西南交通大學(xué)數(shù)學(xué)學(xué)院邀請(qǐng)高牛山老師作了一場(chǎng)題為“Unbounded order convergence and w*-representations of risk measures(無(wú)界階收斂以及w * -風(fēng)險(xiǎn)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(diǎn)學(xué)科一個(gè)：應(yīng)用數(shù)學(xué)；碩士學(xué)位點(diǎn)三個(gè)：基礎(chǔ)數(shù)學(xué)、應(yīng)用數(shù)學(xué)、概率論與數(shù)理統(tǒng)計(jì)；本科專(zhuān)業(yè)三個(gè)：數(shù)學(xué)與應(yīng)用數(shù)學(xué)、信息與計(jì)算科學(xué)、統(tǒng)計(jì)學(xué)。講座的主要內(nèi)容是：

　　在這次演講中，我們將討論無(wú)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(gè)議題：(1)無(wú)界階收斂的功能分析方面；(2)申請(qǐng)順序連續(xù)preduals的研究;(3)應(yīng)用的風(fēng)險(xiǎn)的措施表示理論。特別是，我們會(huì)告訴每一個(gè)Banach格至多有一個(gè)階連續(xù)前雙和表征那些確實(shí)有這樣一個(gè)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(xiǎn)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.