More Like this

1. On Torsor Structures on Spanning Trees

   https://doi.org/10.1137/22M149154X  

   Shokrieh, Farbod; Wright, Cameron (September 2023, SIAM Journal on Discrete Mathematics)
2. On Sugawara construction on celestial sphere

   https://doi.org/10.1007/JHEP09(2020)139  

   Fan, Wei; Fotopoulos, Angelos; Stieberger, Stephan; Taylor, Tomasz R. (September 2020, Journal of High Energy Physics)

   null (Ed.)

   A bstract Conformally soft gluons are conserved currents of the Celestial Conformal Field Theory (CCFT) and generate a Kac-Moody algebra. We study celestial amplitudes of Yang-Mills theory, which are Mellin transforms of gluon amplitudes and take the double soft limit of a pair of gluons. In this manner we construct the Sugawara energy-momentum tensor of the CCFT. We verify that conformally soft gauge bosons are Virasoro primaries of the CCFT under the Sugawara energy-momentum tensor. The Sugawara tensor though does not generate the correct conformal transformations for hard states. In Einstein-Yang- Mills theory, we consider an alternative construction of the energy-momentum tensor, similar to the double copy construction which relates gauge theory amplitudes with gravity ones. This energy momentum tensor has the correct properties to generate conformal transformations for both soft and hard states. We extend this construction to supertranslations. 

   more » « less
3. On the general dyadic grids on

   https://doi.org/10.4153/S0008414X22000360  

   Anderson, Theresa C.; Hu, Bingyang (July 2022, Canadian Journal of Mathematics)

   Abstract Adjacent dyadic systems are pivotal in analysis and related fields to study continuous objects via collections of dyadic ones. In our prior work (joint with Jiang, Olson, and Wei), we describe precise necessary and sufficient conditions for two dyadic systems on the real line to be adjacent. Here, we extend this work to all dimensions, which turns out to have many surprising difficulties due to the fact that $d+1$ , not $2^d$ , grids is the optimal number in an adjacent dyadic system in $$\mathbb {R}^d$$ . As a byproduct, we show that a collection of $d+1$ dyadic systems in $$\mathbb {R}^d$$ is adjacent if and only if the projection of any two of them onto any coordinate axis are adjacent on $$\mathbb {R}$$ . The underlying geometric structures that arise in this higher-dimensional generalization are interesting objects themselves, ripe for future study; these lead us to a compact, geometric description of our main result. We describe these structures, along with what adjacent dyadic (and n -adic, for any n ) systems look like, from a variety of contexts, relating them to previous work, as well as illustrating a specific exa. 

   more » « less
4. Active learning: “Hands-on” meets “minds-on”

   https://doi.org/10.1126/science.abj9957  

   Yannier, Nesra; Hudson, Scott E.; Koedinger, Kenneth R.; Hirsh-Pasek, Kathy; Golinkoff, Roberta Michnick; Munakata, Yuko; Doebel, Sabine; Schwartz, Daniel L.; Deslauriers, Louis; McCarty, Logan; et al (October 2021, Science)
5. Active learning:“Hands-on” meets “minds-on”

   Nesra Yannier, Scott E (October 2021, Science)