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• Mehtaab Sawhney wins Clay Research Fellowship 1/25/2024
  
• Papers by MIT combinatorialists—Fall 2023 12/22/2023
  Summaries of recent papers by students and postdocs
• Schildkraut: Equiangular lines and large multiplicity of fixed second eigenvalue 3/6/2023
  Graph with high second eigenvalue multiplicity for a fixed eigenvalue
• Nearly all k-SAT functions are unate 9/19/2022
  We proved the Bollobás--Brightwell--Leader conjecture characterizing the structure of a typical k-SAT function.
• Kwan–Sah–Sawhney–Simkin: High-girth Steiner triple systems 1/13/2022
  Resolution of a 1973 Erdős conjecture showing the existence of Steiner triple systems with arbitrarily high girth.
• Graphs with high second eigenvalue multiplicity 9/28/2021
  How high can the second eigenvalue multiplicity of a connected bounded degree graph get?
• Enumerating k-SAT functions 7/21/2021
  How many k-SAT functions are there? What does a typical one look like?
• Mathematical tools for large graphs 7/12/2021
  General audience essay on the graph regularity lemma, graph limits, and additive combinatorics
• How I manage my BibTeX references, and why I prefer not initializing first names 7/4/2021
  A how-to guide, and my rationale
• The cylindrical width of transitive sets 1/28/2021
  A finite transitive subset of a high dimensional sphere lies close to a subspace
• Ashwin Sah and Mehtaab Sawhney win the Morgan Prize 10/29/2020
  For outstanding research by undergraduates
• Jain–Sah–Sawhney: Singularity of discrete random matrices 10/13/2020
  The singularity probability for discrete random matrices.
• Gunby: Upper tails for random regular graphs 10/5/2020
  Ben Gunby's new paper determining the large deviation rate for sparse random regular graphs.
• Joints of varieties 9/12/2020
  Generalizing the joints theorem from lines to varieties
• Ashwin Sah's new diagonal Ramsey number upper bound 5/20/2020
  New upper bound to diagonal Ramsey numbers
• Joints tightened 11/21/2019
  Tight bounds for the joints problem in incidence geometry
• Equiangular lines with a fixed angle 7/30/2019
  Determining the maximum number of equiangular lines in high dimensions with a fixed given angle
• Impartial digraphs 6/27/2019
  Which directed graphs have constant density in all tournaments?
• A reverse Sidorenko inequality 9/26/2018
  New results on graph colorings and homomorphisms
• The number of independent sets in an irregular graph 5/12/2018
  Resolution of Kahn's conjecture on the maximum number of independent sets in a graph with prescribed degree-degree distributions.