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Short Character Sums and the Pólya–Vinogradov Inequality (2022)
Journal Article
Mangerel, A. P. (2022). Short Character Sums and the Pólya–Vinogradov Inequality. The Quarterly Journal of Mathematics, 71(4), 1281–1308. https://doi.org/10.1093/qmath/haaa031

We show in a quantitative way that any odd primitive character χ modulo q of fixed order g ≥ 2 satisfies the property that if the Pólya–Vinogradov inequality for χ can be improved to max1≤t≤q∣∣∣∣∑n≤tχ(n)∣∣∣∣=oq→∞(q√logq) then for any ɛ > 0 one may ex... Read More about Short Character Sums and the Pólya–Vinogradov Inequality.

MGnify: the microbiome sequence data analysis resource in 2023 (2022)
Journal Article
Richardson, L., Allen, B., Baldi, G., Beracochea, M., Bileschi, M., Burdett, T., …Finn, R. (2023). MGnify: the microbiome sequence data analysis resource in 2023. Nucleic Acids Research, 51(D1), D753-D759. https://doi.org/10.1093/nar/gkac1080

The MGnify platform (https://www.ebi.ac.uk/metagenomics) facilitates the assembly, analysis and archiving of microbiome-derived nucleic acid sequences. The platform provides access to taxonomic assignments and functional annotations for nearly half a... Read More about MGnify: the microbiome sequence data analysis resource in 2023.

Deposition, diffusion, and nucleation on an interval (2022)
Journal Article
Georgiou, N., & Wade, A. R. (2022). Deposition, diffusion, and nucleation on an interval. Annals of Applied Probability, 32(6), 4849-4892. https://doi.org/10.1214/22-aap1804

Motivated by nanoscale growth of ultra-thin films, we study a model of deposition, on an interval substrate, of particles that perform Brownian motions until any two meet, when they nucleate to form a static island, which acts as an absorbing barrier... Read More about Deposition, diffusion, and nucleation on an interval.

Nearly critical holographic superfluids (2022)
Journal Article
Donos, A., & Kailidis, P. (2022). Nearly critical holographic superfluids. Journal of High Energy Physics, 2022(12), Article 28. https://doi.org/10.1007/jhep12%282022%29028

We study the nearly critical behaviour of holographic superfluids at finite temperature and chemical potential in their probe limit. This allows us to examine the coupled dynamics of the full complex order parameter with the charge density of the sys... Read More about Nearly critical holographic superfluids.

Squarefrees are Gaussian in short intervals (2022)
Journal Article
Gorodetsky, O., Mangerel, A., & Rodgers, B. (2023). Squarefrees are Gaussian in short intervals. Journal für die reine und angewandte Mathematik, 2023(795), 1-44. https://doi.org/10.1515/crelle-2022-0066

We show that counts of squarefree integers up to X in short intervals of size H tend to a Gaussian distribution as long as H ! 1 and H D Xo.1/. This answers a question posed by R. R. Hall in 1989. More generally, we prove a variant of Donsker’s theor... Read More about Squarefrees are Gaussian in short intervals.

Free groups generated by two parabolic maps (2022)
Journal Article
Kalane, S. B., & Parker, J. R. (2023). Free groups generated by two parabolic maps. Mathematische Zeitschrift, 303, Article 9. https://doi.org/10.1007/s00209-022-03160-y

In this paper we consider a group generated by two unipotent parabolic elements of SU(2, 1) with distinct fixed points. We give several conditions that guarantee the group is discrete and free. We also give a result on the diameter of a finite R-circ... Read More about Free groups generated by two parabolic maps.

Branching random walk in a random time-independent environment (2022)
Journal Article
Chernousova, E., Hryniv, O., & Molchanov, S. (2023). Branching random walk in a random time-independent environment. Mathematical Population Studies, 30(2), 73-94. https://doi.org/10.1080/08898480.2022.2140561

In a lattice population model, particles move randomly from one site to another as independent random walks, split into two offspring, or die. If duplication and mortality rates are equal and take the same value over all lattice sites, the resulting... Read More about Branching random walk in a random time-independent environment.

The SAGEX review on scattering amplitudes chapter 8: half BPS correlators (2022)
Journal Article
Heslop, P. J. (2022). The SAGEX review on scattering amplitudes chapter 8: half BPS correlators. Journal of Physics A: Mathematical and Theoretical, 55(44), https://doi.org/10.1088/1751-8121/ac8c71

Half BPS correlators in $\mathcal{N}=4$ super Yang–Mills theory are key quantities both in the AdS/CFT correspondence as well as in scattering amplitudes research. They are dual at strong coupling to quantum gravity amplitudes. At weak coupling on th... Read More about The SAGEX review on scattering amplitudes chapter 8: half BPS correlators.