114 research outputs found
Claude Ambrose Rogers. 1 November 1920 â 5 December 2005
Claude Ambrose Rogers and his identical twin brother, Stephen Clifford, were born in Cambridge in 1920 and came from a long scientific heritage. Their great-great-grandfather, Davies Gilbert, was President of the Royal Society from 1827 to 1830; their father was a Fellow of the Society and distinguished for his work in tropical medicine. After attending boarding school at Berkhamsted with his twin brother from the age of 8 years, Ambrose, who had developed very different scientific interests from those of his father, entered University College London in 1938 to study mathematics. He completed the course in 1940 and graduated in 1941 with first-class honours, by which time the UK had been at war with Germany for two years. He joined the Applied Ballistics Branch of the Ministry of Supply in 1940, where he worked until 1945, apparently on calculations using radar data to direct anti-aircraft fire. However, this did not lead to research interests in applied mathematics, but rather to several areas of pure mathematics. Ambrose's PhD research was at Birkbeck College, London, under the supervision of L. S. Bosanquet and R. G. Cooke, his first paper being on the subject of geometry of numbers. Later, Rogers became known for his very wide interests in mathematics, including not only geometry of numbers but also Hausdorff measures, convexity and analytic sets, as described in this memoir. Ambrose was married in 1952 to Joan North, and they had two daughters, Jane and Petra, to form a happy family
Discrete Geometry
The workshop on Discrete Geometry was attended by 53 participants, many of them young researchers. In 13 survey talks an overview of recent developments in Discrete Geometry was given. These talks were supplemented by 16 shorter talks in the afternoon, an open problem session and two special sessions. Mathematics Subject Classification (2000): 52Cxx. Abstract regular polytopes: recent developments. (Peter McMullen) Counting crossing-free configurations in the plane. (Micha Sharir) Geometry in additive combinatorics. (JoÌzsef Solymosi) Rigid components: geometric problems, combinatorial solutions. (Ileana Streinu) âą Forbidden patterns. (JaÌnos Pach) âą Projected polytopes, Gale diagrams, and polyhedral surfaces. (GuÌnter M. Ziegler) âą What is known about unit cubes? (Chuanming Zong) There were 16 shorter talks in the afternoon, an open problem session chaired by JesuÌs De Loera, and two special sessions: on geometric transversal theory (organized by Eli Goodman) and on a new release of the geometric software Cinderella (JuÌrgen Richter-Gebert). On the one hand, the contributions witnessed the progress the field provided in recent years, on the other hand, they also showed how many basic (and seemingly simple) questions are still far from being resolved. The program left enough time to use the stimulating atmosphere of the Oberwolfach facilities for fruitful interaction between the participants
Concerning the semistability of tensor products in Arakelov geometry
We study the semistability of the tensor product of hermitian vector bundles
by using the -tensor product and the geometric (semi)stability of
vector subspaces in the tensor product of two vector spaces
Uniformizable families of -motives
Abelian -modules and the dual notion of -motives were introduced by
Anderson as a generalization of Drinfeld modules. For such Anderson defined and
studied the important concept of uniformizability. It is an interesting
question, and the main objective of the present article to see how
uniformizability behaves in families. Since uniformizability is an analytic
notion, we have to work with families over a rigid analytic base. We provide
many basic results, and in fact a large part of this article concentrates on
laying foundations for studying the above question. Building on these, we
obtain a generalization of a uniformizability criterion of Anderson and, among
other things, we establish that the locus of uniformizability is Berkovich
open.Comment: 40 pages, v2: Section 7 rewritten; to appear in Trans. Amer. Math.
So
Sphere packings revisited
AbstractIn this paper we survey most of the recent and often surprising results on packings of congruent spheres in d-dimensional spaces of constant curvature. The topics discussed are as follows:âHadwiger numbers of convex bodies and kissing numbers of spheres;âtouching numbers of convex bodies;âNewton numbers of convex bodies;âone-sided Hadwiger and kissing numbers;âcontact graphs of finite packings and the combinatorial Kepler problem;âisoperimetric problems for Voronoi cells, the strong dodecahedral conjecture and the truncated octahedral conjecture;âthe strong Kepler conjecture;âbounds on the density of sphere packings in higher dimensions;âsolidity and uniform stability.Each topic is discussed in details along with some of the âmost wantedâ research problems
Geometrie
The program covered a wide range of new developments in geometry. To name some of them, we mention the topics âMetric space geometry in the style of Alexandrov/Gromovâ, âPolyhedra with prescribed metricâ, âWillmore surfacesâ, âConstant mean curvature surfaces in three-dimensional Lie groupsâ. The official program consisted of 21 lectures and included four lectures by V. Schroeder (ZuÌrich) and S. Buyalo (Sankt-Petersburg) on âAsymptotic geometry of Gromov hyperbolic spacesâ
Discrete Geometry
A number of important recent developments in various branches of discrete geometry were presented at the workshop. The presentations illustrated both the diversity of the area and its strong connections to other fields of mathematics such as topology, combinatorics or algebraic geometry. The open questions abound and many of the results presented were obtained by young researchers, confirming the great vitality of discrete geometry
Convex Geometry and its Applications
The geometry of convex domains in Euclidean space plays a central role in several branches of mathematics: functional and harmonic analysis, the theory of PDE, linear programming and, increasingly, in the study of other algorithms in computer science. High-dimensional geometry, both the discrete and convex branches of it, has experienced a striking series of developments in the past 10 years. Several examples were presented at this meeting, for example the work of Rudelson et al. on conjunction matrices and their relation to conïŹdential data analysis, that of Litvak et al. on remote sensing and a series of results by Nazarov and Ryabogin et al. on Mahlerâs conjecture for the volume product of domains and their polars
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