蘇州大學(xué)數(shù)學(xué)科學(xué)學(xué)院邀請(qǐng)美國(guó)加州大學(xué)戴維斯分校夏青嵐教授作了題為“Ramified optimal transportation and its applications(網(wǎng)狀最佳運(yùn)輸及其應(yīng)用)”的講座。蘇州大學(xué)數(shù)學(xué)科學(xué)學(xué)院現(xiàn)有數(shù)學(xué)一級(jí)學(xué)科博、碩士學(xué)位授予點(diǎn)(下設(shè)基礎(chǔ)數(shù)學(xué)、應(yīng)用數(shù)學(xué)、計(jì)算數(shù)學(xué)、概率論與數(shù)理統(tǒng)計(jì)、運(yùn)籌學(xué)與控制論、數(shù)學(xué)教育六個(gè)二級(jí)學(xué)科博、碩士點(diǎn))，統(tǒng)計(jì)學(xué)一級(jí)學(xué)科博、碩士學(xué)位授予點(diǎn)(下設(shè)數(shù)理統(tǒng)計(jì)、應(yīng)用概率、金融風(fēng)險(xiǎn)管理、生物統(tǒng)計(jì)、經(jīng)濟(jì)統(tǒng)計(jì)五個(gè)二級(jí)學(xué)科博、碩士點(diǎn))；應(yīng)用統(tǒng)計(jì)、金融工程、學(xué)科教育(數(shù)學(xué))三個(gè)專業(yè)碩士學(xué)位點(diǎn)。講座的主要內(nèi)容是：

　　最佳的運(yùn)輸問(wèn)題的目標(biāo)是尋求從源目標(biāo)的具有成本效益的運(yùn)輸。在數(shù)學(xué)中，有至少兩個(gè)非常重要的類型優(yōu)化交通：蒙赫 - 坎托羅維奇問(wèn)題，分枝最佳交通工具。在這次報(bào)告中，我會(huì)給出一個(gè)簡(jiǎn)要介紹了理論的網(wǎng)狀最佳運(yùn)輸通道.一個(gè)動(dòng)機(jī)的理論來(lái)源于自然界中發(fā)現(xiàn)的分支結(jié)構(gòu)的研究。許多生命系統(tǒng)，如樹(shù)木，在葉中脈，以及動(dòng)物心血管/循環(huán)系統(tǒng)展覽分支結(jié)構(gòu)，為主要非生命系統(tǒng)，如河道網(wǎng)絡(luò)，鐵路，航空網(wǎng)絡(luò)，電力供應(yīng)和通信網(wǎng)絡(luò).為什么做自然和工程師都喜歡這些枝狀結(jié)構(gòu)?什么是對(duì)非分支結(jié)構(gòu)，這些分支結(jié)構(gòu)的優(yōu)勢(shì)是什么?這些問(wèn)題部分激勵(lì)我們?nèi)ヌ剿髌浔澈蟮臄?shù)學(xué)。在這次演講中，我將討論如何建立一個(gè)數(shù)學(xué)理論的這一普遍現(xiàn)象的最佳傳送路徑條款。兩個(gè)概率的措施之間的最優(yōu)傳送路徑可以被看作是在概率測(cè)度的空間的短程線。在這次演講中，我也將調(diào)查多學(xué)科領(lǐng)域的理論，如數(shù)學(xué)生物學(xué)一些應(yīng)用(如動(dòng)力形成樹(shù)的葉子)，度量幾何結(jié)構(gòu)(例如，在quasimetric空間測(cè)地問(wèn)題)，分形幾何(如修改后的彌散限制聚集)，幾何分析(的措施，如運(yùn)輸尺寸)和數(shù)理經(jīng)濟(jì)學(xué)(如網(wǎng)狀最優(yōu)分配問(wèn)題)。

　　The optimal transportation problem aims at finding a costefficient transport from sources to targets. In mathematics, there areat least two very important types of optimal transportation:Monge-Kantorovich problem and ramified optimal transportation. In thistalk, I will give a brief introduction to the theory of ramifiedoptimal transportation.One motivation of the theory comes from the study of the branching structures found in nature. Many living systems such as trees, the veins on a leaf, as well as animal cardiovascular/circulatory systems exhibit branching structures, as domany non-living systems such as river channel networks, railways,airline networks, electric power supply and communication networks.Why do nature and engineers both prefer these ramifying structures? What are the advantages of these branching structures over non-branching structures? These questions partially motivates us to explore the mathematics behind them. In this talk, I will talk about how to set up a mathematical theory for this general phenomenon in terms of optimal transport paths. An optimal transport path between two probability measures can be viewed as a geodesic in the space of probability measures. In this talk, I will also survey some applications of the theory in multidisciplinary areas such as mathematical biology (e.g. the dynamical formation of tree leaves),metric geometry (e.g. the geodesic problems in quasimetric spaces),fractal geometry (e.g. the modified diffusion-limited aggregation),geometric analysis (e.g. transport dimension of measures) and mathematical economics (e.g. ramified optimal allocation problem).