Oberwolfach Publications (Mathematisches Forschungsinst. Oberwolfach)
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2063 research outputs found
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Mini-Workshop: Analysis of Data-driven Optimal Control (hybrid meeting)
No full textThis hybrid mini-workshop discussed recent mathematical methods for analyzing the opportunities and limitations of data-driven and machine-learning approaches to optimal feedback control. The analysis concerned all aspects of such approaches, ranging from approximation theory particularly for high-dimensional problems via complexity analysis of algorithms to robustness issues
Describing distance: from the plane to spectral triples
No full textGeometry draws its power from the abstract structures that govern the shapes found in the real world. These abstractions often provide deeper insights into the underlying mathematical objects. In this snapshot, we give a glimpse into how certain “curved spaces” called manifolds can be better understood by looking at the (complex) differentiable functions they admit
Diophantine Approximation in Metric Space
No full textDiophantine approximation is traditionally the study of how well real numbers are approximated by rationals. We propose a model for studying Diophantine approximation in an arbitrary totally bounded metric space where the rationals are replaced with a countable hierarchy of “well-spread” points, which we refer to as . We prove various Jarník–Besicovitch type dimension bounds and investigate their sharpnes
Arbeitsgemeinschaft: Derived Galois Deformation Rings and Cohomology of Arithmetic Groups (hybrid meeting)
No full textThe purpose of the workshop was to study derived generalizations of Mazur's deformation ring of Galois representations,
and the relationship of such a derived deformation ring to the homology of arithmetic groups
Geometry, Dynamics and Spectrum of Operators on Discrete Spaces (online meeting)
No full textSpectral theory is a gateway to fundamental insights in geometry and mathematical physics. In recent years the study of spectral problems in discrete spaces has gained enormous momentum. While there are some relations to continuum spaces, fascinating new phenomena have been discovered in the discrete setting throughout the last decade. The goal of the workshop was to bring together experts reporting about the recent developments in a broad variety of dynamical or geometric models and to
reveal new connections and research directions
Mini-Workshop: Three Facets of R-Matrices (hybrid meeting)
No full textBy definition, an -matrix with spectral parameter is a solution to the
Yang-Baxter equation, introduced in the 1970's by C.N. Yang
and R.J. Baxter. Such a matrix encodes the Boltzmann weights
of a lattice model of statistical mechanics, and the
Yang-Baxter equation appears naturally as a sufficient
condition for its solvability.
In the last decade, several mathematical and physical
theories have led to seemingly different constructions of -matrices.
The theme of this workshop was the interaction of three such approaches,
each of which has independently proven to be valuable:
the geometric, analytic and gauge-theoretic
constructions of -matrices.
Its aim was to bring together leading experts and researchers from each school of thought,
whose recent works have given novel interpretations to
this nearly classical topic
MFO-RIMS Tandem Workshop: Symmetries on Polynomial Ideals and Varieties (hybrid meeting)
No full textThe study of symmetry as a structural property of algebraic objects is one of the fundamental pillows of the developments of modern mathematics, most prominently beginning with the work of Abel and Galois. The focus of the workshop was on permutation actions of the symmetric group on polynomial rings and algebraic and semi-algebraic sets. More concretely, it was centered around recent developments in the asymptotic setup of symmetric ideals in the polynomial ring in infinitely many variables
Classical Algebraic Geometry (hybrid meeting)
No full textProgress in algebraic geometry often comes through the introduction of new tools and ideas to tackle the classical problems in the development of the field. Examples include new invariants that capture some aspect of geometry in a novel way, such as the derived category, and the extension of the class of geometric objects considered to allow constructions not previously
possible, such as the transition from varieties to schemes or from schemes to
stacks. Many famous old problems and outstanding conjectures have been
resolved in this way over the last 50 years. While the new theories are sometimes studied for their own sake, they are in the end best understood in the
context of the classical questions they illuminate. The goal of the workshop
was to study new developments in algebraic geometry, with a view toward
their application to the classical problems
Geometry and Optimization in Quantum Information (hybrid meeting)
No full textQuantum information theory seeks to understand the fundamental limits set by quantum mechanics for information processing tasks.
The mathematical aspects of quantum information rely on tools from various fields including mathematical optimization, high-dimensional convex geometry, operator algebras and representation theory.
The goal of this meeting is to focus on the mathematical aspects connecting geometry, optimization and quantum information theory and develop new tools to solve some of the open problems at the intersection of these fields
-algebras: structure and classification
No full textThe theory of -algebras traces its origins back to
the development of quantum mechanics and it has
evolved into a large and highly active field of mathematics.
Much of the progress over the last couple
of decades has been driven by an ambitious program
of classification launched by George A. Elliott in the
1980s, and just recently this project has succeeded
in achieving one of its central goals in an unexpectedly
dramatic fashion. This Snapshot aims to recount
some of the fundamental ideas at play