生物数学系列演讲

许世壁教授，台湾清华大学

地点：中国人民大学环境楼316室

时间：2018年9月11-13日

许世壁教授简介：1970年在台湾清华大学获得理学学士学位，1976年在爱荷华大学获得博士学位；1976-1979年在犹他大学任教；1979-1985年在台湾交通大学先后任副教授、教授；1985年至今在台湾清华大学任职教授；曾访问马里兰大学、埃默里大学、德克萨斯A&M大学等；1987-1990任台湾清华大学应用数学研究所所长；1998-2004任台湾清华大学理学院院长。

许世壁教授是生物数学领域的国际知名专家。在J. Math. Biol., SIAM J. Math. Anal., Math. Biosci., Bull. Math. Biol., J. Differ. Equations, J. Theoret. Biol.等国际知名期刊上发表论文110余篇，并出版专著2部。2011-2014年被授予讲座教授，任台湾清华大学杰出讲座教授。2013年当选SIAM Fellow。

演讲一： “ My Journey to Mathematical Biology”

时间/地点: 9月11日4点-5点半， 中国人民大学环境楼316

Abstract：In this talk I shall survey my work in Mathematical Biology in the past forty years. I would like to share my experience in doing research in mathematical biology with the young people. Several open problems are proposed to challenge the young people.

演讲二： “On the Mathematical Models of Intra-guild Predation

时间/地点：9月12日10点-11点半，中国人民大学环境楼316

Abstract: The theory of Intra-guild predation was developed by Polis and Holt. Many works follow from their theory. However there are no experiments to justify their theory. In this talk we shall study the mathematical models with Droop type proposed by Huisman et based on their experiment in chemostat. First we consider ODE model and its mathematical analysis. We study the extinction and uniform persistence of the species. Then we consider the corresponding PDE models in unstirred chemostat. We establish the threshold dynamics for the growth of single species using the method developed in the paper of Hsu-Lam-Wang ( JMB 2017). Then we prove the uniform persistence of two species and conclude that intra-guild predation promotes the coexistence of the species. The talk is based on the joint works with Feng-Bin Wang and Nie Hua.

演讲三： “Mathematical Models of Drug Resistance Bacteria”

时间：9月13日10点-11点半，中国人民大学环境楼316

Abstract: In this talk I first introduce my work with Paul Waltman on the simple chemostat with inhibition (SIAP 1992). In this work we consider a system of four equations for the dynamics of nutrient, wild-type, mutant and inhibitor. We reduced it to a system of three dimensional competitive system and apply Poicare-Bendixson Theorem. We present the results on extinction and existence of positive periodic solutions.

Next we propose a system of reaction diffusion equations with nutrient, wild-type and N mutants. The system is used to describe the dynamics of drug resistance bacteria in the paper of Kishony et. in Science 2016. We discuss two cases: forward mutation and forward-backward mutation. A Lyapunov functional is constructed to prove the global dynamics of the bacteria. This is a joint work with Jifa Jiang.