Báo cáo khoa học 演講訊息

Recent remarkable results of Bourgain, Katz and Tao on the sum-product problem in finite fields have stimulated a series of studies and the results consequently have been quantified and generalized by some people, including myself. A related problem raised by Bourgain and Widgerson asks to find two variables polynomials which satisfy expanding property in a certain sense. In this talk we will give a solution of this problem and show that in certain cases our bounds are sharp. We also address that in reals one can get Elekes type bound. At the end, we will discuss a version of Balog-Szemeredi-Gowers type estimate established by Bourgain and Garaev which plays a crucial role in our proof.