http://publications.mfo.de/handle/mfo/2816 Oberwolfach Reports Volume 12 (2015) Thu, 09 Apr 2026 20:36:13 GMT 2026-04-09T20:36:13Z http://publications.mfo.de/handle/mfo/3504 Non-Archimedean Geometry and Applications 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. Thu, 01 Jan 2015 00:00:00 GMT http://publications.mfo.de/handle/mfo/3504 2015-01-01T00:00:00Z 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. http://publications.mfo.de/handle/mfo/3503 Convex Geometry and its Applications 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. Thu, 01 Jan 2015 00:00:00 GMT http://publications.mfo.de/handle/mfo/3503 2015-01-01T00:00:00Z 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. http://publications.mfo.de/handle/mfo/3502 Geometric Partial Differential Equations: Surface and Bulk Processes 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. Thu, 01 Jan 2015 00:00:00 GMT http://publications.mfo.de/handle/mfo/3502 2015-01-01T00:00:00Z 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. http://publications.mfo.de/handle/mfo/3501 Complexity Theory 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. Thu, 01 Jan 2015 00:00:00 GMT http://publications.mfo.de/handle/mfo/3501 2015-01-01T00:00:00Z 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. http://publications.mfo.de/handle/mfo/3500 Mini-Workshop: Scales in Plasticity 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. Thu, 01 Jan 2015 00:00:00 GMT http://publications.mfo.de/handle/mfo/3500 2015-01-01T00:00:00Z 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. http://publications.mfo.de/handle/mfo/3499 Mini-Workshop: Recent Developments in Statistical Methods with Applications to Genetics and Genomics 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. Thu, 01 Jan 2015 00:00:00 GMT http://publications.mfo.de/handle/mfo/3499 2015-01-01T00:00:00Z 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. http://publications.mfo.de/handle/mfo/3498 Mini-Workshop: Singular Curves on K3 Surfaces and Hyperkähler Manifolds 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. Thu, 01 Jan 2015 00:00:00 GMT http://publications.mfo.de/handle/mfo/3498 2015-01-01T00:00:00Z 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. http://publications.mfo.de/handle/mfo/3497 Mini-Workshop: Recent Developments on Approximation Methods for Controlled Evolution Equations 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. Thu, 01 Jan 2015 00:00:00 GMT http://publications.mfo.de/handle/mfo/3497 2015-01-01T00:00:00Z 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. http://publications.mfo.de/handle/mfo/3496 Mini-Workshop: Mathematics of Differential Growth, Morphogenesis, and Pattern Selection 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. Thu, 01 Jan 2015 00:00:00 GMT http://publications.mfo.de/handle/mfo/3496 2015-01-01T00:00:00Z 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. http://publications.mfo.de/handle/mfo/3495 Mini-Workshop: Friezes 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. Thu, 01 Jan 2015 00:00:00 GMT http://publications.mfo.de/handle/mfo/3495 2015-01-01T00:00:00Z 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.