Oberwolfach Publications (Mathematisches Forschungsinst. Oberwolfach)
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2063 research outputs found
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Mathematical Aspects of General Relativity (hybrid meeting)
No full textGeneral relativity is an area that naturally combines differential geometry, partial differential
equations, global analysis and dynamical systems with astrophysics, cosmology, high energy physics, and numerical
analysis. It is rapidly expanding and has witnessed remarkable developments in recent years
Partial Differential Equations (hybrid meeting)
No full textThe workshop covered topics in nonlinear elliptic and parabolic Partial Differential Equations as well as topics in Geometric Measure Theory, touching topics such as geometric variational problems and minimal surfaces, geometric flows, free boundaries and the structure of nodal sets of eigenfunctions as well as real and complex Monge-Amp\`ere equations
Arbeitsgemeinschaft: Thin Groups and Super-approximation (hybrid meeting)
No full textThe aim of this workshop was to discuss the super-approximation of thin groups, its dynamical implications in terms of the mixing
of geodesic flows, and applications to various problems in arithmetic, geometry, and dynamics
Enveloping Algebras and Geometric Representation Theory (hybrid meeting)
No full textThe workshop brought together experts investigating algebraic Lie theory from the geometric and categorical viewpoints
Complexity Theory (hybrid meeting)
No full textComputational 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
interactive proof systems, quantum information and computation, algorithmic coding theory,
arithmetic complexity, expansion of hypergraphs and simplicial complexes, Markov chain Monte Carlo,
and pseudorandomness.
Many of the developments are related to diverse mathematical fields
such as algebraic geometry, extremal combinatorics, combinatorial number theory,
probability theory, representation theory,
and operator algebras
Applied Harmonic Analysis and Data Science (hybrid meeting)
No full textData science has become a field of major importance for science and technology
nowadays and poses a large variety of
challenging mathematical questions.
The area
of applied harmonic analysis has a significant impact on such problems by providing methodologies
both for theoretical questions and for a wide range of applications
in signal and image processing and machine learning.
Building on the success of three previous workshops on applied harmonic analysis in 2012, 2015 and 2018,
this workshop focused
on several exciting novel directions such as mathematical theory of
deep learning, but also reported progress on long-standing open problems in the field
Mini-Workshop: Variable Curvature Bounds, Analysis and Topology on Dirichlet Spaces (hybrid meeting)
No full textA Dirichlet form is a densely defined bilinear form on a Hilbert space of the form , subject to some additional properties, which make sure that can be considered as a natural abstraction of the usual Dirichlet energy on a domain in . The main strength of this theory, however, is that it allows also to treat nonlocal situations such as energy forms on graphs simultaneously. In typical applications, is a metrizable space, and the theory of Dirichlet forms makes it possible to define notions such as curvature bounds on (although need not be a Riemannian manifold), and also to obtain topological information on in terms of such geometric information
Lagrangian mean curvature flow
No full textLagrangian mean curvature flow is a powerful tool in modern mathematics with connections to topics in analysis, geometry, topology and mathematical physics. I will describe some of the key aspects of Lagrangian mean curvature flow, some recent progress, and some major open problems
Automorphic Forms, Geometry and Arithmetic (hybrid meeting)
No full textThe workshop on automorphic forms, geometry and arithmetic focused on important recent developments
within the research area, in particular, on the different recent approaches
towards the Langlands functoriality principle and the Langlands
correspondence, on their relative analogues, and on the relations between
those advances and more arithmetic questions
Amorphic Complexity of Group Actions with Applications to Quasicrystals
No full textIn this article, we define amorphic complexity for actions of locally compact -compact amenable groups on compact metric spaces. Amorphic complexity, originally introduced for -actions, is a topological invariant which measures the complexity of dynamical systems in the regime of zero entropy. We show that it is tailor-made to study strictly ergodic group actions with discrete spectrum and continuous eigenfunctions. This class of actions includes, in particular, Delone dynamical systems related to regular model sets obtained via Meyer's cut and project method. We provide sharp upper bounds on amorphic complexity of such systems. In doing so, we observe an intimate relationship between amorphic complexity and fractal geometry