@article{18958,
  abstract     = {This 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.},
  author       = {Hainzl, Christian and Schlein, Benjamin and Seiringer, Robert and Warzel, Simone},
  issn         = {1660-8941},
  journal      = {Oberwolfach Reports},
  number       = {3},
  pages        = {2247--2302},
  publisher    = {EMS Press},
  title        = {{Many-body quantum systems}},
  doi          = {10.4171/owr/2023/39},
  volume       = {20},
  year         = {2024},
}

@article{18970,
  abstract     = {Given a smooth projective curve C, nonabelian Hodge theory gives a diffeomorphism between two different moduli spaces associated to C. The first is the moduli space of Higgs bundles on C of rank n, which is equipped with the structure of an algebraic completely integrable Hamiltonian system. The second is the character variety of representations of the fundamental group of C into GL(n). In 2012, de Cataldo, Hausel, and Migliorini [1] proposed the P=W conjecture which identifies the perverse filtration on the cohomology of the Higgs moduli space with the weight filtration on the cohomology of the character variety. Recently, in 2022, two independent proofs of the P=W Conjecture appeared, in work of Maulik &Shen [2] and Hausel, Mellit, Minets &Schiffmann [6]. The aim of the Arbeitsgemeinschaft was to understand the P=W Conjecture and these two recent proofs.},
  author       = {Hausel, Tamás and Maulik, Davesh and Mellit, Anton and Schiffmann, Olivier and Shen, Junliang},
  issn         = {1660-8941},
  journal      = {Oberwolfach Reports},
  number       = {2},
  pages        = {949--1004},
  publisher    = {EMS Press},
  title        = {{Arbeitsgemeinschaft: Geometry and representation theory around the P=W conjecture}},
  doi          = {10.4171/owr/2024/16},
  volume       = {21},
  year         = {2024},
}

@article{18959,
  abstract     = {This workshop continues a series of workshops whose current format originated in 1981 under then-organizers Moser and Zehnder, and whose latest iteration took place in July 2023. The general goal of this series of workshops is to discuss the latest developments in the field of dynamical systems, broadly construed, and its connections with neighboring areas of mathematics such as differential geometry, partial differential equations, and more recently contact and symplectic geometry. We continued this tradition, bringing in new participants working in areas of dynamical systems and its connections with other areas of mathematics that are currently highly active and/or showing great promise for future development. Key focus areas for the 2023 workshop include spectral rigidity for planar domains, chaotic and oscillatory motions in celestial mechanics, conformal symplectic dynamics, and relations between dynamics.he workshop by the grant DMS-2230648, “US Junior Oberwolfach Fellows”.},
  author       = {Arnaud, Marie-Claude and Hutchings, Michael and Kaloshin, Vadim},
  issn         = {1660-8941},
  journal      = {Oberwolfach Reports},
  number       = {3},
  pages        = {1671--1730},
  publisher    = {EMS Press},
  title        = {{Dynamische Systeme}},
  doi          = {10.4171/owr/2023/30},
  volume       = {20},
  year         = {2023},
}

@article{17063,
  abstract     = {This workshop continued a biannual series of workshops at Oberwolfach on dynamical systems that started with a meeting organized by Moser and Zehnder in 1981. Workshops in this series focus on new results and developments in dynamical systems and related areas of mathematics, with symplectic geometry playing an important role in recent years in connection with Hamiltonian dynamics. In this year special emphasis was placed on various kinds of spectra (in contact geometry, in Riemannian geometry, in dynamical systems and in symplectic topology) and their applications to dynamics.},
  author       = {Arnaud, Marie-Claude and Hofer, Helmut W. and Hutchings, Michael and Kaloshin, Vadim},
  issn         = {1660-8941},
  journal      = {Oberwolfach Reports},
  number       = {3},
  pages        = {1735--1803},
  publisher    = {EMS Press},
  title        = {{Dynamische Systeme}},
  doi          = {10.4171/owr/2021/33},
  volume       = {18},
  year         = {2022},
}

@article{22093,
  abstract     = {Nonlinear dispersive equations are models for nonlinear waves in a wide range of physical contexts. Mathematically they display an interplay between linear dispersion and nonlinear interactions, which can result in a wide range of outcomes from finite time blow-up to solitons and scattering. They are linked to many areas of mathematics and physics, ranging from integrable systems and harmonic analysis to fluid dynamics, geometry, general relativity and probability.},
  author       = {Koch, Herbert and Raphaël, Pierre and Tataru, Daniel and Visan, Monica},
  issn         = {1660-8941},
  journal      = {Oberwolfach Reports},
  number       = {2},
  pages        = {1681--1745},
  publisher    = {EMS Press},
  title        = {{Nonlinear waves and dispersive equations}},
  doi          = {10.4171/owr/2017/27},
  volume       = {14},
  year         = {2018},
}