Combinatorics in the news

 https://www.quantamagazine.org/mit-undergraduate-math-student-pushes-frontier-of-graph-theory-20201130/?fbclid=IwAR0JEIZqokv7WZ_PWlGgJcVjbChLLDdHLu9OWNN_765UDvCnmStlmonGC9U

Undergraduate Math Student Pushes Frontier of Graph Theory

At 21, Ashwin Sah has produced a body of work that senior mathematicians say is nearly unprecedented for a college student.
"The May proof focused on an important feature of combinatorics called Ramsey numbers, which quantify how big a graph (a collection of dots, or vertices, connected by edges) can get before it necessarily contains a certain kind of substructure.
...
Sah’s proof, in contrast, improved the upper bound for two-color Ramsey numbers. He achieved it by optimizing a method that originated with Erdős and Szekeres, and which a small number of mathematicians have managed to improve since. Sah’s result proves that once a graph reaches a certain size, it inevitably contains a clique of some corresponding size. Many in the field see Sah’s proof as the best result that can be achieved using the existing line of research."

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