welldeveloped theories for very low dimensions and for all sufficiently large dimensions, but between these ranges there are some dimensions in which the answers to many fundamental