More Like this

1. Root Cones and the Resonance Arrangement

   https://doi.org/10.37236/8759  

   Gutekunst, Samuel C.; Mészáros, Karola; Petersen, T. Kyle (January 2021, The Electronic Journal of Combinatorics)

   null (Ed.)

   We study the connection between triangulations of a type $$A$$ root polytope and the resonance arrangement, a hyperplane arrangement that shows up in a surprising number of contexts. Despite an elementary definition for the resonance arrangement, the number of resonance chambers has only been computed up to the $n=8$ dimensional case. We focus on data structures for labeling chambers, such as sign vectors and sets of alternating trees, with an aim at better understanding the structure of the resonance arrangement, and, in particular, enumerating its chambers. Along the way, we make connections with similar (and similarly difficult) enumeration questions. With the root polytope viewpoint, we relate resonance chambers to the chambers of polynomiality of the Kostant partition function. With the hyperplane viewpoint, we clarify the connections between resonance chambers and threshold functions. In particular, we show that the base-2 logarithm of the number of resonance chambers is asymptotically $n^2$. 

   more » « less
2. The radiation field on product cones

   https://doi.org/10.1016/j.aim.2022.108589  

   Baskin, Dean; Marzuola, Jeremy L. (October 2022, Advances in Mathematics)
3. Locating resonances on hyperbolic cones

   https://doi.org/10.4310/MRL.2019.v26.n2.a2  

   Baskin, Dean; Marzuola, Jeremy L. (January 2019, Mathematical Research Letters)
4. Scattering resonances on truncated cones

   https://doi.org/10.2140/paa.2020.2.385  

   Baskin, Dean; Yang, Mengxuan (January 2020, Pure and Applied Analysis)
5. Deformation cones of Tesler polytopes

   Lee, Yonggyu; Liu, Fu (April 2024, Advances in geometry)