西南交通大學(xué)數(shù)學(xué)學(xué)院邀請高牛山老師作了一場題為“Unbounded order convergence and w*-representations of risk measures(無界階收斂以及w * -風(fēng)險的措施表示)”的講座，數(shù)學(xué)學(xué)院現(xiàn)有鐵道部和四川省重點學(xué)科一個：應(yīng)用數(shù)學(xué)；碩士學(xué)位點三個：基礎(chǔ)數(shù)學(xué)、應(yīng)用數(shù)學(xué)、概率論與數(shù)理統(tǒng)計；本科專業(yè)三個：數(shù)學(xué)與應(yīng)用數(shù)學(xué)、信息與計算科學(xué)、統(tǒng)計學(xué)。講座的主要內(nèi)容是：

　　在這次演講中，我們將討論無限階收斂的概念和它的一些應(yīng)用，以功能分析和金融數(shù)學(xué)。具體而言，我們將討論三個議題：(1)無界階收斂的功能分析方面；(2)申請順序連續(xù)preduals的研究;(3)應(yīng)用的風(fēng)險的措施表示理論。特別是，我們會告訴每一個Banach格至多有一個階連續(xù)前雙和表征那些確實有這樣一個predual。我們也將展示雙Orlicz空間，這使我們能夠建立W *的一些秩序拓?fù)湫再|(zhì) - 的風(fēng)險的措施表示。講座是基于弗拉基米爾Troitsky和Foivos Xanthos聯(lián)合工作。

　　原文：In this talk, we will discuss the notion of unbounded order convergence and some of its applications to Functional Analysis and Mathematical Finance. Specifically, we will cover three topics: (1) functional analytic aspects of unbounded order convergence; (2) application to the study of order continuous preduals; (3)application to representation theory of risk measures. In particular, we will show that every Banach lattice has at most one order continuous pre-dual and characterize those which do have such a predual. We will also demonstrate some order-topology properties of dual Orlicz spaces, which enable us to establish w*-representations of risk measures. The talk is based on joint work with Vladimir Troitsky and Foivos Xanthos.