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We compute the RO(G)‐graded equivariant algebraic K‐groups of a finite field with an action by its Galois group G. Specifically, we show these K‐groups split as the sum of an explicitly computable term and the well‐studied RO(G)‐graded coefficient groups of the equivariant Eilenberg–MacLane spectrum HZ. Our comparison between the equivariant K‐theory spectrum and HZ further shows they share the same Tate spectra and geometric fixed point spectra. In the case where G has prime order, we provide an explicit presentation of the equivariant K‐groups. 

Barrier islands provide a first line of defense against ocean flooding and storm surge. Biogeomorphic interactions are recognized as important in coastal system processes, but current barrier island models are primarily dominated by physical processes. Recent research has demonstrated different biogeomorphic states that influence response to sea level rise and other disturbance. Building on this understanding, we present a cellular model utilizing biotic and abiotic processes and their interactions for barrier island evolution. Using the literature and field derived parameters, we model barrier island evolution and compare to three decades of change for Smith Island, a Virginia Coast Reserve barrier island. We conduct simulations that show the impact of biogeomorphic states on island migration under different sea level rise scenarios. We find that migration is highest in areas with low topography and light vegetation cover (i.e. disturbance reinforcing) compared to areas with greater topographic complexity and high cover of woody vegetation i.e. disturbance resisting). This study demonstrates the importance of biogeomorphic interactions for barrier island evolution with sea level rise and will aid future predictions for these important ecosystems with climate change. 

Tambara functors are an equivariant generalization of rings that appear as the homotopy groups of genuine equivariant commutative ring spectra. In recent work, Blumberg and Hill have studied the corresponding algebraic structures, called bi-incomplete Tambara functors, that arise from ring spectra indexed on incomplete G-universes. We answer a conjecture of Blumberg and Hill by proving a generalization of the Hoyer–Mazur theorem in the bi-incomplete setting. Bi-incomplete Tambara functors are characterized by indexing categories which parametrize incomplete systems of norms and transfers. In the course of our work, we develop several new tools for studying these indexing categories. In particular, we provide an easily checked, combinatorial characterization of when two indexing categories are compatible in the sense of Blumberg and Hill.