Jörg Wills

Jörg Wills 2017

Jörg Michael Wills (born March 5, 1937 in Berlin ) is a German mathematician who deals with discrete , convex and combinatorial geometry.

Wills received his doctorate in 1965 under Ernst Max Mohr at the TU Berlin ( two problems of the inhomogeneous Diophantine approximation ). He was professor at the TU Berlin and since 1974 professor at the University of Siegen , in 2002 he retired. He was visiting professor at the Hungarian Academy of Sciences (1982, 1997), the University of Toronto (1986, 1988, 1993), the University of Trieste (1990), the Academia Sinica in Beijing (1994) and the University of Mexico City (1995 ).

1994–2004 he was a member of the Minerva Foundation (Germany-Israel / Max Planck Society).

In 1995 he received the Austrian Cross of Honor for Science and Art 1st Class and in 2003 he received an honorary doctorate from the Vienna University of Technology . In 2002 he received the Golden Badge of Honor from the German Mathematicians Association .

His areas of work are discrete geometry, geometry of numbers (Minkowski-type theorems, grid point problems, zeros of the Ehrhart polynomial), finite spherical packings (sausage sentences, sausage catastrophe, crystal growth, Wulff shape, cluster), Diophantine approximation (view obstruction, lonely runner ), combinatorial geometry (realizations of regular maps, regular and semi-regular polyhedral manifolds).

For some important contributions by Wills and his students to spherical packing, sausage conjecture and sausage catastrophe, see Theory of Finite Spherical Packings . In particular, in 1993 he developed a theory of finite packing of spheres with the introduction of a parametric density that unifies the theory with the classical infinite packing of spheres. The sausage guess was the students of Will Martin Henk and Ulrich Betke to 1998 for dimensions shown after Betke, Henk and Wills in 1994 (J. Reine Angew. Math.) A breakthrough achieved in which they showed that they for dimensions applies . In 1992 he and Pier Maria Gandini showed that in d = 3 for n = 57, 58, 63, 64 and a cluster is denser than the sausage pack. For the other quantities, it is assumed that the sausage pack is denser. The sudden appearance of a denser packing is like a kind of phase transition and is known as a sausage disaster. ${\ displaystyle d \ geq 42}$ ${\ displaystyle d \ geq 13386}$ ${\ displaystyle n \ geq 56}$

In 1967 he formulated the Lonely Runner Conjecture : k runners start at the same time on a circle with circumference 1 at different speeds in pairs. A runner is lonely at some point when his or her minimum distance from the other runners is. It is believed that every runner is lonely at some point. The conjecture is generally unsolved (proved for k <8, of which the case k = 4 was the first by Betke and Wills). The name of the conjecture comes from Luis Goddyn (1998). ${\ displaystyle {\ frac {1} {k}}}$

His doctoral students include Professors Ulrich Betke (University of Siegen), Jürgen Bokowski (TH Darmstadt), Peter Gritzmann (TU Munich), Martin Henk (University of Magdeburg) and Achill Schürmann (University of Rostock).

From 1980 to 1986 he was a member of the Research Institute for the Humanities and Social Sciences and from 1990 to 2014 a member of the editorial team and co-author of DIAGONAL (interdisciplinary journal of the University of Siegen). Various contributions and lectures on mathematics and art come from him.

Fonts

with Peter Gruber (Ed.): Handbook of convex geometry. 2 volumes, North Holland 1993.
with Peter Gruber (Ed.): Convexity and its applications. Birkhäuser 1983.
Editor with Jürgen Tolke: Contributions to geometry, Birkhäuser 1979. (Proceedings Geometry Symposium, Siegen 1978)
with J. Bokowski and Hugo Hadwiger : An inequality between volume, surface and number of grid points of convex bodies in n-dimensional Euclidean space , Math. Zeitschrift, Volume 127, 1972, pp. 363–364
with Peter McMullen and Ch. Schulz: Polyhedral 2-manifolds in with unusual large genus ${\ displaystyle E ^ {3}}$ , Israel J. Math., Volume 46, 1983, pp. 127-144.
with E. Schulte: A polyhedral realization of Felix Klein's map on a Riemann surface of genus 3 ${\ displaystyle (3.7) _ {8}}$ , J. London Math. Soc. (2), Vol. 32, 1985, pp. 539-547.
The combinatorially regular polyhedra of index 2 , Aequationes Math., Volume 34, 1987, pp. 326-330.
with P. Gritzmann: Lattice Points , in: Handbook of Convex Geometry, Vol. A, B, 765-797, North-Holland, Amsterdam 1993.
with U. Betke and M. Henk: Successive-Minima-type inequalities , Discrete Comp. Geometry, Vol. 9, 1993, pp. 165-175.
Finite sphere packings and sphere coverings , Rend. Sem. Mat. Messina, Series 3, Volume 2, 1993, pp. 91-97, pdf
Ball packings - old and new , Mitteilungen DMV, 1995, No. 4, p. 21
Parametric density and Wulff shapes , Mathematika, Volume 43, 1996, pp. 229-236
On large packings of spheres , Geometria Dedicata, Vol. 65, 1997, pp. 117-126
with Peter Gritzmann: Finite packing and covering , in: Gruber, Wills (Ed.) Handbook of Convex Geometry, B, North Holland 1993
with U. Betke, M. Henk: Sausages are good packings , Discrete Comp. Geom., Vol. 13, 1995, pp. 297-311
with U. Betke, M. Henk: Finite and infinite packings , J. Reine and Applied Mathematics, Volume 453, 1994, pp. 165-191, pdf
with Betke, Henk: A new approach to covering , Mathematika, Volume 42, 1995, pp. 251-263
Spheres and sausages, crystal and catastrophes - and a joint packing theory. In: Mathematical Intelligencer. Volume 20, 1998, Issue 1, pp. 16-21.
with M. Henk and A. Schürmann: Ehrhart polynomials and successive minima , Mathematika, Volume 52, 2005, pp. 1–16

Web links

Commons : Jörg Wills (mathematician) - Collection of images, videos and audio files

Homepage
List of PhD students in the Mathematics Genealogy Project
Literature by and about Jörg Wills in the catalog of the German National Library

Individual evidence

^ Pier Mario Gandini, Jörg Michael Wills: On finite sphere packings. In: Math. Pannonica 3, No. 1, 1992, pp. 19-29
↑ Leppmeier, sphere packings of Kepler today. Braunschweig / Wiesbaden 1997, p. 121
↑ U. Betke, J. Wills: Lower bounds for two Diophantine approximation functions ,months booklet for mathematics, volume 76, 1972, p. 214. The cases k = 1,2 are trivial.

personal data
SURNAME	Wills, Jörg
ALTERNATIVE NAMES	Wills, Jörg Michael (full name)
BRIEF DESCRIPTION	German mathematician
DATE OF BIRTH	March 5, 1937
PLACE OF BIRTH	Berlin

[1] Pier Mario Gandini, Jörg Michael Wills: On finite sphere packings. In: Math. Pannonica 3, No. 1, 1992, pp. 19-29

[2] Leppmeier, sphere packings of Kepler today. Braunschweig / Wiesbaden 1997, p. 121

[3] U. Betke, J. Wills: Lower bounds for two Diophantine approximation functions ,months booklet for mathematics, volume 76, 1972, p. 214. The cases k = 1,2 are trivial.