Localization Properties of Chern InsulatorsArnold Mathematical Journal - Tập 5 - Trang 15-21 - 2019
Roman Bezrukavnikov, Anton Kapustin
We study the localization properties of the equal-time electron Green’s function in a Chern insulator in an arbitrary dimension and with an arbitrary number of bands. We prove that the Green’s function cannot decay super-exponentially if the Hamiltonian is finite-range and the quantum Hall response is nonzero. For a general band Hamiltonian (possibly infinite-range), we prove that the Green’s func...... hiện toàn bộ
More About Areas and Centers of Poncelet PolygonsArnold Mathematical Journal - Tập 7 - Trang 91-106 - 2020
Ana C. Chavez-Caliz
We study the locus of the Circumcenter of Mass of Poncelet polygons, and the limit of the Center of Mass (when we consider the polygon as a “homogeneous lamina”) for degenerate Poncelet polygons. We also provide a proof for one of Dan Reznik invariants for billiard trajectories. Plus, we take a look at how the scene looks like when we shift to spherical geometry.
A Topological Bound on the Cantor–Bendixson Rank of Meromorphic DifferentialsArnold Mathematical Journal - Tập 7 - Trang 213-223 - 2020
Guillaume Tahar
In translation surfaces of finite area (corresponding to holomorphic differentials), directions of saddle connections are dense in the unit circle. On the contrary, saddle connections are fewer in translation surfaces with poles (corresponding to meromorphic differentials). The Cantor–Bendixson rank of their set of directions is a measure of descriptive set-theoretic complexity. Drawing on a previ...... hiện toàn bộ
Affine Hecke Algebras via DAHAArnold Mathematical Journal - Tập 4 Số 1 - Trang 69-85 - 2018
Cherednik, Ivan
A method is suggested for obtaining the Plancherel measure for Affine Hecke Algebras as a limit of integral-type formulas for inner products in the polynomial and related modules of Double Affine Hecke Algebras. The analytic continuation necessary here is a generalization of “picking up residues” due to Arthur, Heckman, Opdam and others, which can be traced back to Hermann Weyl. Generally, it is a...... hiện toàn bộ
Solvability of Equations by Quadratures and Newton’s TheoremArnold Mathematical Journal - Tập 4 - Trang 193-211 - 2018
Askold Khovanskii
Picard–Vessiot theorem (1910) provides a necessary and sufficient condition for solvability of linear differential equations of order n by quadratures in terms of its Galois group. It is based on the differential Galois theory and is rather involved. Liouville in 1839 found an elementary criterium for such solvability for
...... hiện toàn bộ
Disconjugacy and the Secant ConjectureArnold Mathematical Journal - Tập 1 - Trang 339-342 - 2015
Alexandre Eremenko
We discuss the so-called secant conjecture in real algebraic geometry, and show that it follows from another interesting conjecture, about disconjugacy of vector spaces of real polynomials in one variable.