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1. Tropical moments of tropical Jacobians

   https://doi.org/10.4153/S0008414X22000220  

   de_Jong, Robin; Shokrieh, Farbod (August 2023, Canadian Journal of Mathematics)

   Abstract Each metric graph has canonically associated to it a polarized real torus called its tropical Jacobian. A fundamental real-valued invariant associated to each polarized real torus is its tropical moment. We give an explicit and efficiently computable formula for the tropical moment of a tropical Jacobian in terms of potential theory on the underlying metric graph. We show that there exists a universal linear relation between the tropical moment, a certain capacity called the tau invariant, and the total length of a metric graph. To put our formula in a broader context, we relate our work to the computation of heights attached to principally polarized abelian varieties. 

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2. Tropical Combinatorics

   https://doi.org/10.1090/noti2597  

   Rincón, Felipe; Tran, Ngoc Mai; Yu, Josephine (January 2023, Notices of the American Mathematical Society)
3. Tropical flag varieties

   https://doi.org/10.1016/j.aim.2021.107695  

   Brandt, Madeline; Eur, Christopher; Zhang, Leon (June 2021, Advances in Mathematics)
4. Global coupled dynamics of tropical easterly waves and tropical cyclone genesis

   https://doi.org/10.1038/s41612-025-01014-y  

   Du, Xueqing; Chu, Jung-Eun; Jin, Fei-Fei; Cheung, Hung Ming (December 2025, npj Climate and Atmospheric Science)

   Tropical easterly waves (TEWs) are westward-moving waves often within trade winds but occur ubiquitously in the tropics and play a significant role in the genesis of tropical cyclones (TCs). They are well-known as primary precursors of TCs in the Atlantic, yet their global relationship with TCs has been less explored. This study, for the first time, presents the global distribution of TEW activity using a combined thermodynamic and dynamic framework based on 6-hourly Outgoing Longwave Radiation and curvature vorticity. We then demonstrate that TEWs play a dominant role in approximately 22–71% of global TC genesis, with their highest impacts in the North Atlantic (71%) and Western Pacific (54%). We further identify that TEWs, in their general coupling with TC genesis dynamics, act to intensify TC convection and vorticity in all TC main development regions, albeit the vorticity enhancement is relatively weaker in the North Atlantic. To understand the cross-basin differences in this general TEW-TC relationship, we further investigated background conditions for TC genesis in each basin and found an additional dry environment constraint in the Atlantic TC genesis, yet still delineating the critical role of TEWs in TC development. 

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5. Summertime stationary waves integrate tropical and extratropical impacts on tropical cyclone activity

   https://doi.org/10.1073/pnas.2010547117  

   Wang, Zhuo; Zhang, Gan; Dunkerton, Timothy J.; Jin, Fei-Fei (September 2020, Proceedings of the National Academy of Sciences)

   null (Ed.)

   Tropical cyclones (TC) are one of the most severe storm systems on Earth and cause significant loss of life and property upon landfall in coastal areas. A better understanding of their variability mechanisms will help improve the TC seasonal prediction skill and mitigate the destructive impacts of the storms. Early studies focused primarily on tropical processes in regulating the variability of TC activity, while recent studies suggest also some long-range impacts of extratropical processes, such as lateral transport of dry air and potential vorticity by large-scale waves. Here we show that stationary waves in the Northern Hemisphere integrate tropical and extratropical impacts on TC activity in July through October. In particular, tropical upper-tropospheric troughs (TUTTs), as part of the summertime stationary waves, are associated with the variability of large-scale environmental conditions in the tropical North Atlantic and North Pacific and significantly correlated to the variability of TC activity in these basins. TUTTs are subject to the modulation of diabatic heating in various regions and are the preferred locations for extratropical Rossby wave breaking (RWB). A strong TUTT in a basin is associated with enhanced RWB and tropical−extratropical stirring in that basin, and the resultant changes in the tropical atmospheric conditions modulate TC activity. In addition, the anticorrelation of TUTTs between the North Atlantic and North Pacific makes the TC activity indices over the two basins compensate each other, rendering the global TC activity less variable than otherwise would be the case if TUTTs were independent. 

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