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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. Warming-induced contraction of tropical convection delays and reduces tropical cyclone formation

   https://doi.org/10.1038/s41467-023-41911-5  

   Zhang, Gan (December 2023, Nature Communications)

   The future risk of tropical cyclones (TCs) strongly depends on changes in TC frequency, but models have persistently produced contrasting projections. A satisfactory explanation of the projected changes also remains elusive. Here we show a warming-induced contraction of tropical convection delays and reduces TC formation. This contraction manifests as stronger equatorial convection and weaker off-equatorial convection. It has been robustly projected by climate models, particularly in the northern hemisphere. This contraction shortens TC seasons by delaying the poleward migration of the intertropical convergence zone. At seasonal peaks of TC activity, the equatorial and off-equatorial components of this contraction are associated with TC-hindering environmental changes. Finally, the convection contraction and associated warming patterns can partly explain the ensemble spread in projecting future TC frequency. This study highlights the role of convection contraction and provides motivation for coordinated research to solidify our confidence in future TC risk projections. 

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