报告人：Professor Xiaochun Li (University of Illinois at Urbana-Champaign)
地点：Room 1560, Sciences Building No. 1
Time: June 14, Friday, 14:00-16:00 Venue: 1560, Sciences Building No. 1
Time: June 16, Sunday, 14:00-16:00 Venue: 1560, Sciences Building No. 1
Time: June 18, Tuesday, 14:00-16:00 Venue: 1560, Sciences Building No. 1
Introduction: I have been working in harmonic analysis, PDE and number theory etc. There is a new trend developed in last twenty years, showing interesting connections and interaction of different fields, for instance, additive number theory, combinatorics, geometry, topology, Ergodic theory and harmonic analysis. That reshapes significantly the modern Fourier analysis. I hope this short course will reflect a small part of this trend and become a starting point for students, who are willing to face to challenging mathematical problems, especially from fields of number theory and analysis.
Abstract: Involved with other areas such as harmonic analysis, Ergodic theory and analytic number theory, etc, additive combinatorics becomes a fast-growing and very active field of modern mathematics. One of central theories in additive combinatorics is Roth’s theorem, which asserts that any large enough subset of integers between 1 and N contains an arithmetic progression of length 3. In this course, I plan to cover Roth’s theorem, via using different proofs, for showing how to use tools from Fourier analysis to solve very classical problems in the field of number theory and combinatorics.