We verify the inductive blockwise Alperin weight condition in odd characteristic for the finite exceptional Chevalley groups F4(q) for q not divisible by.

Uploaded April 2025

This article investigates the asymptotics of G₂-monopoles. First, we prove that when the underlying G₂-manifold is nonparabolic (i.e. admits a positive Green's function), finite intermediate energy monopoles with bounded curvature have finite mass. The second main result restricts to the case when the underlying G₂-manifold is asymptotically conical.

Uploaded April 2025

When first published in 2005, Matrix Mathematics quickly became the essential reference book for users of matrices in all branches of engineering, science, and applied mathematics. In this fully updated and expanded edition, the author brings together the latest results on matrix theory to make this the most complete, current, and easy-to-use book on matrices.

Uploaded April 2025

This work is devoted to the study of integral p-adic Hodge theory in the context of Artin stacks. For a Hodge-proper stack, using the formalism of prismatic cohomology, we establish a version of p-adic Hodge theory with the étale cohomology of the Raynaud generic fiber as an input.

Uploaded March 2025

On the Problem of Infinite Spin in Total Collisions of the Planar N-body Problem solves the problem for almost every choice of the masses of the four-body problem.

Uploaded March 2025

Methods of Graph Decompositions discusses some state-of-the-art decomposition methods of graph theory, which are highly instrumental when dealing with a number of fundamental concepts such as unigraphs, isomorphism, reconstruction conjectures, k-dimensional graphs, degree sequences, line graphs and line hypergraphs.

Uploaded March 2025

We present a modern formulation of Élie Cartan's structure theory for Lie pseudogroups and prove a reduction theorem that clarifies the role of Cartan's systatic system.

Uploaded March 2025

We study Hamiltonicity in random subgraphs of the hypercube Qn. Our first main theorem is an optimal hitting time result. Our techniques also show that, with high probability, for all fixed p ∈ (0, 1] the graph Qn p contains an almost spanning cycle. Our methods involve branching processes, the R¨odl nibble, and absorption.

Uploaded March 2025

In this paper, we complete the program on the (non-)construction of the focusing Hartree Gibbs measures in the three-dimensional setting. More precisely, we study a focusing Φ43-modelwith a Hartree-type nonlinearity, where the potential for the Hartree nonlinearity is given by the Bessel potential of order β.

Uploaded March 2025

For each positive integer t and each sufficiently large integer r, we show that the maximum number of elements of a simple, rank-r, C-representable matroid with no U₂, t+₃-minor is t(r2)+r. We derive this as a consequence of a much more general result concerning matroids on group-labeled graphs.

Uploaded March 2025