报告主题：A brief introduction of affine valuation theory
报告人：李晋 博士 （Vienna University of Technology）
报告时间：2018年12月28日（周五）10：00
报告地点：校本部G507
邀请人：冷岗松
报告摘要：Following the idea of F. Klein's Erlangen program, we can say that the theory of valuations is the study of the invariance of valuations (finitely additive measures) under geometric transformations. Systematically starting from the Hadwiger theorem, many valuations were studied with respect to different type of geometric transformations, e.g., translation, rotation, unitary, spin group and affine transformations. Although the earliest studied valuations (volumes and Dehn's invariant) are functionals from polytopes to real numbers, many intersting valuations are functionals on other domains and having different ranges. For example, valuations on convex bodies, star bodies and function spaces; and valuations taking values in tensors, convex bodies, functions and measures. In the talk I will show some classifications of valuations and some interesting open problems and conjectures.
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