报告人：郭铁信 教授（中南大学）

时间：2026年5月15日 17:00-

地点：理科楼LA104

摘要：We present a new development of the theory of L^0-simplicial subdivisions of L^0-simplexes, which enables us to overcome noticeable limitations of an earlier approach. This is carried out by introducing a general notion of an L^0-simplicial subdivision of an L^0-simplex in connection with a usual simplicial subdivision of a classcial simplex. Then a key representation theorem of a proper L^0-labeling function by usual proper labeling functions is established so that we can formulate a general random Sperner lemma in a concise way. We thus achieve a new complete proof of the random Brouwer fixed theorem in random Euclidean spaces, which can provide a solid foundation for various contemporary applications of interest. Afterward, we unify the works currently available and closely related to the random Brouwer fixed theorem: we first prove that the stochastic Brouwer fixed point theorem occurring in stochastic analysis is equivalent to a special case of our random Brouwer fixed theorem, and then prove a general random Borsuk theorem and its equivalence with random Brouwer fixed theorem. Finally, we conclude this paper with commentaries on recent state of study of the famous Schauder conjecture.

邀请人：算子理论团队

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