Some results of the project Topological Methods in Discrete Geometry of the Summer Program for Undergraduate Research 2016 and 2017. There will be a continuation of the project during the summer of 2018: apply here.
About our Work
Splitting Rent with Triangles. Episode of PBS Infinite Series about fairly dividing rent. See also this supplemental note coauthored with Kelsey Houston-Edwards.
Manuscripts
Fair division and generalizations of Sperner- and KKM-type results
Megumi Asada, Florian Frick, Vivek Pisharody, Maxwell Polevy, David Stoner, Ling Hei Tsang, and Zoe Wellner
SIAM J. Discrete Math., to appear, 18 pages
On Reay's relaxed Tverberg conjecture and generalizations of Conway's thrackle conjecture
Megumi Asada, Ryan Chen, Florian Frick, Frederick Huang, Maxwell Polevy, David Stoner, Ling Hei Tsang, and Zoe Wellner
Preprint, submitted, 10 pages
On the generalized Erdős−Kneser conjecture: proofs and reductions
Jai Aslam, Shuli Chen, Ethan Coldren, Florian Frick, and Linus Setiabrata
Preprint, 8 pages
Splitting Loops and Necklaces
Jai Aslam, Shujian Chen, Florian Frick, Sam Saloff-Coste, Linus Setiabrata, and Hugh Thomas
in preparation
Kneser-type results for power sets and obstructions for embeddings
Yu Hin Chan, Florian Frick, Tristan Hull, Linus Setiabrata, and George Spahn
in preparation
Borsuk−Ulam theorems for joins, products, and Stiefel manifolds
Yu Hin Chan, Shujian Chen, Florian Frick, and Tristan Hull
in preparation
Posters
Mass Equipartitions and Restricted Necklace Splittings
presented by Megumi Asada at the Young Mathematicians Conference 2016 at The Ohio State University
On k-fold Intersections of Convex Sets
presented by Ryan Chen at the Joint Mathematics Meetings 2017 in Atlanta
Generalizations of Conway's Thrackle Conjecture
presented by Zoe Wellner at the Joint Mathematics Meetings 2017 in Atlanta