Speaker : Professor Bang-He Li (Chinese Academy of Sciences)
Title : Infinitesimals in Differential and Algebraic Geometry
Time : 2013-08-02 (Fri) 15:00 - 16:30
Place : Seminar Room 722, Institute of Mathematics (NTU Campus)
Abstract: The idea of infinitesimals was used extensively by mathematicians before the appearance of - method. But actually, the - method could only make part of arguments concerning infinitesimals rigorous. And the rigorous theory of infinitesimals, i. e., the so called nonstandard analysis has much more content, e. g. in differential geometry, we can get the Frenet frames for a curve directly from infinitesimal pieces of the curve. In algebraic geometry, we can find generic points in the infinitesimal neighborhood of any point in a variety, in the sense of classical algebraic geometry; and the quotient space obtained from the nonstandard version of a variety modulo an equivalence relation, is just the scheme, in the sense of modern algebraic geometry.