Oberwolfach Publications (Mathematisches Forschungsinst. Oberwolfach)
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2063 research outputs found
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Convex Geometry and its Applications (hybrid meeting)
No full textThe geometry of convex domains in Euclidean space plays a central role
in several branches of mathematics: functional and harmonic analysis, the
theory of PDE, linear programming and, increasingly, in the study of
algorithms in computer science.
The purpose
of this meeting was to bring together researchers from the analytic, geometric and probabilistic
groups who have contributed to these developments
Boundary Conditions for Scalar Curvature
No full textBased on the Atiyah-Patodi-Singer index formula, we construct an obstruction to positive scalar curvature metrics with mean convex boundaries on spin manifolds of infinite -area. We also characterize the extremal case. Next we show a general deformation principle for boundary conditions of metrics with lower scalar curvature bounds. This implies that the relaxation of boundary conditions often induces weak homotopy equivalences of spaces of such metrics. This can be used to refine the smoothing of codimension-one singularites à la Miao and the deformation of boundary conditions à la Brendle-Marques-Neves, among others. Finally, we construct compact manifolds for which the spaces of positive scalar curvature metrics with mean convex boundaries have nontrivial higher homotopy groups
Numerical Methods for Fully Nonlinear and Related PDEs (hybrid meeting)
No full textThe aim of this workshop was to discuss the challenges, latest trends and advancements on numerical methods
for fully nonlinear PDEs. The construction of numerical schemes and their convergence analysis is still an emerging field
in computational mathematics with several fundamental open problems. Nonetheless, significant breakthroughs have recently appeared, including
the design of accurate finite element schemes for non-variational problems, a priori error estimates for monotone schemes,
and the construction of high-order and adaptive methods
Algebraic Groups (hybrid meeting)
No full textLinear algebraic groups is an active research area in contempo-
rary mathematics. It has rich connections to algebraic geometry, representa-
tion theory, algebraic combinatorics, number theory, algebraic topology, and
differential equations. The foundations of this theory were laid by A. Borel,
C. Chevalley, J.-P. Serre, T. A. Springer and J. Tits in the second half of
the 20th century. The Oberwolfach workshops on algebraic groups, led by
Springer and Tits, played an important role in this effort as a forum for re-
searchers, meeting at approximately 3 year intervals since the 1960s. The
present workshop continued this tradition, covering a range of topics, with
an emphasis on recent developments in the subject
Mini-Workshop: Non-semisimple Tensor Categories and Their Semisimplification (online meeting)
No full textFinite tensor categories are, despite their
many applications and great interest, notoriously hard to classify.
Among them, the semisimple ones (called fusion categories) have been intensively studied.
Those with non-integral dimensions form a remarkable class.
Already more than 20 years ago, tilting modules
have been proposed as a source of such fusion categories. In this way,
the Verlinde categories associated to the pair of a simple complex
Lie algebra and an integer level have been recovered
in a purely algebraic framework - called semisimplification of tensor categories.
Recently efforts to understand how to go beyond these examples emerged.
This mini-workshop aims at bringing together experts
from various branches of representation theory and topological
field theory to deepen our understanding of finite tensor categories and to
compare new ways to understand semisimplification
Homogenization Theory: Periodic and Beyond (online meeting)
No full textThe objective of the workshop has been to review the latest developments in homogenization theory for a large category of equations and settings arising in the modeling of solid, fluids, wave propagation, heterogeneous media, etc. The topics approached have covered periodic and nonperiodic deterministic homogenization, stochastic homogenization, regularity theory, derivation of wall laws and detailed study of boundary layers,..
Spaces of Riemannian metrics
No full textLas métricas riemannianas dan a las variedades suaves, como las superficies, propiedades geométricas intrínsecas, por ejemplo la curvatura. También permiten medir cantidades como distancias, ángulos y volúmenes. Estas son las nociones que utilizamos para caracterizar la "forma'' de una variedad. El espacio de métricas riemannianas de una variedad suave es un objeto matemático que codifica las posibles maneras en las que podemos deformar geométricamente la forma de la variedad
Enumerative Geometry of Surfaces (hybrid meeting)
No full textThe recent developments in hyperbolic geometry and flat geometry in real dimension formed the core of the workshop, with an emphasis on enumerative aspects. A particularly important role in this regard was played by intersection-theoretic techniques on , the geometry of the strata of differentials, the geometry of Hurwitz spaces, topological recursion techniques, and large genus asymptotics. The workshop included an exploration of relations with similar problems in complex dimension , tropical techniques for enumerative problems, and relations to mathematical physics
Positive Scalar Curvature and Applications
No full textIntroducimos la idea de curvatura, incluyendo su desarrollo histórico, y nos enfocamos en la curvatura escalar de una variedad. Uno de los temas principales de investigación actual es entender la curvatura escalar positiva. Discutiremos por qué es interesante y su relación con la teoría general de la relatividad
Mini-Workshop: Mathematics of Dissipation – Dynamics, Data and Control (hybrid meeting)
No full textDissipation of energy --- as well as its sibling the increase of entropy --- are fundamental facts inherent to any physical system.
The concept of dissipativity has been extended to a more general system theoretic setting via port-Hamiltonian systems and this framework is a driver of innovations in many of areas of science and technology. The particular strength of the approach lies in the modularity of modeling, the strong geometric, analytic and algebraic properties and the very good approximation properties