演講公告

演講主題：Fourier analysis and expanding phenomena in finite fields
主講人：沈俊嚴先生(印地安那大學伯明頓分校數學系)
演講日期：98年12月29日(星期二) 下午2:30 –3:20
演講地點：(光復校區)科學一館223室
摘要內容：
Recent remarkable results of Bourgain, Katz and Tao on the sum-product problem in finite fields have found many important applications in various areas, and stimulated a seriers of studies. In this talk we will discuss the recent developments in sum-product problems. We address that by using Fourier analytic methods we characterize the polynomials such that when A behaves like an arithmetic progression, then the size of its image under the polynomials is large. The Gauss and Weil's exponential sums estimates play an important role in our proof. If time permits, we will also discuss an analogous result in real setting, in which a small amount of algebraic geometry is used, in particular the Bezout's theorem.
相關檔案：981229-2.doc

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