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   Xing, Lu; Aref, Walid G (June 2024, arXiv arXiv:2406.09372)

   Submitted to Conference Publication Also, available as arXiv preprint arXiv:2406.09372, 2024 

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2. A Survey of Learned Indexes for the Multi-dimensional Space

   Al-Mamun, Abdullah; Wu, Hao; He, Qiyang; Wang, Jianguo; Aref, Walid G (March 2024, arXiv arXiv:2403.06456)

   Submitted for Journal Publication Also available as arXiv preprint arXiv:2403.06456, 2024 

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3. Data Files for "Quadrupolar magnetic excitations in an isotropic spin-1 antiferromagnet"

   https://doi.org/10.5281/zenodo.6394852  

   Nag, A.; Nocera, A.; Agrestini, A.; Garcia-Fernandez, M.; Walters, A. C.; Cheong, Sang-Wook; Johnston, S.; Zhou, Ke-Jin (January 2022, Zenodo)

   {"Abstract":["Data files for the manuscript "Quadrupolar magnetic excitations in an isotropic spin-1 antiferromagnet".<\/p>\n\nReference: A. Nag, A. Nocera, S. Agrestini, M. Garcia-Fernandez, A. C. Walters, Sang-Wook Cheong, S. Johnston, and Ke-Jin Zhou, "Quadrupolar magnetic excitations in an isotropic spin-1 antiferromagnet". arXiv:2111.03625 (2021).<\/p>\n\nPreprint: arXiv:2111.03625 (2021), URL: https://arxiv.org/abs/2111.03625<\/p>"]} 

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4. Colored Interacting Particle Systems on the Ring: Stationary Measures from Yang–Baxter Equations

   Aggarwal, Amol; Nicoletti, Matthew; Petrov, Leonid (June 2025, Compositio mathematica)

   Recently, there has been much progress in understanding stationary measures for colored (also called multi-species or multi-type) interacting particle systems, motivated by asymptotic phenomena and rich underlying algebraic and combinatorial structures (such as nonsymmetric Macdonald polynomials). In this paper, we present a unified approach to constructing stationary measures for most of the known colored particle systems on the ring and the line, including (1) the Asymmetric Simple Exclusion Process (multispecies ASEP, or mASEP); (2) the q-deformed Totally Asymmetric Zero Range Process (TAZRP) also known as the q-Boson particle system; (3) the q-deformed Pushing Totally Asymmetric Simple Exclusion Process (q-PushTASEP). Our method is based on integrable stochastic vertex models and the Yang-Baxter equation. We express the stationary measures as partition functions of new "queue vertex models" on the cylinder. The stationarity property is a direct consequence of the Yang-Baxter equation. For the mASEP on the ring, a particular case of our vertex model is equivalent to the multiline queues of Martin (arXiv:1810.10650). For the colored q-Boson process and the q-PushTASEP on the ring, we recover and generalize known stationary measures constructed using multiline queues or other methods by Ayyer-Mandelshtam-Martin (arXiv:2011.06117, arXiv:2209.09859), and Bukh-Cox (arXiv:1912.03510). Our proofs of stationarity use the Yang-Baxter equation and bypass the Matrix Product Ansatz used for the mASEP by Prolhac-Evans-Mallick (arXiv:0812.3293). On the line and in a quadrant, we use the Yang-Baxter equation to establish a general colored Burke's theorem, which implies that suitable specializations of our queue vertex models produce stationary measures for particle systems on the line. We also compute the colored particle currents in stationarity. 

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5. An L2 to L∞ Framework for the Landau Equation

   Jinoh Kim, Yan Guo (January 2020, Peking mathematical journal)

   Consider the Landau equation with Coulomb potential in a periodic box. We develop a new L2 to L∞ framework to construct global unique solutions near Maxwellian with small L∞ norm. The first step is to establish global L2 estimates with strong velocity weight and time decay, under the assumption of L∞ bound, which is further controlled by such L2 estimates via De Giorgi’s method (Golse et al. in Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 19(1), 253–295 (2019), Imbert and Mouhot in arXiv :1505.04608 (2015)). The second step is to employ estimates in Sp spaces to control velocity derivatives to ensure uniqueness, which is based on Hölder estimates via De Giorgi’s method (Golse et al. in Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 19(1), 253–295 (2019), Golse and Vasseur in arXiv :1506.01908 (2015), Imbert and Mouhot in arXiv :1505.04608 (2015)). 

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