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1. Faltings height and Néron–Tate height of a theta divisor

   https://doi.org/10.1112/S0010437X21007661  

   de Jong, Robin; Shokrieh, Farbod (January 2022, Compositio Mathematica)

   We prove a formula, which, given a principally polarized abelian variety $$(A,\lambda )$$ over the field of algebraic numbers, relates the stable Faltings height of $$A$$ with the Néron–Tate height of a symmetric theta divisor on $$A$$ . Our formula completes earlier results due to Bost, Hindry, Autissier and Wagener. The local non-archimedean terms in our formula can be expressed as the tropical moments of the tropicalizations of $$(A,\lambda )$$ . 

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2. Brauer's Height Zero Conjecture

   https://doi.org/10.4007/annals.2024.200.2.4  

   Malle, Gunter; Navarro, Gabriel; Schaeffer_Fry, Amanda; Tiep, Pham (September 2024, Annals of Mathematics)
3. What sets aeolian dune height?

   https://doi.org/10.1038/s41467-022-30031-1  

   Gunn, Andrew; Casasanta, Giampietro; Di Liberto, Luca; Falcini, Federico; Lancaster, Nicholas; Jerolmack, Douglas J. (December 2022, Nature Communications)

   Abstract Wherever a loose bed of sand is subject to sufficiently strong winds, aeolian dunes form at predictable wavelengths and growth rates. As dunes mature and coarsen, however, their growth trajectories become more idiosyncratic; nonlinear effects, sediment supply, wind variability and geologic constraints become increasingly relevant, resulting in complex and history-dependent dune amalgamations. Here we examine a fundamental question: do aeolian dunes stop growing and, if so, what determines their ultimate size? Earth’s major sand seas are populated by giant sand dunes, evolved over tens of thousands of years. We perform a global analysis of the topography of these giant dunes, and their associated atmospheric forcings and geologic constraints, and we perform numerical experiments to gain insight on temporal evolution of dune growth. We find no evidence of a previously proposed limit to dune size by atmospheric boundary layer height. Rather, our findings indicate that dunes may grow indefinitely in principle; but growth depends on morphology, slows with increasing size, and may ultimately be limited by sand supply. 

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4. Height-conserving quantum dimer models

   https://doi.org/10.1103/PhysRevB.106.L041115  

   Yan, Zheng; Meng, Zi Yang; Huse, David A.; Chan, Amos (July 2022, Physical Review B)
5. Standard conjectures and height pairings

   https://doi.org/10.4310/PAMQ.2022.v18.n5.a7  

   Zhang, Shou-Wu (January 2022, Pure and Applied Mathematics Quarterly)