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1. Gauge invariants of linearized gravity with a general background metric

   https://doi.org/10.1088/1361-6382/aca067  

   Garg, Deepen ; Dodin, I Y ( November 2022 , Classical and Quantum Gravity)

   Abstract In linearized gravity with distributed matter, the background metric has no generic symmetries, and decomposition of the metric perturbation into global normal modes is generally impractical. This complicates the identification of the gauge-invariant part of the perturbation, which is a concern, for example, in the theory of dispersive gravitational waves (GWs) whose energy–momentum must be gauge-invariant. Here, we propose how to identify the gauge-invariant part of the metric perturbation and the six independent gauge invariants per se for an arbitrary background metric. For the Minkowski background, the operator that projects the metric perturbation on the invariant subspace is proportional to the well-known dispersion operator of linear GWs in vacuum. For a general background, this operator is expressed in terms of the Green’s operator of the vacuum wave equation. If the background is smooth, it can be found asymptotically using the inverse scale of the background metric as a small parameter. 

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2. Set-valued state estimation of nonlinear discrete-time systems with nonlinear invariants based on constrained zonotopes

   https://doi.org/10.1016/j.automatica.2021.109638  

   Rego, Brenner S. ; Scott, Joseph K. ; Raimondo, Davide M. ; Raffo, Guilherme V. ( July 2021 , Automatica)
3. On the Growth of $L^2$-Invariants of Locally Symmetric Spaces, II: Exotic Invariant Random Subgroups in Rank One

   https://doi.org/10.1093/imrn/rny080  

   Abert, Miklos ; Bergeron, Nicolas ; Biringer, Ian ; Gelander, Tsachik ; Nikolov, Nikolay ; Raimbault, Jean ; Samet, Iddo ( May 2018 , International Mathematics Research Notices)
4. Cohomological Invariants in Positive Characteristic

   https://doi.org/10.1093/imrn/rnaa321  

   Totaro, Burt ( January 2021 , International Mathematics Research Notices)

   Abstract We determine the mod $p$ cohomological invariants for several affine group schemes $G$ in characteristic $p$. These are invariants of $G$-torsors with values in étale motivic cohomology, or equivalently in Kato’s version of Galois cohomology based on differential forms. In particular, we find the mod 2 cohomological invariants for the symmetric groups and the orthogonal groups in characteristic 2, which Serre computed in characteristic not 2. We also determine all operations on the mod $p$ étale motivic cohomology of fields, extending Vial’s computation of the operations on the mod $p$ Milnor K-theory of fields. 

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5. Laplace invariants of differential operators

   https://doi.org/10.1215/00192082-8746137  

   Hobby, D. ; Shemyakova, E. ( January 2021 , Illinois Journal of Mathematics)

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