Achill's Publications

outdated since September 2010
new page at University of Rostock

Book Achill Schürmann, Computational Geometry of Positive Definite Quadratic Forms, AMS University Lecture Series, 2009. Articles Renaud Coulangeon and Achill Schürmann, Energy minimization, periodic sets and spherical designs, preprint at arXiv:1005.4373. Henry Cohn, Abhinav Kumar and Achill Schürmann, Ground states and formal duality relations in the Gaussian core model, Phys. Rev. E 80, 061116 (2009), preprint at arXiv:0911.2169. Mathieu Dutour Sikiric, Achill Schürmann and Frank Vallentin, The contact polytope of the Leech lattice, Discrete Comput. Geom., to appear, complete version at arXiv:0906.1427. Wolfgang Keller, Jacques Martinet and Achill Schürmann, On classifying Minkowskian sublattices, preprint at arXiv:0904.3110. Achill Schürmann, Enumerating Perfect Forms, in Quadratic Forms -- Algebra, Arithmetic, and Geometry, AMS Contemporary Mathematics 437 (2009), 359-378, preprint at arXiv:0901.1587. Henry Cohn, Noam Elkies, Abhinav Kumar and Achill Schürmann, Point configurations that are asymmetric yet balanced, Proc. Amer. Math. Soc. 138 (2010), 2863-2872, preprint at arXiv:0812.2579. Achill Schürmann, Perfect, strongly eutactic lattices are periodic extreme, Advances in Mathematics, 225 (2010), 2546-2564, preprint at arXiv:0808.2013. Mathieu Dutour Sikiric, Achill Schürmann and Frank Vallentin, Complexity and algorithms for computing Voronoi cells of lattices, Math. Comp. 267 (2009), 1713-1731 preprint at arXiv:0804.0036. Maria A. Hernandez Cifre, Achill Schürmann and Frank Vallentin, The isodiametric problem with lattice-point constraints, Monatsh. Math. , 155 (2008), 125-134, preprint at arXiv:0709.2587. David Bremner, Mathieu Dutour Sikiric and Achill Schürmann, Polyhedral representation conversion up to symmetries, Proceedings of the 2006 CRM workshop on polyhedral computation, AMS/CRM Lecture Notes, 48 (2009), 45-71, preprint at arXiv:math/0702239. Brandon Ballinger, Grigoriy Blekherman, Henry Cohn, Noah Giansiracusa, Elizabeth Kelly and Achill Schürmann, Experimental study of energy-minimizing point configurations on spheres, Experiment. Math., 18 (2009), 257-283, preprint at arXiv:math/0611451. Mathieu Dutour Sikiric, Achill Schürmann and Frank Vallentin, Classification of eight dimensional perfect forms, Electron. Res. Announc. Amer. Math. Soc., 13 (2007), preprint at arXiv:math/0609388. Mathieu Dutour Sikiric, Achill Schürmann and Frank Vallentin, A generalization of Voronoi's reduction theory and its application, Duke Math. J., 142 (2008), 127-164, preprint at arXiv:math/0601084. Martin Henk, Achill Schürmann and Jörg M. Wills, Ehrhart polynomials and successive minima, Mathematika, 52 (2005), 1-16, preprint at at arXiv:math/0507528. Francisco Santos, Achill Schürmann and Frank Vallentin, Lattice Delone simplices with super-exponential volume, European J. Combin, 28 (2007), 801-806, preprint at arXiv:math/0507119. Achill Schürmann, On packing spheres into containers (about Kepler's finite sphere packing problem), Doc. Math., 11 (2006), 393-406, preprint at arXiv:math/0506200. Achill Schürmann, Instability of discrete point sets, Period. Math. Hungar., 53 (2006), 257-264. Achill Schürmann and Konrad Swanepoel, Three-dimensional antipodal and norm-equilateral sets, Pacific J. Math, 228 (2006), 101-121. Preprint arXiv:math/0506240, Achill Schürmann and Frank Vallentin, Methods in the Local Theory of Packing and Covering Lattices, Preprint arXiv:math/0412320, appeared in Proceeding of COE Workshop on Sphere Packings, Fukuoka, Japan, 2004. Achill Schürmann and Frank Vallentin, Local Covering Optimality of Lattices: Leech Lattice versus Root Lattice E8, Internat. Math. Res. Notices, vol. 2005, No. 32, 1937-1955. Preprint at arXiv:math/0405441. Achill Schürmann and Frank Vallentin, Computational Approaches to Lattice Packing and Covering Problems, Discrete Comput. Geom., 35 (2006), 73-116. Preprint at arXiv:math/0403272. Ulrich Betke and Achill Schürmann, Lattices of Optimal Finite Lattice Packings, Monatsh. Math. , 144 (2005), 31-38. Achill Schürmann, The Spherical Conjecture in Minkowski Geometry, Arch. Math., 83 (2004), 381-384. Peter Scholl, Achill Schürmann and Jörg M. Wills, A discrete isoperimetric inequality and its application to sphere packings, in Discrete and Computational Geometry - The Goodman-Pollack Festschrift , Springer, 2003, 751-765. Peter Scholl, Achill Schürmann and Jörg M. Wills, Polyhedral models of Felix Klein's quartic , Math. Intelligencer , 24 (2002), 37-42. Achill Schürmann, On Extremal Finite Packings , Discrete Comput. Geom., 28 (2002), 389-403. Uwe Schnell and Achill Schürmann, A Criterion for Finite Lattice Coverings , Period. Math. Hungar., 45 (2002), 131-134. Achill Schürmann, Dense Ellipsoid Packings , Discrete Math., 247 (2002), 243-249. Achill Schürmann, On Parametric Density of Finite Circle Packings , Beiträge Algebra Geom. , 41 (2000), 329-334. Theses Achill Schürmann, Computational Geometry of Positive Definite Quadratic Forms, Habilitationsschrift, University of Magdeburg, 2007. Achill Schürmann, Plane Finite Packings, Dissertation, University of Siegen, 2000; Shaker-Verlag, Aachen, 2000. Achill Schürmann, Dichteste endliche gitterförmige Kreispackungen, Diplom Thesis, University of Siegen, 1997. [ .ps ] [ .ps.gz ] [ .pdf ] Lecture Notes Achill Schürmann, From positive definite quadratic forms to lattice sphere packings and coverings, 2006. [ .ps ] [ .ps.gz ] [ .pdf ] Achill Schürmann, Skript zu Geometrie für ComputervisualistInnen, 2007. [ .ps ] [ .ps.gz ] [ .pdf ] Achill Schürmann, Skript zu Konvexe Polytope, 2003/2004. [ .ps ] [ .ps.gz ] [ .pdf ] Theo Overhagen and Achill Schürmann, Skript zu Optimierung II (Kombinatorische Optimierung und Spieltheorie), 2000. [ .ps ] [ .ps.gz ] [ .pdf ]