Casey Tompkins: Localized versions of extremal problems

Abstract:
We generalize some classic theorems in extremal combinatorics by replacing a global constraint with an inequality which holds for all objects in a given class. For example instead of a bound on the number of edges in a $Kr$-free graph we obtain an inequality on a weight function on the edges which holds for an arbitrary graph. In particular we obtain extensions of Turán's theorem, the Erdős-Gallai theorem, the LYM-inequality, the Erdős-Ko-Rado theorem and the Erdős-Szekeres theorem on sequences.  This is joint work with David Malec.

The lecture can be followed by zoom:

• Zoom link: https://us06web.zoom.us/j/89547528463?pwd=Z0ZiU1NXZkpyY2NNUy9PYXptY0JuZz09
• Meeting ID: 895 4752 8463
• Passcode: 890941