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This volume contains 17 surveys that cover many recent developments
in Discrete Geometry and related fields. Besides presenting the
state-of-the-art of classical research subjects like packing and
covering, it also offers an introduction to new topological,
algebraic and computational methods in this very active research
field. The readers will find a variety of modern topics and many
fascinating open problems that may serve as starting points for
research.
This volume presents easy-to-understand yet surprising properties
obtained using topological, geometric and graph theoretic tools in
the areas covered by the Geometry Conference that took place in
Mulhouse, France from September 7-11, 2014 in honour of Tudor
Zamfirescu on the occasion of his 70th anniversary. The
contributions address subjects in convexity and discrete geometry,
in distance geometry or with geometrical flavor in combinatorics,
graph theory or non-linear analysis. Written by top experts, these
papers highlight the close connections between these fields, as
well as ties to other domains of geometry and their reciprocal
influence. They offer an overview on recent developments in
geometry and its border with discrete mathematics, and provide
answers to several open questions. The volume addresses a large
audience in mathematics, including researchers and graduate
students interested in geometry and geometrical problems.
Szemeredi's influence on today's mathematics, especially in
combinatorics, additive number theory, and theoretical computer
science, is enormous. This volume is a celebration of Szemeredi's
achievements and personality, on the occasion of his seventieth
birthday. It exemplifies his extraordinary vision and unique way of
thinking. A number of colleagues and friends, all top authorities
in their fields, have contributed their latest research papers to
this volume. The topics include extension and applications of the
regularity lemma, the existence of k-term arithmetic progressions
in various subsets of the integers, extremal problems in
hypergraphs theory, and random graphs, all of them beautiful,
Szemeredi type mathematics. It also contains published accounts of
the first two, very original and highly successful Polymath
projects, one led by Tim Gowers and the other by Terry Tao.
This volume presents easy-to-understand yet surprising properties
obtained using topological, geometric and graph theoretic tools in
the areas covered by the Geometry Conference that took place in
Mulhouse, France from September 7-11, 2014 in honour of Tudor
Zamfirescu on the occasion of his 70th anniversary. The
contributions address subjects in convexity and discrete geometry,
in distance geometry or with geometrical flavor in combinatorics,
graph theory or non-linear analysis. Written by top experts, these
papers highlight the close connections between these fields, as
well as ties to other domains of geometry and their reciprocal
influence. They offer an overview on recent developments in
geometry and its border with discrete mathematics, and provide
answers to several open questions. The volume addresses a large
audience in mathematics, including researchers and graduate
students interested in geometry and geometrical problems.
This volume collects together research and survey papers written by
invited speakers of the conference celebrating the 70th birthday of
Laszlo Lovasz. The topics covered include classical subjects such
as extremal graph theory, coding theory, design theory,
applications of linear algebra and combinatorial optimization, as
well as recent trends such as extensions of graph limits, online or
statistical versions of classical combinatorial problems, and new
methods of derandomization. Laszlo Lovasz is one of the pioneers in
the interplay between discrete and continuous mathematics, and is a
master at establishing unexpected connections, "building bridges"
between seemingly distant fields. His invariably elegant and
powerful ideas have produced new subfields in many areas, and his
outstanding scientific work has defined and shaped many research
directions in the last 50 years. The 14 contributions presented in
this volume, all of which are connected to Laszlo Lovasz's areas of
research, offer an excellent overview of the state of the art of
combinatorics and related topics and will be of interest to
experienced specialists as well as young researchers.
This volume collects together research and survey papers written by
invited speakers of the conference celebrating the 70th birthday of
Laszlo Lovasz. The topics covered include classical subjects such
as extremal graph theory, coding theory, design theory,
applications of linear algebra and combinatorial optimization, as
well as recent trends such as extensions of graph limits, online or
statistical versions of classical combinatorial problems, and new
methods of derandomization. Laszlo Lovasz is one of the pioneers in
the interplay between discrete and continuous mathematics, and is a
master at establishing unexpected connections, "building bridges"
between seemingly distant fields. His invariably elegant and
powerful ideas have produced new subfields in many areas, and his
outstanding scientific work has defined and shaped many research
directions in the last 50 years. The 14 contributions presented in
this volume, all of which are connected to Laszlo Lovasz's areas of
research, offer an excellent overview of the state of the art of
combinatorics and related topics and will be of interest to
experienced specialists as well as young researchers.
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