Bulletin of the London Mathematical Society最新文献

Let $�\Gamma$ be a finitely generated group, and let $�\mu$ be a nondegenerate, finitely supported probability measure on $�\Gamma$. We show that every co-compact $�\Gamma$ action on a locally compact Hausdorff space admits a nonzero $�\mu$-stationary Radon measure. The main ingredient of the proof is a stationary analog of Tarski's theorem: we show that for every nonempty subset $��A�\subseteq �\Gamma �$ there is a $�\mu$-stationary, finitely additive measure on $�\Gamma$ that assigns unit mass to $�A$.

We study the Milnor fiber boundary for hyperplane arrangements in $�C^3$. This is one of the examples of non-isolated surface singularities, which are studied by Némethi–Szilárd. In this paper, we compute the first homology group of the Milnor fiber boundary for a generic arrangement, which gives an affirmative answer to the conjecture of Suciu. Also, we give an example of an arrangement with $�n$ hyperplanes, whose torsion part in the Milnor fiber boundary homology contains a direct summand other than $�Z_n$, for certain value of $�n$.

We prove that an asymmetric unimodal map has no wandering intervals.

We study localized versions of spectral action of Fargues–Scholze, using methods from higher algebra. As our main motivation and application, we deduce a formula for the cohomology of moduli spaces of local shtukas under certain genericity assumptions, and discuss its relation with the Kottwitz conjecture.

We consider the kinetic wave equation, or phonon Boltzmann equation, set on the torus (physical system set on the lattice). We describe entropy maximizers for fixed mass and energy; our framework is very general, being valid in any dimension, for any dispersion relation, and even including the quantum kinetic wave equation. Of particular interest is the presence of condensation in certain regimes which we characterize.

In this paper, we study elliptic equations of the form

The classical Petty projection inequality is an affine isoperimetric inequality which constitutes a cornerstone in the affine geometry of convex bodies. By extending the polar projection body to an inter-dimensional operator, Petty's inequality was generalized in Haddad, Langharst, Putterman, Roysdon, and Ye to the so-called $��(�L_p�,�Q�)�$ setting, where $�Q$ is an $�m$-dimensional compact convex set. In this work, we further extend the $��(�L_p�,�Q�)�$ Petty projection inequality to the broader realm of rotationally invariant measures with concavity properties, namely, those with $�\gamma$-concave density (for $��\gamma �⩾�-�1�/�n�m�$). Moreover, when $��p�=�1�$, and motivated by a contemporary empirical reinterpretation of Petty's result by Paouris, Pivovarov, and Tatarko, we explore empirical analogues of this inequality.

If $�G$ is a linearly reductive group acting rationally on a polynomial ring $�S$, then the inclusion $��S^G�\hookrightarrow �S�$ possesses a unique $�G$-equivariant splitting, called the Reynolds operator. We describe algorithms for computing the Reynolds operator for the classical actions as in Weyl's book. The groups are the general linear group, the special linear group, the orthogonal group, and the symplectic group, with their classical representations: direct sums of copies of the standard representation and copies of the dual representation.

For an analytic function $��\varphi �\left(�z�\right)�$ with a Laurent expansion at $�\infty$ of the form