报告题目：The case of the Missing Cage
报告人： Professor Moshe Rosenfeld
（University of Washington, Tacoma, USA）
时间：2011年11月7号（周一）上午10:00-11:00
地点：华东师大闵行校区数学系102报告厅
Abstrast: Does the strongly regular graph G(3250, 57, 0, 1) (a regular graph of order 3250, regular of degree 57, with girth 5) exist?
A beautiful theorem of Hoffman and Singleton asserts that the only possible graphs G(r^2+1, r, 0, 1) are for r = 2, 3, 7, 57.The unique graphs with these parameters are C_5,
Petersen's graph and the Hoffman-Singleton G(50,7,0,1) graph. The existence of G(3250, 57, 0, 1), the missing cage, is still open.
There is a unified construction that constructs the Petersen and Hoffman-Singleton graphs. It suggest a strategy for constructing the "missing cage."
It has the "correct" ingredients and "arithmetic". In this talk I will go over Hoffman-Singleton's beautiful proof and the constructions using finite projective spaces.