Yufei Zhao's blog https://yufeizhao.com/ Wed, 30 Oct 2024 00:15:49 -0400 Wed, 30 Oct 2024 00:15:49 -0400 Mehtaab Sawhney wins Clay Research Fellowship Thu, 25 Jan 2024 00:00:00 -0500 https://yufeizhao.com/blog/2024/01/25/sawhney-clay/ https://yufeizhao.com/blog/2024/01/25/sawhney-clay/ blog Papers by MIT combinatorialists—Fall 2023 Summaries of recent papers by students and postdocs Fri, 22 Dec 2023 00:00:00 -0500 https://yufeizhao.com/blog/2023/12/22/papers/ https://yufeizhao.com/blog/2023/12/22/papers/ blog Schildkraut: Equiangular lines and large multiplicity of fixed second eigenvalue Graph with high second eigenvalue multiplicity for a fixed eigenvalue Mon, 06 Mar 2023 00:00:00 -0500 https://yufeizhao.com/blog/2023/03/06/schildkraut-eigval/ https://yufeizhao.com/blog/2023/03/06/schildkraut-eigval/ blog Nearly all k-SAT functions are unate We proved the Bollobás--Brightwell--Leader conjecture characterizing the structure of a typical k-SAT function. Mon, 19 Sep 2022 00:00:00 -0400 https://yufeizhao.com/blog/2022/09/19/k-sat/ https://yufeizhao.com/blog/2022/09/19/k-sat/ blog Kwan–Sah–Sawhney–Simkin: High-girth Steiner triple systems Resolution of a 1973 Erdős conjecture showing the existence of Steiner triple systems with arbitrarily high girth. Thu, 13 Jan 2022 00:00:00 -0500 https://yufeizhao.com/blog/2022/01/13/steiner-triple/ https://yufeizhao.com/blog/2022/01/13/steiner-triple/ blog Graphs with high second eigenvalue multiplicity How high can the second eigenvalue multiplicity of a connected bounded degree graph get? Tue, 28 Sep 2021 00:00:00 -0400 https://yufeizhao.com/blog/2021/09/28/eig-mult/ https://yufeizhao.com/blog/2021/09/28/eig-mult/ blog Enumerating k-SAT functions How many k-SAT functions are there? What does a typical one look like? Wed, 21 Jul 2021 00:00:00 -0400 https://yufeizhao.com/blog/2021/07/21/enumerating-k-sat/ https://yufeizhao.com/blog/2021/07/21/enumerating-k-sat/ blog Mathematical tools for large graphs General audience essay on the graph regularity lemma, graph limits, and additive combinatorics Mon, 12 Jul 2021 00:00:00 -0400 https://yufeizhao.com/blog/2021/07/12/large-graphs/ https://yufeizhao.com/blog/2021/07/12/large-graphs/ blog How I manage my BibTeX references, and why I prefer not initializing first names A how-to guide, and my rationale Sun, 04 Jul 2021 00:00:00 -0400 https://yufeizhao.com/blog/2021/07/04/bibtex/ https://yufeizhao.com/blog/2021/07/04/bibtex/ blog The cylindrical width of transitive sets A finite transitive subset of a high dimensional sphere lies close to a subspace Thu, 28 Jan 2021 00:00:00 -0500 https://yufeizhao.com/blog/2021/01/28/cylindrical-width-transitive-set/ https://yufeizhao.com/blog/2021/01/28/cylindrical-width-transitive-set/ blog Ashwin Sah and Mehtaab Sawhney win the Morgan Prize For outstanding research by undergraduates Thu, 29 Oct 2020 00:00:00 -0400 https://yufeizhao.com/blog/2020/10/29/sah-sawhney-morgan-prize/ https://yufeizhao.com/blog/2020/10/29/sah-sawhney-morgan-prize/ blog Jain–Sah–Sawhney: Singularity of discrete random matrices The singularity probability for discrete random matrices. Tue, 13 Oct 2020 00:00:00 -0400 https://yufeizhao.com/blog/2020/10/13/jain-sah-sawhney-singularity/ https://yufeizhao.com/blog/2020/10/13/jain-sah-sawhney-singularity/ blog Gunby: Upper tails for random regular graphs Ben Gunby's new paper determining the large deviation rate for sparse random regular graphs. Mon, 05 Oct 2020 00:00:00 -0400 https://yufeizhao.com/blog/2020/10/05/random-regular-tails/ https://yufeizhao.com/blog/2020/10/05/random-regular-tails/ blog Joints of varieties Generalizing the joints theorem from lines to varieties Sat, 12 Sep 2020 00:00:00 -0400 https://yufeizhao.com/blog/2020/09/12/joints-varieties/ https://yufeizhao.com/blog/2020/09/12/joints-varieties/ blog Ashwin Sah's new diagonal Ramsey number upper bound New upper bound to diagonal Ramsey numbers Wed, 20 May 2020 00:00:00 -0400 https://yufeizhao.com/blog/2020/05/20/ashwin-sahs-new-diagonal-ramsey-number-upper-bound/ https://yufeizhao.com/blog/2020/05/20/ashwin-sahs-new-diagonal-ramsey-number-upper-bound/ blog Joints tightened Tight bounds for the joints problem in incidence geometry Thu, 21 Nov 2019 00:00:00 -0500 https://yufeizhao.com/blog/2019/11/21/joints-tightened/ https://yufeizhao.com/blog/2019/11/21/joints-tightened/ blog Equiangular lines with a fixed angle Determining the maximum number of equiangular lines in high dimensions with a fixed given angle Tue, 30 Jul 2019 00:00:00 -0400 https://yufeizhao.com/blog/2019/07/30/equiangular-lines-with-a-fixed-angle/ https://yufeizhao.com/blog/2019/07/30/equiangular-lines-with-a-fixed-angle/ blog Impartial digraphs Which directed graphs have constant density in all tournaments? Thu, 27 Jun 2019 00:00:00 -0400 https://yufeizhao.com/blog/2019/06/27/impartial-digraphs/ https://yufeizhao.com/blog/2019/06/27/impartial-digraphs/ blog A reverse Sidorenko inequality New results on graph colorings and homomorphisms Wed, 26 Sep 2018 00:00:00 -0400 https://yufeizhao.com/blog/2018/09/26/a-reverse-sidorenko-inequality/ https://yufeizhao.com/blog/2018/09/26/a-reverse-sidorenko-inequality/ blog The number of independent sets in an irregular graph Resolution of Kahn's conjecture on the maximum number of independent sets in a graph with prescribed degree-degree distributions. Sat, 12 May 2018 00:00:00 -0400 https://yufeizhao.com/blog/2018/05/12/the-number-of-independent-sets-in-an-irregular-graph/ https://yufeizhao.com/blog/2018/05/12/the-number-of-independent-sets-in-an-irregular-graph/ blog