【短期课程】线上短课程:Introduction to Matroid Theory

【短期课程】线上短课程:Introduction to Matroid Theory

Year:    2023

CAM-Net Digest, Vol. 20 (2023), Iss. 9 : p. 6

Abstract

1. 授课专家

董峰明,现为新加坡南洋理工大学副教授、博士生导师,是图的色多项式领域的知名专家。1997年新加坡国立大学博士。主要研究兴趣为图论,特别是图和拟阵的结构与多项式的关系。和他人合作,已出版专著和其他书籍四本, 发表学术论文近100篇,发表在JCTA, JCTB, JGT等国际组合数学重要学术刊物上。解决了若干公开问题及猜想,包括牛津大学的Welsh和Bartel提出的“Shameful Conjecture”。2008年被剑桥大学聘为客座研究员,参与剑桥大学牛顿数学研究所的组合学与统计物理的研究工作。2015年被邀请参与《the CRC Handbook on the Tutte Polynomial and Related Topics》手册的撰写工作。

2.  短课程介绍

A matroid is a structure that generalizes the notion of linear independence in vector spaces. Matroids have found applications in many mathematical subjects such as geometry, topology, combinatorial optimization, network theory and coding theory.  I will give a series of talks for the beginners of Matroid theory. These talks cover the following topics: (a)Definition of matroids and equivalent statements; (b)Basic concepts: bases, rank function, closures, etc; (c)Transversal matroids, the lattice of flats; (d)Duality; (e)Tutte polynomials and recent advances.

3.  授课时间与内容

5月17日  9:00-12:00
Examples, Independent sets, Graphic matroids and representable matroids

5月18日  9:00-12:00
Basic concepts: circuits, bases, rank function, closures, etc

5月19日  9:00-12:00
Affine matroids, Geometric representation of a matroid with rank at most 4,Transversal  matroids, the lattice of flats

5月22日  9:00-12:00
Duality: the dual of a matroid, clutters in a matroid, matroids characterized by hyperplanes

5月23日  14:30-17:30
Characteristic polynomials, Tutte polynomials and recent advances

4. 授课地点 Course Link:

线下:厦门大学海韵园数理大楼686【仅限集美大学与厦门大学师生参加】

线上:腾讯会议ID:374-7808-4513(无密码)

对本次课程感兴趣的老师、同学可自行线上参加,无需报名。如果出现网络或其他意外故障,请大家及时访问此网页获得最新信息。

5. 联系人 Contact
叶老师,0592-2580036,tymath2@xmu.edu.cn

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Journal Article Details

Publisher Name:    Global Science Press

Language:    Chinese

DOI:    https://doi.org/2023-CAM-21695

CAM-Net Digest, Vol. 20 (2023), Iss. 9 : p. 6

Published online:    2023-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    1

Keywords: