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European Mathematical Society Publishing House
2024-03-29 13:35:05
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https://www.ems-ph.org/meta/jmeta-stream.php?jrn=OWR&vol=12&iss=4&update_since=2024-03-29
Oberwolfach Reports
Oberwolfach Rep.
OWR
1660-8933
1660-8941
General
10.4171/OWR
http://www.ems-ph.org/doi/10.4171/OWR
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© Mathematisches Forschungsinstitut Oberwolfach
12
2015
4
Arbeitsgemeinschaft: Mathematical Quasicrystals
Alan
Haynes
University of York, YORK, UNITED KINGDOM
Rodrigo
Treviño
New York University, NEW YORK, UNITED STATES
Barak
Weiss
Tel Aviv University, TEL AVIV, ISRAEL
This introductory workshop encouraged participants to read important recent works in the topology, geometry and dynamics of highly regular (but aperiodic) discrete sets in Euclidean spaces, and their corresponding tiling spaces. These sets have been recently under intensive investigation by researchers in topology, mathematical physics, dynamics, diophantine approximation, and discrete mathematics, and various different perspectives were emphasized.
Convex and discrete geometry
2605
2635
10.4171/OWR/2015/44
http://www.ems-ph.org/doi/10.4171/OWR/2015/44
Computational Geometric and Algebraic Topology
Benjamin
Burton
The University of Queensland, BRISBANE, AUSTRALIA
Herbert
Edelsbrunner
Institute of Science and Technology Austria, KLOSTERNEUBURG, AUSTRIA
Jeff
Erickson
University of Illinois at Urbana-Champaign, URBANA, UNITED STATES
Stephan
Tillmann
University of Sydney, SYDNEY, AUSTRALIA
Computational topology is a young, emerging field of mathematics that seeks out practical algorithmic methods for solving complex and fundamental problems in geometry and topology. It draws on a wide variety of techniques from across pure mathematics (including topology, differential geometry, combinatorics, algebra, and discrete geometry), as well as applied mathematics and theoretical computer science. In turn, solutions to these problems have a wide-ranging impact: already they have enabled significant progress in the core area of geometric topology, introduced new methods in applied mathematics, and yielded new insights into the role that topology has to play in fundamental problems surrounding computational complexity. At least three significant branches have emerged in computational topology: algorithmic 3-manifold and knot theory, persistent homology and surfaces and graph embeddings. These branches have emerged largely independently. However, it is clear that they have much to offer each other. The goal of this workshop was to be the first significant step to bring these three areas together, to share ideas in depth, and to pool our expertise in approaching some of the major open problems in the field.
Combinatorics
Algebraic topology
Manifolds and cell complexes
Statistics
2637
2699
10.4171/OWR/2015/45
http://www.ems-ph.org/doi/10.4171/OWR/2015/45
Mixed-integer Nonlinear Optimization: A Hatchery for Modern Mathematics
Leo
Liberti
Ecole Polytechnique, PALAISEAU CEDEX, FRANCE
Sebastian
Sager
Otto-von-Guericke-Universität, MAGDEBURG, GERMANY
Angelika
Wiegele
Alpen-Adria Universität Klagenfurt, KLAGENFURT, AUSTRIA
The aim of this workshop was fostering the growth of new mathematical ideas arising from mixed-integer nonlinear optimization. In this regard, the workshop has been a resounding success. It has covered a very diverse scientific landscape, including automated proof in computational geometry, the analysis of computational complexity of MINO in fixed and variable dimension, the solution of infinite MINO such as those appearing in mixed-integer optimal control, the theoretical and computational deployment of traditional integer and continuous approaches to achieve new solution algorithms for large-scale MINO, a classification of the most interesting engineering and technology applications of MINO, and more. It has synthesized twenty open questions and challenges which will serve as a roadmap for the years to come.
Operations research, mathematical programming
2701
2766
10.4171/OWR/2015/46
http://www.ems-ph.org/doi/10.4171/OWR/2015/46
History of Mathematics: Models and Visualization in the Mathematical and Physical Sciences
Jeremy
Gray
The Open University, MILTON KEYNES, UNITED KINGDOM
Ulf
Hashagen
Deutsches Museum, MÜNCHEN, GERMANY
Tinne
Hoff Kjeldsen
University of Copenhagen, COPENHAGEN, DENMARK
David
Rowe
Johannes Gutenberg-Universität Mainz, MAINZ, GERMANY
This workshop brought together historians of mathematics and science as well as mathematicians to explore important historical developments connected with models and visual elements in the mathematical and physical sciences. It addressed the larger question of what has been meant by a model, a notion that has seldom been subjected to careful historical study. Most of the talks dealt with case studies from the period 1800 to 1950 that covered a number of analytical, geometrical, mechanical, astronomical, and physical phenomena. The workshop also considered the role of visual thinking as a component of mathematical creativity and understanding.
History and biography
2767
2858
10.4171/OWR/2015/47
http://www.ems-ph.org/doi/10.4171/OWR/2015/47
Mini-Workshop: Friezes
Thorsten
Holm
Leibniz-Universität Hannover, HANNOVER, GERMANY
Peter
Jørgensen
University of Newcastle, NEWCASTLE UPON TYNE, UNITED KINGDOM
Sophie
Morier-Genoud
Université Pierre et Marie Curie - Paris 6, PARIS CEDEX 05, FRANCE
Frieze patterns were introduced in the early 1970s by Coxeter. They are infinite arrays of numbers in which every four neighbouring entries always satisfy the same arithmetic relation. Amazingly, friezes appear in many situations from various areas of mathematics: projective geometry, number theory, algebraic combinatorics, difference equations, integrable systems, representation theory, cluster algebras… The mini-workshop aimed to gather researchers with diverse fields of expertise to present recent developments and to discuss new directions of investigation and open problems around friezes.
Combinatorics
Commutative rings and algebras
Dynamical systems and ergodic theory
Difference and functional equations
2859
2894
10.4171/OWR/2015/48
http://www.ems-ph.org/doi/10.4171/OWR/2015/48
Mini-Workshop: Mathematics of Differential Growth, Morphogenesis, and Pattern Selection
Krishna
Garikipati
University of Michigan, College of Engineering, ANN ARBOR, UNITED STATES
Alain
Goriely
University of Oxford, OXFORD, UNITED KINGDOM
Ellen
Kuhl
Stanford University, STANFORD, UNITED STATES
Andreas
Menzel
Technische Universität Dortmund, DORTMUND, GERMANY
Living structures are highly heterogeneous systems that consist of distinct regions made up of characteristic cell types with a specific structural organization. During evolution, development, disease, or environmental adaptation each region may grow at its own characteristic rate. Differential growth creates a balanced interplay between tension and compression and plays a critical role in biological function. In plant physiology, typical every-day examples include the petioles of celery, caladium, or rhubarb with a slower growing compressive outer surface and a faster growing tensile inner core. In developmental biology, differential growth is critical to the organogenesis of various structures including the gut, the heart, and the brain. From a structural point of view, these phenomena are close associated with instabilities, of twisting, looping, folding, and wrinkling. From a mathematical point of view, the governing equations of organogenesis are highly nonlinear and often characterized through multiple bifurcation points. Bifurcation is critical in symmetry breaking, pattern formation, and selection of shape. While biologists are studying differential growth, morphogenesis, and pattern selection merely by observation, our goal in this workshop is to explore, discuss, and advance the fundamental theory of differential growth to characterize morphogenesis and pattern selection by mathematical modeling. This workshop will bring together scientists with similar interests and complementary backgrounds in applied mathematics, mathematical biology, developmental biology, plant biology, dynamical systems, biophysics, biomechanics, and clinical sciences. We will identify common features of growth phenomena in living systems with the overall objectives to establish a unified mathematical theory for growing systems and to identify the necessary mathematical tools to address challenging questions in biology and medicine.
Biology and other natural sciences
Dynamical systems and ergodic theory
2895
2910
10.4171/OWR/2015/49
http://www.ems-ph.org/doi/10.4171/OWR/2015/49
Mini-Workshop: Recent Developments on Approximation Methods for Controlled Evolution Equations
Birgit
Jacob
Universität Wuppertal, WUPPERTAL, GERMANY
Enrique
Zuazua
Universidad Autónoma de Madrid, MADRID, SPAIN
Hans
Zwart
Universiteit Twente, ENSCHEDE, NETHERLANDS
This mini-workshop brought together mathematicians engaged in partial differential equations, functional analysis, numerical analysis and systems theory in order to address a number of current problems in the approximation of controlled evolution equations.
Systems theory; control
Numerical analysis
2911
2938
10.4171/OWR/2015/50
http://www.ems-ph.org/doi/10.4171/OWR/2015/50
Mini-Workshop: Singular Curves on $K3$ Surfaces and Hyperkähler Manifolds
Concettina
Galati
Università degli Studi della Calabria, ARCAVACATA DI RENDE (COSENZA), ITALY
Andreas
Knutsen
University of Bergen, BERGEN, NORWAY
Alessandra
Sarti
Université de Poitiers, FUTUROSCOPE CHASSENEUIL, FRANCE
The workshop focused on Severi varieties on $K3$ surfaces, hyperkähler manifolds and their automorphisms. The main aim was to bring researchers in deformation theory of curves and singularities together with researchers studying hyperkähler manifolds for mutual learning and interaction, and to discuss recent developments and open problems.
Algebraic geometry
2939
2967
10.4171/OWR/2015/51
http://www.ems-ph.org/doi/10.4171/OWR/2015/51
Mini-Workshop: Recent Developments in Statistical Methods with Applications to Genetics and Genomics
Iuliana
Ionita-Laza
Columbia University, NEW YORK, UNITED STATES
Michael
Krawczak
Christian-Albrechts-Universität zu Kiel, KIEL, GERMANY
Xihong
Lin
Harvard School of Public Health, BOSTON, UNITED STATES
Michael
Nothnagel
Universität zu Köln, KÖLN, GERMANY
Recent progress in high-throughput genomic technologies has revolutionized the field of human genetics and promises to lead to important scientific advances. With new improvements in massively parallel biotechnologies, it is becoming increasingly more efficient to generate vast amounts of information at the genomics, transcriptomics, proteomics, metabolomics etc. levels, opening up as yet unexplored opportunities in the search for the genetic causes of complex traits. Despite this tremendous progress in data generation, it remains very challenging to analyze, integrate and interpret these data. The resulting data are high-dimensional and very sparse, and efficient statistical methods are critical in order to extract the rich information contained in these data. The major focus of the mini-workshop, entitled “Recent Developments in Statistical Methods with Applications to Genetics and Genomics”, has been on integrative methods. Relevant research questions included the optimal study design for integrative genomic analyses; appropriate handling and pre-processing of different types of omics data; statistical methods for integration of multiple types of omics data; adjustment for confounding due to latent factors such as cell or tissue heterogeneity; the optimal use of omics data to enhance or make sense of results identified through genetic studies; and statistical and computational strategies for analysis of multiple types of high-dimensional data.
Statistics
Biology and other natural sciences
2969
3005
10.4171/OWR/2015/52
http://www.ems-ph.org/doi/10.4171/OWR/2015/52
Mini-Workshop: Scales in Plasticity
Gilles
Francfort
Université Paris-Nord, VILLETANEUSE, FRANCE
Stephan
Luckhaus
Universität Leipzig, LEIPZIG, GERMANY
This mini-workshop was devoted to the current state of our understanding of dislocations (essentially slips of lines of atoms in a crystalline solid) and of their impact on the macroscopic behavior of those solids.
Mechanics of deformable solids
Partial differential equations
Calculus of variations and optimal control; optimization
3007
3048
10.4171/OWR/2015/53
http://www.ems-ph.org/doi/10.4171/OWR/2015/53
Complexity Theory
Peter
Bürgisser
Technische Universität Berlin, BERLIN, GERMANY
Oded
Goldreich
Weizmann Institute of Science, REHOVOT, ISRAEL
Madhu
Sudan
The Stata Center, CAMBRIDGE, UNITED STATES
Salil
Vadhan
Harvard University, CAMBRIDGE, UNITED STATES
Computational Complexity Theory is the mathematical study of the intrinsic power and limitations of computational resources like time, space, or randomness. The current workshop focused on recent developments in various sub-areas including arithmetic complexity, Boolean complexity, communication complexity, cryptography, probabilistic proof systems, pseudorandomness and randomness extraction. Many of the developments are related to diverse mathematical fields such as algebraic geometry, combinatorial number theory, probability theory, representation theory, and the theory of error-correcting codes.
Computer science
Information and communication, circuits
3049
3099
10.4171/OWR/2015/54
http://www.ems-ph.org/doi/10.4171/OWR/2015/54
Geometric Partial Differential Equations: Surface and Bulk Processes
Klaus
Deckelnick
Otto-von-Guericke-Universität Magdeburg, MAGDEBURG, GERMANY
Charles
Elliott
University of Warwick, COVENTRY, UNITED KINGDOM
Ralf
Kornhuber
Freie Universität Berlin, BERLIN, GERMANY
James
Sethian
University of California, BERKELEY, UNITED STATES
The workshop brought together experts representing a wide range of topics in geometric partial differential equations ranging from analyis over numerical simulation to real-life applications. The main themes of the conference were the analysis of curvature energies, new developments in pdes on surfaces and the treatment of coupled bulk/surface problems.
Partial differential equations
Calculus of variations and optimal control; optimization
Numerical analysis
3101
3178
10.4171/OWR/2015/55
http://www.ems-ph.org/doi/10.4171/OWR/2015/55
Convex Geometry and its Applications
Franck
Barthe
Université Toulouse III, TOULOUSE CEDEX, FRANCE
Martin
Henk
Technische Universität Berlin, BERLIN, GERMANY
Monika
Ludwig
Technische Universität Wien, WIEN, AUSTRIA
The past 30 years have not only seen substantial progress and lively activity in various areas within convex geometry, e.g., in asymptotic geometric analysis, valuation theory, the $L_p$-Brunn-Minkowski theory and stochastic geometry, but also an increasing amount and variety of applications of convex geometry to other branches of mathematics (and beyond), e.g. to PDEs, statistics, discrete geometry, optimization, or geometric algorithms in computer science. Thus convex geometry is a flourishing and attractive field, which is also reflected by the considerable number of talented young mathematicians at this meeting.
Convex and discrete geometry
Probability theory and stochastic processes
Computer science
3179
3269
10.4171/OWR/2015/56
http://www.ems-ph.org/doi/10.4171/OWR/2015/56
Non-Archimedean Geometry and Applications
Vladimir
Berkovich
Weizmann Institute of Science, REHOVOT, ISRAEL
Walter
Gubler
Universität Regensburg, REGENSBURG, GERMANY
Peter
Schneider
Universität Münster, MÜNSTER, GERMANY
Annette
Werner
Johann Wolfgang Goethe-Universität, FRANKFURT AM MAIN, GERMANY
The workshop focused on recent developments in non-Archimedean analytic geometry with various applications to other fields, in particular to number theory and algebraic geometry. These applications included Mirror Symmetry, the Langlands program, p-adic Hodge theory, tropical geometry, resolution of singularities and the geometry of moduli spaces. Much emphasis was put on making the list of talks to reflect this diversity, thereby fostering the mutual inspiration which comes from such interactions.
Mathematical logic and foundations
Number theory
Algebraic geometry
Several complex variables and analytic spaces
3271
3331
10.4171/OWR/2015/57
http://www.ems-ph.org/doi/10.4171/OWR/2015/57