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Category: Mathematics

  • Expository overview links systole, kissing number, and arithmetic manifolds

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    What the study found The article presents an expository introduction to arithmetic groups and arithmetic manifolds. It uses two geometric questions about the growth of systole and kissing number in hyperbolic manifolds as a motivating guide, and it says these questions have so far been answered with the help of arithmetic manifolds. Why the authors…

  • Local Lipschitz regularity proved for minimizers of certain functionals

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    What the study found The authors prove local Lipschitz regularity for minimizers of a class of functionals, meaning the minimizers have locally bounded slopes. They also show, as a byproduct, that a locally Lipschitz minimizer exists for a related class of functionals in which the function f may be nonconvex. Why the authors say this…

  • Finite element scheme achieves optimal error bounds for corotational heat flow

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    What the study found The study found optimal order discretization error bounds for a finite element approximation of the corotational harmonic map heat flow problem. The analysis applies to smooth solutions of the continuous problem. Why the authors say this matters The authors indicate that the method's key analytical tools help with discrete stability and…

  • Improved Omega bound for lattice point discrepancy in bodies of revolution

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    What the study found The study found an improved Omega-bound for the error term in a lattice counting problem for bodies of revolution in three-dimensional space. In this setting, a body of revolution is a shape formed by rotating a curve around an axis. Why the authors say this matters The authors say this strengthens…

  • Subnormalisers of semisimple elements are determined

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    What the study found The paper determines the subnormalisers of semisimple elements of prime power order in finite quasi-simple groups of Lie type. It also determines the maximal overgroups of normalisers of Sylow tori. Why the authors say this matters The authors say the work is motivated by the recent character correspondence conjecture by Moretó…

  • Exact maximum diameter found for 2-dimensional simplicial complexes

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    What the study found The study determines the exact maximum diameter for 2-dimensional abstract simplicial complexes on n vertices for every n. It also identifies an infinite sequence of explicit constructions that achieve this bound. Why the authors say this matters The authors present their result as an answer to a problem posed by Santos…

  • Synthetic Lorentzian Cartan-Hadamard theorem established

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    What the study found The authors formulate and prove a synthetic Lorentzian Cartan-Hadamard theorem. They show that, under additional assumptions of global hyperbolicity and future one-connectedness, there is existence and uniqueness of timelike geodesics between any pair of timelike related points. Why the authors say this matters The study suggests this result transfers the corresponding…

  • Upper bounds improve for residual finiteness growth in two-step nilpotent groups

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    What the study found The authors report an improved polylogarithmic upper bound for the residual finiteness growth of two-step nilpotent groups. They also state that this bound depends only on the group’s complex Mal’cev completion, and that it is exact when the commutator subgroup is one- or two-dimensional. Why the authors say this matters The…

  • Schur multiplier norm and its dual are expressed by minimization formulas

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    What the study found The study shows that for a complex self-adjoint matrix, the Schur multiplier norm can be determined by a minimization formula involving a diagonal bound. It also gives a corresponding formula for the dual norm of the Schur multiplier norm. Why the authors say this matters The authors say they study the…

  • Reformulation of q-middle convolution adds composition additivity

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    What the study found The authors reformulated q-convolution and q-middle convolution, which are operations used in the study of q-difference equations. They also introduced q-analogues of addition linked to gauge transformation, and found that the reformulation gives additivity for the composition of two q-middle convolutions. Why the authors say this matters The study suggests that…