Oberwolfach Publications (Mathematisches Forschungsinst. Oberwolfach)
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New Perspectives and Computational Challenges in High Dimensions
No full textHigh-dimensional systems are frequent in mathematics and applied sciences, and the understanding of
high-dimensional phenomena has become increasingly important. The mathematical subdisciplines most
strongly related to such phenomena are functional analysis, convex geometry, and probability theory.
In fact, a new area emerged, called asymptotic geometric analysis, which is at the very core of these
disciplines and bears a number of deep connections to mathematical physics, numerical analysis, and
theoretical computer science. The last two decades have seen a tremendous growth in this area. Far
reaching results were obtained and various powerful techniques have been developed, which rather
often have a probabilistic flavor. The purpose of this workshop was to explored these new perspectives, to reach out to other areas concerned with high-dimensional problems, and to bring together researchers having different angles on high-dimensional phenomena
Arithmetic Geometry (hybrid meeting)
No full textArithmetic geometry is at the interface between algebraic geometry and number theory, and studies schemes over the ring of integers of number fields, or their -adic completions, and connects with representation theory, automorphic forms, Hodge theory, algebraic topology, and many other fields
New Directions in Rough Path Theory (online meeting)
No full textRough path theory emerged as novel approach for dealing with interactions
in complex random systems.
It settled significant questions and provided an effective deterministic alternative to Itô
calculus, itself a major contribution to 20 century mathematics.
Its impact has grown substantially in recent years: most prominently, rough paths ideas are at the
core of Martin Hairer's Fields Medal-winning work on regularity structures, but there are also
original and successful applications in other areas.
The workshop focused on three areas that have been strongly influenced by
the core ideas in rough
path theory and which have witnessed considerable activity over the past few years: applications to
data science, algebraic aspects and connections with stochastic analysis
Model Theory: Groups, Geometries and Combinatorics
No full textThe focus of the conference were recent interactions between model theory, group theory and combinatorics in finite geometries. In some cases, in particular in non-archimedean geometry or combinatorics in finite geometries, model theory appeared as tool. In other cases, like in ergodic theory and dynamics or in the theory of stable groups and more general neo-stable algebraic structures like valued fields, the focus was on model theoretic questions and classification results for such structures. In this way, the conference presented the broad range of topics of modern model theory
Quantum symmetry
No full textThe symmetry of objects plays a crucial role in many
branches of mathematics and physics. It allowed, for
example, the early prediction of the existence of new
small particles. “Quantum symmetry” concerns a
generalized notion of symmetry. It is an abstract
way of characterizing the symmetry of a much richer
class of mathematical and physical objects. In this
snapshot we explain how quantum symmetry emerges
as matrix symmetries using a famous example: Mermin’s
magic square. It shows that quantum symmetries
can solve problems that lie beyond the reach of
classical symmetries, showing that quantum symmetries
play a central role in modern mathematics
Quantum symmetry
No full textIn mathematics, symmetry is usually captured using
the formalism of groups. However, the developments
of the past few decades revealed the need to go beyond
groups: to “quantum groups”. We explain the
passage from spaces to quantum spaces, from groups
to quantum groups, and from symmetry to quantum
symmetry, following an analytical approach
Statistics meets Machine Learning
No full textTheory and application go hand in hand in most areas of statistics. In a world flooded with huge amounts of data waiting to be analyzed, classified and transformed into useful outputs, the designing of fast, robust and stable algorithms has never been as important as it is today. On the other hand, irrespective of whether the focus is put on estimation, prediction, classification or other purposes, it is equally crucial to provide clear guarantees that such algorithms have strong theoretical guarantees. Many statisticians, independently of their original research interests, have become increasingly aware of the importance of the numerical needs faced in numerous applications including gene expression profiling, health care, pattern and speech recognition, data security, marketing personalization, natural language processing, to name just a few.
The goal of this workshop is twofold: (a) exchange knowledge on successful algorithmic approaches and discuss some of the existing challenges, and (b) to bring together researchers in statistics and machine learning with the aim of sharing expertise and exploiting possible differences in points of views to obtain a better understanding of some of the common important problems
Mechanics of Materials: Towards Predictive Methods for Kinetics in Plasticity, Fracture, and Damage
No full textThe workshop dealt with current advances of computational methods, mathematics and continuum mechanics directed at thermodynamically consistent
forms of constitutive equations for complex evolutionary phenomena in modern materials such as plasticity, fracture and damage.
The main aspects addressed in presentations and discussions were multiphysical description of new materials, (visco)plasticity, fracture, damage,
structural mechanics, mechanics of materials and dislocation dynamics
Geometric Structures in Group Theory (hybrid meeting)
No full textThe conference focused on the use of geometric methods to study infinite groups and the interplay of group theory with other areas.
One of the central techniques in geometric group theory is to study infinite discrete groups by their actions on nice, suitable spaces.
These spaces often carry an interesting large-scale geometry, such as non-positive curvature or hyperbolicity in the sense of Gromov, or are equipped with
rich geometric or combinatorial structure. From these actions one can investigate structural properties of the groups.
This connection has become very prominent during the last years.
In this context non-discrete topological groups, such as profinite groups or locally
compact groups appear quite naturally. Likewise, analytic methods and operator theory play an increasing role in the area
Mini-Workshop: Superpotentials in Algebra and Geometry
No full textMirror symmetry has been at the epicenter of many mathematical discoveries in the past twenty years.
It was discovered by physicists in the setting of super conformal field theories (SCFTs) associated to closed string theory, mathematically described by -models.
These -models turn out in two different ways: the A-model and the B-model.
Physical considerations predict that deformations of the SCFT of either -model should be isomorphic.
Thus the mirror symmetry conjecture states that the A-model of a particular Calabi-Yau space must be isomorphic to the B-model of its mirror .
Mirror symmetry has been extended beyond the Calabi-Yau setting, in particular to Fano varieties, using the so called Landau-Ginzburg models. That is a non-compact manifold equipped with a complex valued function called the \emph{superpotential}.
In general, there is no clear recipe to construct the mirror for a given variety which demonstrates the need of joining mathematical forces from a wide range.
The main aim of this Mini-Workshop was to bring together experts from the different communities (such as symplectic geometry and topology, the theory of cluster varieties, Lie theory and algebraic combinatorics) and to share the state of the art on superpotentials and explore connections between different constructions