@article{14343,
  abstract     = {The total energy of an eigenstate in a composite quantum system tends to be distributed equally among its constituents. We identify the quantum fluctuation around this equipartition principle in the simplest disordered quantum system consisting of linear combinations of Wigner matrices. As our main ingredient, we prove the Eigenstate Thermalisation Hypothesis and Gaussian fluctuation for general quadratic forms of the bulk eigenvectors of Wigner matrices with an arbitrary deformation.},
  author       = {Cipolloni, Giorgio and Erdös, László and Henheik, Sven Joscha and Kolupaiev, Oleksii},
  issn         = {2050-5094},
  journal      = {Forum of Mathematics, Sigma},
  publisher    = {Cambridge University Press},
  title        = {{Gaussian fluctuations in the equipartition principle for Wigner matrices}},
  doi          = {10.1017/fms.2023.70},
  volume       = {11},
  year         = {2023},
}

@article{13178,
  abstract     = {We consider the large polaron described by the Fröhlich Hamiltonian and study its energy-momentum relation defined as the lowest possible energy as a function of the total momentum. Using a suitable family of trial states, we derive an optimal parabolic upper bound for the energy-momentum relation in the limit of strong coupling. The upper bound consists of a momentum independent term that agrees with the predicted two-term expansion for the ground state energy of the strongly coupled polaron at rest and a term that is quadratic in the momentum with coefficient given by the inverse of twice the classical effective mass introduced by Landau and Pekar.},
  author       = {Mitrouskas, David Johannes and Mysliwy, Krzysztof and Seiringer, Robert},
  issn         = {2050-5094},
  journal      = {Forum of Mathematics},
  pages        = {1--52},
  publisher    = {Cambridge University Press},
  title        = {{Optimal parabolic upper bound for the energy-momentum relation of a strongly coupled polaron}},
  doi          = {10.1017/fms.2023.45},
  volume       = {11},
  year         = {2023},
}

@article{14239,
  abstract     = {Given a resolution of rational singularities  π:X~→X  over a field of characteristic zero, we use a Hodge-theoretic argument to prove that the image of the functor  Rπ∗:Db(X~)→Db(X)
  between bounded derived categories of coherent sheaves generates  Db(X)
  as a triangulated category. This gives a weak version of the Bondal–Orlov localization conjecture [BO02], answering a question from [PS21]. The same result is established more generally for proper (not necessarily birational) morphisms  π:X~→X , with  X~
  smooth, satisfying  Rπ∗(OX~)=OX .},
  author       = {Mauri, Mirko and Shinder, Evgeny},
  issn         = {2050-5094},
  journal      = {Forum of Mathematics, Sigma},
  publisher    = {Cambridge University Press},
  title        = {{Homological Bondal-Orlov localization conjecture for rational singularities}},
  doi          = {10.1017/fms.2023.65},
  volume       = {11},
  year         = {2023},
}

@article{10643,
  abstract     = {We prove a generalised super-adiabatic theorem for extended fermionic systems assuming a spectral gap only in the bulk. More precisely, we assume that the infinite system has a unique ground state and that the corresponding Gelfand–Naimark–Segal Hamiltonian has a spectral gap above its eigenvalue zero. Moreover, we show that a similar adiabatic theorem also holds in the bulk of finite systems up to errors that vanish faster than any inverse power of the system size, although the corresponding finite-volume Hamiltonians need not have a spectral gap.

},
  author       = {Henheik, Sven Joscha and Teufel, Stefan},
  issn         = {2050-5094},
  journal      = {Forum of Mathematics, Sigma},
  keywords     = {computational mathematics, discrete mathematics and combinatorics, geometry and topology, mathematical physics, statistics and probability, algebra and number theory, theoretical computer science, analysis},
  publisher    = {Cambridge University Press},
  title        = {{Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk}},
  doi          = {10.1017/fms.2021.80},
  volume       = {10},
  year         = {2022},
}

@article{9583,
  abstract     = {We show that for any n divisible by 3, almost all order-n Steiner triple systems admit a decomposition of almost all their triples into disjoint perfect matchings (that is, almost all Steiner triple systems are almost resolvable).},
  author       = {Ferber, Asaf and Kwan, Matthew Alan},
  issn         = {2050-5094},
  journal      = {Forum of Mathematics},
  publisher    = {Cambridge University Press},
  title        = {{Almost all Steiner triple systems are almost resolvable}},
  doi          = {10.1017/fms.2020.29},
  volume       = {8},
  year         = {2020},
}