Abstract: Flag algebras is a method, developed by Razborov, to attack problems in extremal combinatorics. Razborov formulated the method in a very general way which made it applicable to various settings. The method was introduced in 2007 and since then its applications have led to solutions or significant improvements of best bounds on many long-standing open problems, including problems of Erd\H{o}s. The main contribution of the method was transferring problems from finite settings to limits settings. This allows for clean calculations ignoring lower order terms. The method can utilize semidefinite programming and computers to produce asymptotic results. This is often followed by stability type arguments with the goal of obtaining exact results. In this talk we will give a brief introduction of the basic notions used in flag algebras and demonstrate how the method works. Then we will discuss applications of the flag algebras in different settings.
Lunch with the speaker: Thursday, September 30, 11:45 a.m., Spoon House Korean Kitchen on Green Street; meet at the restaurant.
Dinner with the speaker: Thursday, September 30, 6:30 p.m., location to be discussed.
Additional event: Friday, October 1, 1:00-1:50 p.m. AH 447; the speakers talk with the students about their favorite problems.
