Oberwolfach Publications (Mathematisches Forschungsinst. Oberwolfach)
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2063 research outputs found
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Regularization by Noise: Theoretical Foundations, Numerical Methods and Applications
No full textThe regularizing effects of noisy perturbations of differential equations is a central
subject of stochastic analysis. Recent breakthroughs initiated a new wave of
interest, particularly concerning non-Markovian, infinite dimensional, and rough-stochastic/Young-stochastic hybrid systems. The mini-workshop aimed to build on
these developments by bringing together young researchers in the field. Particular
emphasis was given to the connection to numerical stochastic analysis, aiming to put
the regularizing effects of the noise into quantitative numeric use
Combinatorics, Probability and Computing
No full textThe main theme of this workshop was the use of probabilistic methods in combinatorics and theoretical computer science. This area is evolving extremely quickly, with the introduction of powerful new methods and the development of increasingly sophisticated techniques, and there have been a number of very significant breakthroughs in the area in recent years. The workshop emphasized several of these recent breakthroughs, which include applications of probabilistic techniques to extremal questions, and of combinatorial techniques to areas of discrete probability theory, such as random matrices and planar percolation
Mini-Workshop: Quantization of Complex Symplectic Varieties
No full textThe mini-workshop featured two main series of lectures:
"Functoriality in non-abelian Hodge theory" by
Tony Pantev, and
"Quantization of the Hitchin system and the analytic Langlands program"
by Jörg Teschner. In addition, four senior mathematicians and
physicists gave two talks each on their recent mysterious discoveries
related to the theme of the workshop. Three junior mathematicians
also gave a talk based on their fresh results. All talks by mathematicians and physicists were coordinated
to form a common ground of understanding. The smallness of the
size of workshop promoted deeper discussions and helped to create friendly and inclusive
atmosphere
New Mathematical Techniques in Information Theory
No full textInformation theory is the richer for a surge of recent
advances in relevant mathematical techniques.
The workshop fostered an exchange of ideas on new
mathematical tools which are typically outside the classical
toolbox of information theorists and that are yet useful in solving
classical and modern problems in information theory and related
areas. The focus was on
mathematical techniques that are of a general nature and that could benefit a
wide class of problems. A number of broad mathematical areas were identified
that held promise with established early successes, and key contributors
were invited to make presentations and initiate discussions
with an emphasis on emergent topics. The areas were:
information measures, measure concentration, hypercontractivity and
correlation measures, Shannon theory and extremal combinatorics,
advanced tools for proving converse results in coding theorems, and
recent techniques for proving Gaussian optimality entailing new
characterizations of Gaussian distributions
C*-Algebras
No full textOperator algebras form a very active area of mathematics which, since its inception in the 1940s, has always been driven by interactions with other fields of mathematics and physics. The scope of these interactions is very wide, ranging over dynamical systems, (non-commutative) geometry, functional analysis, (geometric) group theory, topology, random matrices, harmonic analysis and quantum information theory.
The goals of this workshop were to stimulate new collaborations across these fields of mathematics, to disseminate recent progress by giving participants a global view on the subject and to specially focus on two important developments: the solution of the Connes embedding problem by methods from quantum information theory and the progress on noncommutative dynamical systems, especially in the topological C-algebra context
Charakterisierungen von inneren Volumina auf konvexen Körpern und konvexen Funktionen
No full textIf we want to express the size of a two-dimensional shape with a number, then we usually think about its area or circumference. But what makes these quantities so special? We give an answer to this question in terms of classical mathematical results. We also take a look at applications and new generalizations to the setting of functions.[Also available in German
Interactions between Algebraic Geometry and Noncommutative Algebra
No full textThis workshop was on the interactions between
noncommutative algebra, representation theory and algebraic geometry. The major objective was to
bring together researchers from those areas with the focus on topics and problems where geometric methods are prevalent
Re-thinking High-dimensional Mathematical Statistics
No full textThe workshop highlighted recent theoretical advances on inference in high-dimensional statistical models based on the interplay of techniques from mathematical statistics, machine learning, theoretical computer science and related areas. The workshop brought together about 50 researchers in order to present new results, exchange ideas and explore open problems
Non-Archimedean Geometry and Applications
No full textThe workshop focused on recent developments in non-Archime-dean analytic geometry with various applications to other fields. The topics of the talks included foundational results on analytic spaces as well as applications to the local Langlands conjecture, birational geometry,
p-adic cohomology theories, Shimura varieties and the non-Archimedean Simpson correspondence
Conic Linear Optimization for Computer-Assisted Proofs
No full textFrom a mathematical perspective, optimization is the science of
proving inequalities. In this sense, computational optimization is a
method for computer-assisted proofs.
Conic (linear) optimization is the problem of minimizing a linear
functional over the intersection of a convex cone with an affine
subspace of a topological vector space. For many cones this problem
is computationally tractable, and as a result there is a growing
number of computer-assisted proofs using conic optimization in
discrete geometry, (extremal) graph theory, numerical analysis, and
other fields, the most famous example perhaps being the proof of the
Kepler Conjecture.
The aim of this workshop was to bring researchers from these diverse
fields together to work towards expanding the current scope of conic
optimization as a method of generating proofs, and to identify
problems and challenges to work on together