Search for: All records

Abstract We study conjectures of Ben-Zvi–Sakellaridis–Venkatesh that categorify the relationship between automorphic periods andL-functions in the context of the Geometric Langlands equivalence. We provide evidence for these conjectures in some low-rank examples, by using derived Fourier analysis and the theory of chiral algebras to categorify the Rankin-Selberg unfolding method. 

Over the past three decades, assessments of the contemporary global carbon budget consistently report a strong net land carbon sink. Here, we review evidence supporting this paradigm and quantify the differences in global and Northern Hemisphere estimates of the net land sink derived from atmospheric inversion and satellite-derived vegetation biomass time series. Our analysis, combined with additional synthesis, supports a hypothesis that the net land sink is substantially weaker than commonly reported. At a global scale, our estimate of the net land carbon sink is 0.8 ± 0.7 petagrams of carbon per year from 2000 through 2019, nearly a factor of two lower than the Global Carbon Project estimate. With concurrent adjustments to ocean (+8%) and fossil fuel (−6%) fluxes, we develop a budget that partially reconciles key constraints provided by vegetation carbon, the north-south CO₂gradient, and O₂trends. We further outline potential modifications to models to improve agreement with a weaker land sink and describe several approaches for testing the hypothesis. 

Wildfire modifies the short- and long-term exchange of carbon between terrestrial ecosystems and the atmosphere, with impacts on ecosystem services such as carbon uptake. Dry western US forests historically experienced low-intensity, frequent fires, with patches across the landscape occupying different points in the fire-recovery trajectory. Contemporary perturbations, such as recent severe fires in California, could shift the historic stand-age distribution and impact the legacy of carbon uptake on the landscape. Here, we combine flux measurements of gross primary production (GPP) and chronosequence analysis using satellite remote sensing to investigate how the last century of fires in California impacted the dynamics of ecosystem carbon uptake on the fire-affected landscape. A GPP recovery trajectory curve of more than five thousand fires in forest ecosystems since 1919 indicated that fire reduced GPP by 157.4 ± 7.3 g C m − 2 y − 1 ( mean ± SE,   n = 1926 ) in the first year after fire, with average recovery to prefire conditions after ∼ 12 y. The largest fires in forested ecosystems reduced GPP by 393.8 ± 15.7 g C m − 2 y − 1 ( n = 401) and took more than two decades to recover. Recent increases in fire severity and recovery time have led to nearly 9.9 ± 3.5 MMT CO 2 (3-y rolling mean) in cumulative forgone carbon uptake due to the legacy of fires on the landscape, complicating the challenge of maintaining California’s natural and working lands as a net carbon sink. Understanding these changes is paramount to weighing the costs and benefits associated with fuels management and ecosystem management for climate change mitigation. 

Let X X be an affine spherical variety, possibly singular, and L + X \mathsf L^+X its arc space. The intersection complex of L + X \mathsf L^+X , or rather of its finite-dimensional formal models, is conjectured to be related to special values of local unramified L L -functions. Such relationships were previously established in Braverman–Finkelberg–Gaitsgory–Mirković for the affine closure of the quotient of a reductive group by the unipotent radical of a parabolic, and in Bouthier–Ngô–Sakellaridis for toric varieties and L L -monoids. In this paper, we compute this intersection complex for the large class of those spherical G G -varieties whose dual group is equal to G ˇ \check G , and the stalks of its nearby cycles on the horospherical degeneration of X X . We formulate the answer in terms of a Kashiwara crystal, which conjecturally corresponds to a finite-dimensional G ˇ \check G -representation determined by the set of B B -invariant valuations on X X . We prove the latter conjecture in many cases. Under the sheaf–function dictionary, our calculations give a formula for the Plancherel density of the IC function of L + X \mathsf L^+X as a ratio of local L L -values for a large class of spherical varieties.