Oberwolfach Publications (Mathematisches Forschungsinst. Oberwolfach)
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2063 research outputs found
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Hochschild (Co)Homology and Applications
No full textIn 1945 Gerhard Hochschild published "On the cohomology groups of
an associative algebra" in the "Annals of Mathematics" and
thereby created what is now called Hochschild theory. The subject not
only provides interesting homological invariants; it also serves as a
link connecting algebra, topology, and geometry. The focus of the
meeting was on recent developments, for instance in the study of
singularities, deformations, and representations
Complexity Theory
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
fine-grained complexity, algorithmic fairness, pseudorandomness, cryptography, arithmetic complexity, Markov Chain Monte Carlo, structure vs. randomness in combinatorics and complexity, meta-complexity, and the complexity of approximation problems.
Many of the developments are related to diverse mathematical fields
such as algebra, geometry, combinatorics, analysis, and coding theory
Geometrie
No full textThe workshop Geometrie, organized by Aaron Naber (Evanston), André Neves (Chicago), Eleonora Di Nezza (Paris), and Burkhard Wilking (Münster), was well attended with over 45 participants whose interests covered a considerable part of the current research in Differential Geometry. We had talks in such diverse subjects as geometric evolution equations, Kähler geometry, minimal surfaces, RCD spaces, hyperbolic metrics, or scalar curvature metrics
Mini-Workshop: Artin Groups meet Triangulated Categories
No full textArtin and Coxeter groups are naturally occurring generalisations of the braid and symmetric groups respectively. However, unlike for Coxeter groups, many basic group theoretic questions remain unanswered for general Artin groups - most notably the -conjecture for Artin groups remains open except for certain special families of Artin groups. Recently, Artin groups have also appeared as groups acting on triangulated categories, where the associated spaces of Bridgeland's stability conditions provide new realisations of the corresponding spaces. The aim of the workshop is to bring together experts and early career researchers from two seemingly different areas of research: (i) geometric and combinatorial group theory and topology, and (ii) triangulated categories and stability conditions, to explore their intersection via the -conjecture
Diameter and Connectivity of Finite Simple Graphs II
No full textLet be a finite simple non-complete connected graph on and its vertex connectivity. Let denote the number of free vertices of and the diameter of . The final goal of this paper is to determine all sequences of integers with , , and for which there exists a finite simple non-complete connected graph on with , and .The present paper was completed while the authors stayed at Mathematisches Forschungsinstitut in Oberwolfach, August 18 to 30, 2024, in the frame of the Oberwolfach Research Fellows. Sara Saeedi Madani was in part supported by a grant from IPM (No. 1403130020)
Discrete Geometry
No full textA number of important recent developments in various branches of
discrete geometry were presented at the workshop. The presentations
illustrated both the diversity of the area and its strong connections
to other fields of mathematics such as convex geometry, combinatorics,
or topology. Two open problem sessions highlighted the abundance of
open questions and many of the results presented were obtained by
young researchers, confirming the vitality of the field
Local Existence and Conditional Regularity for the Navier-Stokes-Fourier System Driven by Inhomogeneous Boundary Conditions
No full textWe consider the Navier–Stokes–Fourier system with general inhomogeneous Dirichlet–Neumann boundary conditions. We propose a new approach to the local well-posedness problem based on conditional regularity estimates. By conditional regularity we mean that any strong solution belonging to a suitable class remains regular as long as its amplitude remains bounded. The result holds for general Dirichlet-Neumann boundary conditions provided the material derivative of the velocity field vanishes on the boundary of the physical domain. As a corollary of this result we obtain: Blow up criteria for strong solutions; Local existence of strong solutions in the optimal Lp - Lq framework; Alternative proof of the existing results on local well posedness.∗The work of A.A. is performed under the auspices of the Italian National Group of the Mathematical Physics (GNFM)
of INdAM.
†The work of D.B. was supported by the PRIN project 2022 “Partial differential equations and related geometric-functional
inequalities”, financially supported by the EU, in the framework of the “Next Generation EU initiative”. The Department
of Mathematics of Politecnico di Milano is supported by MUR “Excellence Department 2023-2027”.
‡The work of N.C. was supported by the “Excellence Initiative Research University (IDUB)” program at the University
of Warsaw.
§The work of E.F. was partially supported by the Czech Sciences Foundation (GAˇCR), Grant Agreement 24–11034S. The
Institute of Mathematics of the Academy of Sciences of the Czech Republic is supported by RVO:67985840. E.F. is member
of the Neˇcas Center for Mathematical Modelling.Acknowledgement: This work was done while the authors were participating in the Oberwolfach Research Fellows Program at Mathematisches Forschungsinstitut Oberwolfach. They warmly thank the Institute for its kind hospitality and the excellent research environment it provided
Statistical Physics and Random Surfaces
No full textThis conference featured a diverse group of participants, from various career stages, to study problems in several hot topics that have grown increasingly prominent and interrelated in recent years. These included the following:
(1) random surface models (Liouville quantum gravity, random planar maps, etc.)
(2) random curve models (Schramm-Loewner evolution, conformal loop ensembles, etc.)
(3) gauge theory models (various forms of lattice Yang-Mills, other approximations)
(4) spin models and height functions (including delocalization problems)
(5) dimer models (two and higher dimensions versions)
(6) conformal field theory (Liouville theory, other theories related to SLE)
The conference enabled participants to communicate about the most recent break-throughs and lay the groundwork for further collaborative progress
Constrained Dynamics, Stochastic Numerical Methods and the Modeling of Complex Systems
No full textThe workshop aimed to unite researchers from diverse fields of mathematics and statistics to explore the foundations of high-dimensional modeling and computational studies. It addressed recent advancements in numerical analysis, dynamical systems, and stochastic differential equations that support model reduction for large-scale complex systems.
Incorporating targeted geometric structures, such as Riemannian manifolds, into large-scale statistical models is known to enhance the stability, reliability, and efficiency of numerical methods. However, algorithms are often presented in application contexts without adequate attention to their fundamental properties, limiting the adoption of these advanced modeling methods.
The workshop emphasized understanding the fundamental properties of these structures, their impact on dynamics and stochastic dynamics, and the need to redesign algorithms to capture essential properties, aiming for robustness and suitability for high-performance computation.
By bringing together numerical analysts, statisticians, and modelers, the workshop sought to improve the quality of methods and identify new model frameworks to guide future development
Non-commutative Function Theory and Free Probability
No full textThe workshop brought together researchers in two fields, non-commutative function theory and free probability.
There was a mini-course in each of these areas, and speakers in all the talks were encouraged to give expository talks that illuminated the broader reaches of their fields