@article{10623,
abstract = {We investigate the BCS critical temperature Tc in the high-density limit and derive an asymptotic formula, which strongly depends on the behavior of the interaction potential V on the Fermi-surface. Our results include a rigorous confirmation for the behavior of Tc at high densities proposed by Langmann et al. (Phys Rev Lett 122:157001, 2019) and identify precise conditions under which superconducting domes arise in BCS theory.},
author = {Henheik, Sven Joscha},
issn = {1572-9656},
journal = {Mathematical Physics, Analysis and Geometry},
keywords = {geometry and topology, mathematical physics},
number = {1},
publisher = {Springer Nature},
title = {{ The BCS critical temperature at high density}},
doi = {10.1007/s11040-021-09415-0},
volume = {25},
year = {2022},
}
@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{10856,
abstract = {We study the properties of the maximal volume k-dimensional sections of the n-dimensional cube [−1, 1]n. We obtain a first order necessary condition for a k-dimensional subspace to be a local maximizer of the volume of such sections, which we formulate in a geometric way. We estimate the length of the projection of a vector of the standard basis of Rn onto a k-dimensional subspace that maximizes the volume of the intersection. We nd the optimal upper bound on the volume of a planar section of the cube [−1, 1]n , n ≥ 2.},
author = {Ivanov, Grigory and Tsiutsiurupa, Igor},
issn = {2299-3274},
journal = {Analysis and Geometry in Metric Spaces},
keywords = {Applied Mathematics, Geometry and Topology, Analysis},
number = {1},
pages = {1--18},
publisher = {De Gruyter},
title = {{On the volume of sections of the cube}},
doi = {10.1515/agms-2020-0103},
volume = {9},
year = {2021},
}
@article{8940,
abstract = {We quantise Whitney’s construction to prove the existence of a triangulation for any C^2 manifold, so that we get an algorithm with explicit bounds. We also give a new elementary proof, which is completely geometric.},
author = {Boissonnat, Jean-Daniel and Kachanovich, Siargey and Wintraecken, Mathijs},
issn = {0179-5376},
journal = {Discrete & Computational Geometry},
keywords = {Theoretical Computer Science, Computational Theory and Mathematics, Geometry and Topology, Discrete Mathematics and Combinatorics},
number = {1},
pages = {386--434},
publisher = {Springer Nature},
title = {{Triangulating submanifolds: An elementary and quantified version of Whitney’s method}},
doi = {10.1007/s00454-020-00250-8},
volume = {66},
year = {2021},
}
@article{8422,
abstract = {The Birkhoff conjecture says that the boundary of a strictly convex integrable billiard table is necessarily an ellipse. In this article, we consider a stronger notion of integrability, namely integrability close to the boundary, and prove a local version of this conjecture: a small perturbation of an ellipse of small eccentricity which preserves integrability near the boundary, is itself an ellipse. This extends the result in Avila et al. (Ann Math 184:527–558, ADK16), where integrability was assumed on a larger set. In particular, it shows that (local) integrability near the boundary implies global integrability. One of the crucial ideas in the proof consists in analyzing Taylor expansion of the corresponding action-angle coordinates with respect to the eccentricity parameter, deriving and studying higher order conditions for the preservation of integrable rational caustics.},
author = {Huang, Guan and Kaloshin, Vadim and Sorrentino, Alfonso},
issn = {1016-443X},
journal = {Geometric and Functional Analysis},
keywords = {Geometry and Topology, Analysis},
number = {2},
pages = {334--392},
publisher = {Springer Nature},
title = {{Nearly circular domains which are integrable close to the boundary are ellipses}},
doi = {10.1007/s00039-018-0440-4},
volume = {28},
year = {2018},
}