Nearly all k-SAT functions are unate
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
Resolution of a 1973 Erdős conjecture showing the existence of Steiner triple systems with arbitrarily high girth.
Graphs with high second eigenvalue multiplicity
How high can the second eigenvalue multiplicity of a connected bounded degree graph get?
Enumerating k-SAT functions
How many k-SAT functions are there? What does a typical one look like?
Mathematical tools for large graphs
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
A how-to guide, and my rationale
The cylindrical width of transitive sets
A finite transitive subset of a high dimensional sphere lies close to a subspace
Ashwin Sah and Mehtaab Sawhney win the Morgan Prize
For outstanding research by undergraduates
Jain–Sah–Sawhney: Singularity of discrete random matrices
The singularity probability for discrete random matrices.
Gunby: Upper tails for random regular graphs
Ben Gunby's new paper determining the large deviation rate for sparse random regular graphs.
Joints of varieties
Generalizing the joints theorem from lines to varieties
Ashwin Sah's new diagonal Ramsey number upper bound
New upper bound to diagonal Ramsey numbers
Tight bounds for the joints problem in incidence geometry
Equiangular lines with a fixed angle
Determining the maximum number of equiangular lines in high dimensions with a fixed given angle
Which directed graphs have constant density in all tournaments?
A reverse Sidorenko inequality
New results on graph colorings and homomorphisms
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.