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Skeletal filtrations of the fundamental group of a non-archimedean curve (2023)
Journal Article
Helminck, P. A. (2023). Skeletal filtrations of the fundamental group of a non-archimedean curve. Advances in Mathematics, 431, Article 109242. https://doi.org/10.1016/j.aim.2023.109242

In this paper we study skeleta of residually tame coverings of a marked curve over a non-archimedean field. We first prove a simultaneous semistable reduction theorem for residually tame coverings, which we then use to construct a tropicalization fun... Read More about Skeletal filtrations of the fundamental group of a non-archimedean curve.

On Endomorphism Algebras of Gelfand-Graev Representations II (2023)
Journal Article
Li, T., & Shotton, J. (2023). On Endomorphism Algebras of Gelfand-Graev Representations II. Bulletin of the London Mathematical Society, https://doi.org/10.1112/blms.12899

Let G be a connected reductive group defined over a finite field Fq of characteristic p, with Deligne–Lusztig dual G∗. We show that, over Z[1/pM] where M is the product of all bad primes for G, the endomorphism ring of a Gelfand–Graev representation... Read More about On Endomorphism Algebras of Gelfand-Graev Representations II.

Boundary confining dualities and Askey-Wilson type q -beta integrals (2023)
Journal Article
Okazaki, T., & Smith, D. J. (2023). Boundary confining dualities and Askey-Wilson type q -beta integrals. Journal of High Energy Physics, 2023(8), Article 048. https://doi.org/10.1007/jhep08%282023%29048

We propose confining dualities of N = (0, 2) half-BPS boundary conditions in 3d N = 2 supersymmetric SU(N), USp(2n) and SO(N) gauge theories. Some of these dualities have the novel feature that one (anti)fundamental chiral has Dirichlet boundary... Read More about Boundary confining dualities and Askey-Wilson type q -beta integrals.

Multi-dimensional BSDEs with mean reflection (2023)
Journal Article
Qu, B., & Wang, F. (2023). Multi-dimensional BSDEs with mean reflection. Electronic Journal of Probability, 28, 1-26. https://doi.org/10.1214/23-ejp991

In this paper, we consider multi-dimensional mean reflected backward stochastic differential equations (BSDEs) with possibly non-convex reflection domains along inward normal direction, which were introduced by Briand, Elie and Hu [6] in the scalar c... Read More about Multi-dimensional BSDEs with mean reflection.

The 3-dimensional Lyness map and a self-mirror log Calabi–Yau 3-fold (2023)
Journal Article
Ducat, T. (2024). The 3-dimensional Lyness map and a self-mirror log Calabi–Yau 3-fold. manuscripta mathematica, 174(1-2), 87-140. https://doi.org/10.1007/s00229-023-01497-0

The 2-dimensional Lyness map is a 5-periodic birational map of the plane which may famously be resolved to give an automorphism of a log Calabi–Yau surface, given by the complement of an anticanonical pentagon of (-1)-curves in a del Pezzo surface of... Read More about The 3-dimensional Lyness map and a self-mirror log Calabi–Yau 3-fold.

Cyclic quadrilaterals and smooth Jordan curves (2023)
Journal Article
Greene, J. E., & Lobb, A. (2023). Cyclic quadrilaterals and smooth Jordan curves. Inventiones Mathematicae, https://doi.org/10.1007/s00222-023-01212-6

For every smooth Jordan curve γ and cyclic quadrilateral Q in the Euclidean plane, we show that there exists an orientation-preserving similarity taking the vertices of Q to γ. The proof relies on the theorem of Polterovich and Viterbo that an embedd... Read More about Cyclic quadrilaterals and smooth Jordan curves.

Impact of Anomalous Active Regions on the Large-scale Magnetic Field of the Sun (2023)
Journal Article
Pal, S., Bhowmik, P., Mahajan, S. S., & Nandy, D. (2023). Impact of Anomalous Active Regions on the Large-scale Magnetic Field of the Sun. Astrophysical Journal, 953(1), Article 51. https://doi.org/10.3847/1538-4357/acd77e

One of the major sources of perturbation in the solar cycle amplitude is believed to be the emergence of anomalous active regions that do not obey Hale's polarity law and Joy's law of tilt angles. Anomalous regions containing high magnetic flux that... Read More about Impact of Anomalous Active Regions on the Large-scale Magnetic Field of the Sun.

A Bayesian spatio‐temporal model for short‐term forecasting of precipitation fields (2023)
Journal Article
Johnson, S. R., Heaps, S. E., Wilson, K. J., & Wilkinson, D. J. (2023). A Bayesian spatio‐temporal model for short‐term forecasting of precipitation fields. Environmetrics, https://doi.org/10.1002/env.2824

With extreme weather events becoming more common, the risk posed by surface water flooding is ever increasing. In this work we propose a model, and associated Bayesian inference scheme, for generating short-term, probabilistic forecasts of localised... Read More about A Bayesian spatio‐temporal model for short‐term forecasting of precipitation fields.

A general framework for tropical differential equations (2023)
Journal Article
Giansiracusa, J., & Mereta, S. (2024). A general framework for tropical differential equations. manuscripta mathematica, 173(3-4), 1273-1304. https://doi.org/10.1007/s00229-023-01492-5

We construct a general framework for tropical differential equations based on idempotent semirings and an idempotent version of differential algebra. Over a differential ring equipped with a non-archimedean norm enhanced with additional differential... Read More about A general framework for tropical differential equations.