A refinement of Roth theorem by Green and Tao
沈俊嚴助理教授國立中央大學 下午 2:30–4:00 鴻經館 107 室Abstract：
The celebrated result of Roth (fields medalist 1958) is to assert the existence of arithmetic progressions of length 3 in an integer set with positive density. This result has been improved and generalized by Szemeredi, Gowers, Bourgain, Green and Tao e.t.c. The purpose of this talk is to introduce the proof by Green and Tao on their refinement of Roth's theorem. This talk is almost self-contained as their proofs basically only use finite Fourier analysis. In this talk, we will first recall some basic finite Fourier methods which are needed in the proof, and outline the main ideas of their proofs. The talk should be accessible to a wide audience, in particular the graduate students.