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1. Double bubbles on the line with log-convex density f with (logf)′ bounded

   Sothanaphan, Nat (January 2018, Missouri journal of mathematical sciences)

   We extend results of Bongiovanni et al. [1] on double bubbles on the line with log-convex density to the case where the derivative of the log of the density is bounded. We show that the tie function between the double interval and the triple interval still exists, but may blow up to infinity in finite time. For the first time, a density is presented for which the blowup time is positive and finite. 

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2. Random matrices with log-range correlations, and log-Sobolev inequalities

   https://doi.org/10.5802/ambp.396  

   Kemp, Todd; Zimmermann, David (January 2020, Annales Mathématiques Blaise Pascal)
3. Log canonical pairs with conjecturally minimal volume

   https://doi.org/10.1007/s00229-024-01588-6  

   Esser, Louis; Totaro, Burt (November 2024, manuscripta mathematica)
4. F-theory with worldvolume sectioning

   https://doi.org/10.1007/JHEP04(2021)022  

   Linch, William D.; Siegel, Warren (April 2021, Journal of High Energy Physics)

   null (Ed.)

   A bstract We describe the worldvolume for the bosonic sector of the lower-dimensional F-theory that embeds 5D, N=1 M-theory and the 4D type II superstring. This theory is a complexification of the fundamental 5-brane theory that embeds the 4D, N=1 M-theory of the 3D type II string in a sense that we make explicit at the level of the Lagrangian and Hamiltonian formulations. We find three types of section condition: in spacetime, on the worldvolume, and one tying them together. The 5-brane theory is recovered from the new theory by a double dimensional reduction. 

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5. Fully Dynamic Connectivity in $$O(\log n(\log\log n)^2)$$ Amortized Expected Time

   https://doi.org/10.46298/theoretics.23.6  

   Huang, Shang-En; Huang, Dawei; Kopelowitz, Tsvi; Pettie, Seth; Thorup, Mikkel (May 2023, TheoretiCS)

   Dynamic connectivity is one of the most fundamental problems in dynamic graphalgorithms. We present a randomized Las Vegas dynamic connectivity datastructure with $$O(\log n(\log\log n)^2)$$ amortized expected update time and$$O(\log n/\log\log\log n)$$ worst case query time, which comes very close to thecell probe lower bounds of Patrascu and Demaine (2006) and Patrascu and Thorup(2011). 

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