Oberwolfach Publications (Mathematisches Forschungsinst. Oberwolfach)
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2063 research outputs found
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Teichmüller Theory: Classical, Higher, Super and Quantum
No full textTeichmüller spaces play a major role
in many areas of mathematics and physical science. The subject of the conference was recent developments of Teichmüller theory with its different ramifications that include the classical, the higher, the super and the quantum aspects of the theory
The Simplicial Complex of Brauer Pairs of a Finite Reductive Group
No full textIn this paper we study the simplicial complex induced by the poset of Brauer pairs ordered by inclusion for the family of finite reductive groups. In the defining characteristic case the homotopy type of this simplicial complex coincides with that of the Tits building thanks to a well-known result of Quillen. On the other hand, in the non-defining characteristic case, we show that the simplicial complex of Brauer pairs is homotopy equivalen to a simplicial complex determined by generalised Harish-Chandra theory. This extends earlier results of the author on the Brown complex and makes use of the theory of connected subpairs and twisted block induction developed by Cabanes and Enguehard.This work was carried out during a stay of the author at the Mathematisches Forschungsinstitut Oberwolfach funded by a Leibniz Fellowship.
The author would like to thank Marc Cabanes for useful comments on an earlier version of this
paper
Hypergroups and Twin Buildings, I
No full textWe discuss a conjecture on thick twin buildings the verification of which is needed in order to show that thick twin buildings are mathematically equivalent to regular actions of certain twin Coxeter hypergroups. (A corresponding result for buildings is shown in [5; Sections 10.2, 10.3].) We prove that the conjecture holds in the case where the support of its sagittal has cardinality 2 and in the case where its sagittal has length at most 3. (Sagittals are defined in Section 1.) Our exposition is based on an earlier treatment of the subject; cf. [3].This research was supported through the program "Oberwolfach Research Fellows" by the
Mathematisches Forschungsinstitut Oberwolfach in 2023
Ground State of Bose Gases Interacting through Singular Potentials
No full textWe consider a system of bosons on the three-dimensional unit torus. The particles interact through repulsive pair interactions of the form for . We prove the next order correction to Bogoliubov theory for the ground state and the ground state energy.It is a pleasure to thank Chiara Boccato, Robert Seiringer, Christian Hainzl, Alessandro Olgiati and Phan Th`anh Nam for helpful discussions. We are very grateful to the Oberwolfach Research Institute for Mathematics for their hospitality during a Research in Pairs fellowship, where the first part of this project was completed. L.B. was supported by the German Research Foundation within the Munich Center of Quantum Science and Technology (EXC 2111). N.L. acknowledges funding from the Swiss National Science Foundation through the NCCR SwissMap and support from the European Union’s Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie grant agreement No. 101024712. S.P. acknowledges funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - project number 512258249
Control Methods in Hyperbolic Partial Differential Equations
No full textControl of hyperbolic partial differential equations (PDEs) is a truly interdisciplinary area of research in applied mathematics nurtured by challenging problems arising in most modern applications ranging from road traffic, gas pipeline management, blood circulation, to opinion dynamics and socio-economical models, as well as in environmental and biological issues, or more recently in the analysis of deep learning and machine learning methods. The topic has gained an increasing attraction of researchers in the last twenty years due to fundamental theoretical as well as numerical advances achieved in the field of nonlinear hyperbolic PDEs.
The hyperbolic and the control of PDEs communities, while pursuing separate interests in their respective range of action with a different focus and, often, with a different array of technical tools, do share a substantial body of common knowledge and background. We think the time is right and the momentum is propitious to bring those communities together at a joint workshop, to mutually stimulate each other and interact with one another, for a marked advancement of this area of research on a broad spectrum of control ranging from theoretical to numerical problems and covering also the emerging challenges involving the interplay between (topics of) control and learning. In order to also attract young scientists to this striving field we focus on selected lectures, in-depth discussions, transfer of information from senior to young researchers, and vice versa, and invited plenary talks
Many-Body Quantum Systems
No full textThis workshop brought together experts on the analysis of quantum many-body problems and quantum statistical mechanics, with the goal of discussing the state-of-the-art of the field, recent developments as well as challenges for the future. The main topics of discussion concerned the equilibrium and dynamical behavior of (bosonic or fermionic) quantum gases, quantum spin systems, as well as quantum field theory models like the Nelson or Fröhlich model
Mini-Workshop: Positivity and Inequalities in Convex and Complex Geometry
No full textThe workshop convened researchers from algebraic geometry, convex geometry, and complex geometry to explore themes arising from the Alexandrov-Fenchel and Brunn-Minkowski inequalities. It featured three introductory talks delving into the basics of Lorentzian polynomials, valuations in convex geometry, and plurisubharmonic functions, that served as a foundation for the subsequent research talks. As anticipated, significant overlap emerged among the varied perspectives within these three areas, evident in the presentations and ensuing discussions
Classical and Quantum Mechanical Models of Many-Particle Systems
No full textThe workshop focused on the collective behavior of many-particle systems in various application fields: physics (gas dynamics, plasmas, quantum mechanics), mathematical biology (cell mobility, evolution of trait-structured species), and social sciences (wealth distribution). This includes famous models such as the Boltzmann equation of gas dynamics, Vlasov equation for plasmas, Fokker-Planck equations, Smoluchowski and related equations, Keller-Segel system of chemotaxis
Aspects of Aperiodic Order
No full textThe theory of aperiodic order expanded and developed significantly since the discovery of quasicrystals, and continues to bring many mathematical disciplines together. The focus of this workshop was on harmonic analysis and spectral theory, dynamical systems and group actions, Schrödinger operators, and their roles in aperiodic order - with links into a full range of problems from number theory to operator theory