Oberwolfach Publications (Mathematisches Forschungsinst. Oberwolfach)
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2063 research outputs found
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Differential Equations arising from Organising Principles in Biology
No full textThis workshop brought together experts in modeling and analysis of organising principles of multiscale biological systems such as cell assemblies, tissues and populations. We focused on questions arising in systems biology and medicine which are related to emergence, function and control of spatial and inter-individual heterogeneity in population dynamics. There were three main areas represented of differential equation models in mathematical biology. The first area involved the mathematical description of structured populations. The second area concerned invasion, pattern formation and collective dynamics. The third area treated the evolution and adaptation of populations, following the Darwinian paradigm. These problems led to differential equations, which frequently are non-trivial extensions of classical problems. The examples included but were not limited to transport-type equations with nonlocal boundary conditions, mixed ODE-reaction-diffusion models, nonlocal diffusion and cross-diffusion problems or kinetic equations
The Algebraic Statistics of an Oberwolfach Workshop
No full textAlgebraic Statistics builds on the idea that statistical
models can be understood via polynomials. Many
statistical models are parameterized by polynomials
in the model parameters; others are described implicitly
by polynomial equalities and inequalities. We explore
the connection between algebra and statistics
for some small statistical models
On the Gauss Algebra of Toric Algebras
No full textLet be a -subalgebra of the polynomial ring of dimension , generated by finitely many monomials of degree . Then the Gauss algebra of is generated by monomials of degree in . We describe the generators and the structure of , when is a Borel fixed algebra, a squarefree Veronese algebra, generated in degree , or the edge ring of a bipartite graph with at least one loop. For a bipartite graph with one loop, the embedding dimension of is bounded by the complexity of the graph
Calculus of Variations
No full textThe Calculus of Variations is at once a classical subject, and a very modern one. Its scope encompasses a broad range of topics in geometric analysis, and deep questions about PDE. New frontiers are constantly emerging, where problems from mechanics, physics, and other applications introduce new challenges. The 2018 Calculus of Variations workshop reflected this breadth and diversity
Categorical Linearly Ordered Structures
No full textWe prove that for every computable limit ordinal there exists a computable linear ordering which is -categorical and is smallest such, but nonetheless for every isomorphic computable copy of there exists a such that . This answers a question left open in the earlier work of Downey, Igusa, and Melnikov. We also show that such examples can be found among ordered abelian groups and real-closed fields
Arbeitsgemeinschaft: Rigidity of Stationary Measure
No full textThe aim of this Arbeitsgemeinschaft was to understand the classification of stationary measures for semisimple random walks on a finite volume homogeneous space and its applications as described in the two papers [1] and [2]
The codimension
No full textIn this snapshot we discuss the notion of codimension,
which is, in a sense, “dual” to the notion of dimension
and is useful when studying the relative position of
one object insider another one
Mini-Workshop: Entropy, Information and Control
No full textThis mini-workshop was motivated by the emerging field of networked control, which combines concepts from the disciplines of control theory, information theory and dynamical systems. Many current approaches to networked control simplify one or more of these three aspects, for instance by assuming no dynamical disturbances, or noiseless communication channels, or linear dynamics. The aim of this meeting was to approach a common understanding of the relevant results and techniques from each discipline in order to study the major, multi-disciplinary problems in networked control
Enveloping Algebras and Geometric Representation Theory
No full textThe workshop brought together experts investigating algebraic Lie theory from the geometric and categorical viewpoints
Geometric Methods of Complex Analysis
No full textThe purpose of this workshop was to discuss recent results in Several Complex Variables, Complex Geometry and Complex Dynamical Systems with a special focus on the exchange of ideas and methods among these areas. The main topics of the workshop included Holomorphic Dynamics and Foliations; L2 -methods and Cohomologies; Plurisubharmonic Functions and Pluripotential Theory; Singular Metrics on Vector Bundles, Chern Forms and Residue Currents; Geometric Questions of Complex Analysis (including Uniformization, Polynomial Convexity, Levi-flat Surfaces etc.)