Blog

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 kSAT functions are unate
9/19/2022
We proved the BollobásBrightwellLeader conjecture characterizing the structure of a typical kSAT function. 
Kwan–Sah–Sawhney–Simkin: Highgirth 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 kSAT functions
7/21/2021
How many kSAT 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 howto 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 degreedegree distributions.