Top 20 Mathematical Physics Papers: Oct 26 - Nov 1, 2026

Generalized symmetries are sensitive to the tangential structure of spacetime. We study this interplay for massless QED on oriented non-spin four-manifolds, where the photon becomes a spin$^c$ connection and the path integral sums over spin$^c$ structures.

Here, we prove the existence of an additional root, and hence of a third smooth self-similar profile, in every odd dimension $d\geq11$.

We develop an algebraic theory of fusion, mobility, and statistics in abelian gapped fracton orders and topological phases.

For a Haar-distributed matrix $U \in U(N)$, Rains's power-map theorem represents the spectrum of $U^m$, $m \in \mathbb{N}$, as a superposition of independent lower-dimensional CUE spectra. We determine how this exact decomposition appears in trace moments and in sharp Gaussian and Poisson limit laws.

We define and study a spin version of the open Toda integrable system, using the Iwasawa decomposition of a connected split real Lie group.

We establish a direct connection between the entanglement bootstrap and the Doplicher--Haag--Roberts theory of superselection sectors for two-dimensional quantum spin systems.

We determine the Grothendieck rings of fusion categories over $\mathcal{C}$ containing a nonpointed Tambara--Yamagami fusion subcategory and exactly one further simple object.

For positive semidefinite matrices $A,B$ and $1/2\le\alpha\le1$, we establish $\operatorname{Tr}\!

We study one-dimensional quasiperiodic operators with $\alpha$-Hölder monotone potentials and long-range hopping satisfying $|T(x,y)|\leq \varepsilon e^{-\rho |x-y|}$.

Direct Numerical Simulation (DNS) of the deterministic Navier-Stokes (NS) equations is widely used to provide benchmark solutions of turbulent flow, but its accuracy and reliability have not been rigorously inspected from a mathematical viewpoint.

Here we show that exceptional points (EPs) in the noise-averaged dephasing response can expose observable signatures of non-Gaussian statistics, distinguishing environments with identical lower-order statistics.

We show that despite enhanced spectral response, in finite-dimensional Lindblad systems with a unique stationary state and a nonzero relaxation gap, EPs offer no fundamental advantage in how the observation time required for reliable detection of a weak perturbation scales with the perturbation strength.

We develop a rigorous mathematical framework for the nonequilibrium thermodynamics of semilinear stochastic partial differential equations.

We study the magnetization vector of mixed spherical spin glasses in a weak external field, in the replica symmetric phase.

We derive analytic expressions for observable dynamics under the fully quantized trilinear Hamiltonian, governing quantum three-wave mixing and parametric amplification.

We study minimizers of the Keplerian action functional with homogeneous potential of type $1/|u|^\alpha$ on periodic loops with fixed winding number $k \in \mathbb{Z}\setminus\{0\}$.

We extend this approach to seven dimensions in maximal Cartan-gauged supergravity with all gauge fields active.

In this article, we address the possibility of topological quantum spin liquids with only short-range (spin) correlations in the whole phase diagram in a ladder system, through an exactly solvable model which represents a generalization of the two-dimensional Kitaev honeycomb spin model to a ribbon geometry.

We study directed last passage percolation with geometric weights in a spatially inhomogeneous environment.