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»ã±¨ÌáÒª£ºIn this talk, I will discuss questions related to bounding Castelnuovo-Mumford regularity of algebraic varieties. The study of regularity can be traed back to Castelnuovo¡¯s research in 1893 on the linear system of algebraic curves. It was formally defined by Mumford in 1960s. Nowadays, regularity becomes one of important invariants of algebraic varieties. I will start with the basic definition of Castelnuovo-Mumford regularity through cohomology and syzygy theories. Then I will present a couple of central problems in this area as well as recent progress and results.

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