Annotated Pictures from Fall 2024

Let F be the class of planar 3-connected cubic graphs with n vertices, with all faces (including the outer face) are either pentagons or hexagons. Equivalently, F can be viewed as the family of graphs of simple 3-polytopes with n … Continue reading →

A central problem in combinatorics, probability theory, and analysis is to understand the spectrum of  random d-regular graphs G with vertices. The following paper marks a huge leap in our understanding of this problem.  Ramanujan Property and Edge Universality of … Continue reading →

Consider equipped with a norm. Given a finite set of points and a point , we consider , the sum of distances from to the points in . Next we consider the set of points that attain the minimum of … Continue reading →

Consider equipped with a norm. Given a finite set of points and a point , we consider , the sum of distances from to the points in . Next we consider the set of points that attain the minimum of … Continue reading →

A wish It is time for the horrible war to end Polymath thoughts: Reviving Polymath3? A question for our readers: Should we revive polymath3? Polymath3 dealt with the following problem: Is there a polynomial  such that the graph of every … Continue reading →