NCTS Interdisciplinary Distinguished Lectures - A Dialog between Algebra and Engineering
May 9, 2025
Room 515, Cosmology Building, NTU
Event Website: https://ncts.ntu.edu.tw/events_2_detail.php?nid=510

Invited Speakers:
Prof. Bob Li (Distinguished University Professor, University of Electronic S&T of China)

Organizers:
Yng-Ing Lee (National Taiwan University & NCTS)
Tai-Chia Lin (National Taiwan University)

Aim & Scope
The NCTS Interdisciplinary Distinguished Lecture series aims to introduce important research directions in sciences to the Taiwan mathematical community. And at the same time create a platform that people with different backgrounds can meet, discuss and develop interdisciplinary collaborations. Each Interdisciplinary Distinguished Lecture is designed to be a half day activity with lectures, discussions and a close up.
We are very happy to have Professor Bob Li give the NCTS Interdisciplinary Distinguished Lecture. Li started his career in Mathematics. He is an alumnus of NTU (1970) and Berkeley (1974), and taught at MIT and UI Chicago, all in mathematics. He gradually switched his directions after moving to Bell Lab. in 1979. His seminal work on linear network coding has changed the landscape of the information technology. He is an IEEE Fellow, a member of National Academy of Artificial Intelligence and a foreign member of Serbian National Academy of Sciences. Li considers his works as building connections between mathematics and technology.

Title
A Dialog Between Algebra and Engineering

Abstract
Once a mathematical subject is widely applied to engineering, it is often referred to as “engineering mathematics,” that is, the intersection between the two disciplines. In algebra, such subjects are exemplified by linear algebra. Meanwhile, the classical coding theory is built upon Galois theory. Diverse engineering applications of Fermat’s little theorem are in coding, encryption, network coding, etc.
This presentation is in the form of two contiguous series of algebraic concepts in engineering. The first series revolves around network coding theory. Explicit topics include “changing faces of the Butterfly network,” network encryption/decryption, fast division routines, convolutional network coding, linear algebra over a PID, and local ring.
The second series consists of examples of hardware computation algorithms, multistage switching networks, sorting/routing/multicast networks, Boolean algebra, lattice, and cut-through coding. The examples together provide a taste of algebraic switching theory. Mathematics being the foundation of many engineering fields, occasionally engineering knowledge feedbacks to mathematics. For instance, cut-through codability of lattice is an algebraic concept derived from engineering practice.

摘要：數學的科目一旦在工程上有了廣泛的應用，就常常被視為 “工程數學”，也就是工程學與數學的交集。在代數方面，最明顯的例子就是線性代數。漸漸地比較抽象的代數科目也在加入 “工程數學” 的範疇。例如，Galois theory是古典Coding theory的根基. 又例如，費馬小定理有多方面的工程應用。
本次講座圍繞Network coding theory 和Algebraic switching theory兩個主題. 前者的課題包括“蝴蝶網的變臉”、加密解密、convolutional network coding, linear algebra over a PID, local ring, 等等。后者的課題包括硬體算法、交换網络、排序、路由、多播、Boolean 代數、以及cut-through coding.
數學與工程之間并非只是數學應用到工程上面。偶爾工程的知識對數學也有所回饋。例如，cut-through codability of lattice就是從工程的應用發掘出來的數學觀念。

Agenda
1:30-2:00 Registration
2:00-3:00 Lecture
3:00-3:30 Q&A / Informal Discussion
3:30-4:00 Tea Break
4:00-4:30 Conclusion

Registration：https://pse.is/7gayb4



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