Blog moved to a new location
I am moving this blog to a new location, now integrated as part of my personal website: http://yufeizhao.com/blog/ All future posts will be made there.
Yufei Zhao
Latest posts
Ashwin Sah’s new diagonal Ramsey number upper bound
Ashwin Sah just proved a new upper bound to diagonal Ramsey numbers. See his preprint on the arXiv. This is the first improvement since Conlon’s upper bound published in Annals of Math in 2009, which in turn built on earlier work of Thomason (1988). Obtaining asymptotics of Ramsey numbers is perhaps the central open problem […]
Joints tightened
I’m happy to announce a new paper titled Joints tightened coauthored with Hung-Hsun Hans Yu, an undergraduate student at MIT. In this paper, we determine the tight constant in the joints problem. The joints problem is a classic problem in incidence geometry. A typical question in incidence geometry concerns what kinds of configurations can be […]
Equiangular lines with a fixed angle
I’m happy to announce our new paper Equiangular lines with a fixed angle joint with four MIT coauthors: Zilin Jiang, Jonathan Tidor, Yuan Yao, and Shengtong Zhang. Zilin is an Instructor (postdoc), Jonathan is my PhD student who just finished his second year, and Yuan and Shengtong are undergraduates who just finished their second and […]
Impartial digraphs
I just finished a new paper, Impartial digraphs, coauthored with Yunkun Zhou, who just completed his undergraduate studies at MIT and will be moving to Stanford to start his PhD this fall. The problem (along with the conjecture that we proved) was proposed by Jacob Fox, Hao Huang, and Choongbum Lee. Ron Graham had also […]
A reverse Sidorenko inequality
Together with undergraduates Ashwin Sah, Mehtaab Sawhney, and David Stoner (the same team that proved Kahn’s conjecture on independent sets that I blogged about earlier), we are excited to announce our new paper A reverse Sidorenko inequality. This paper solves several open problems concerning graph colorings and homomorphisms, including one of my favorite problems regarding […]
The number of independent sets in an irregular graph
I am excited to announce our new paper, The number of independent sets in an irregular graph, coauthored with these three amazing collaborators: Ashwin is a freshman at MIT, Mehtaab is a sophomore at MIT, and David is a junior at Harvard. The paper solves a conjecture made by Jeff Kahn in 2001 concerning the […]
Extremal regular graphs
This post is adapted from my new expository survey Extremal regular graphs: independent sets and graph homomorphisms. The earliest result in extremal graph theory is usually credited to Mantel, who proved, in 1907, that a graph on vertices with no triangles contains at most edges, where the maximum is achieved for a complete bipartite graph […]
Upper tails for triangles in sparse random graphs
Eyal Lubetzky and I just finished and uploaded to the arXiv our new paper On the variational problem for upper tails of triangle counts in sparse random graphs. This paper concerns the following question: The upper tail problem for triangles. What is the probability that the number of triangles in an Erdős-Rényi graph graph is […]
Sphere packing bounds via spherical codes
Henry Cohn and I just uploaded to the arXiv our paper “Sphere packing bounds via spherical codes.” [Update: Henry gave a wonderful talk about our paper at the IAS. A video of the talk is available here.] What’s the most space-efficient way to arrange a collection of identical balls? This is known as the sphere packing […]