Math551/752 Seminar in Mathematics | 數學書報討論 || National Sun Yat-sen University

Special Announcement regarding COVID-19

[20200320] According to the school's new policy, we will record the names of the participants for each in-class lecture starting from March 23.
[20200320] So far, this is only to make a plan just in case. If, unfortunately, the classes are suspended due to any health concern, we will follow the new grading scheme and policies below. Please do not hesitate to send me an email and let me know if you have any question.
[20200320] The new grading scheme will be 40% Online video watching + 20% Survey (+ existing participation) + 40% Presentation slides.
[20200320] Online video watching: Overall, you have to attend at least 6 talks, physically or remotely. Beside the talks you have been to, you may watch some seminar videos online. Iowa State University Discrete Seminar, Northeast Combinatorics Network Virtual Combinatorics Colloquium, and Mathnet Korea contain seminar talks on various topics. By June 4, send an email to chlin [at] math.nsysu.edu.tw and tell me at least 6 talks (titles and speakers) that you have attended.
[20200320] Survey (+ existing participation): Visit a conference website and search for the conference program (or book of abstract). For example, you may find many talks here at the 2017 Meeting of the International Linear Algebra Society. Pick a talk that you are interested in and then finish the worksheet Before-attending-a-talk [ tex ]. The 20% will be based on your worksheet (submitted through the Cyber University; deadline June 4).
[20200320] Presentation slides: As mentioned before, the slides for your presentation has to be in \(\LaTeX\). This 40% will be based only on your slides in the case that the presentations are canceled (submitted through the Cyber University; deadline June 4). If you want me to give advice on your slides, send them to me one week before.

Course Info top

Term: Feb 27, 2020 – Jun 24, 2020
Meeting time: Thursday, 2:10 pm – 3:00 pm @ SC4013 (Math 551)
Meeting time: Thursday, 3:10 pm – 4:00 pm @ SC4013 (Math 752)
Meeting time: (Please see the schedule or the department announcement for the time for each talk.)

Instructor: Jephian Lin | 林晉宏
Email: chlin [at] math.nsysu.edu.tw
Office: SC2002-5

Further Resources

大家來學 LaTeX
Edward G.J. Lee 李果正

Minimal beamer presentation
Mahmoud Ahmed

CoCalc (Website for compiling LaTeX, SageMath, Python, and so on.)

TeXnique (A \(\LaTeX\) Typesetting Game.)

Learning objectives

A good presentation is comprised of a convincing motivation, meaningful materials, clear explanations, and maybe some brilliant ideas to make people understand your results easier. While the materials are important, oftenly we ignored the other parts of a talk—thus it becomes boring or hard to understand. In this course, there will be many talks throughout the semester. You may learn mathematics from them, while it is also important for you to learn how to analyze the pros and cons of each talk. Do I want to adopt some speaking technique of this speaker? Is there something that I definitely do not want to be the same as the speaker? Learning from each speaker is one of the keys to give awesome presentation.

Outlines

Talks
Student presentations

Evaluation

40% Attendance + 20% Participation + 40% Presentation

You get 5 participation points whenever you ask a question, or share your thoughts in a talk. The maximum participation point is 20 points for each person. Record your activities using the link above.

Abstract

The typesetting for mathematics expressions are powered by KaTeX.

Introduction to the course
Jephian Lin (林晉宏), National Sun Yat-sen University (國立中山大學)
February 20, 2:10 pm – 4:00 pm @ SC4013
We will explain the syllabus and the outline of this course. You are welcome to give suggestions on what you want to learn through this course. For example, you may let me know if you want to know some more about \(\LaTeX\), BibTeX, TikZ, programming, how to write a paper, or anything that you think would benefit your research. A solid mathematics background is important; however, it is also important to present your idea clearly and typeset your formulas property. Otherwise, you will make some mistakes like \(\frac{sinx}{n}=six\), which is terrible. (You should do \(\frac{\sin x}{n}\) instead.)

Some mathematical studies about the phenomena appeared on the excitable media
Yen-Yu Chen (陳彥宇), National Taiwan University (國立臺灣大學)
February 20, 2:10 pm – 3:00 pm @ SC4009-1
On the excitable media, it contains two different states: excited state and resting state. So we can observe some interesting patterns like traveling pulse, traveling spot, spiral wave and so on. To capture these special patterns mathematically, we first consider the wave front interaction model introduced by Zykov and Showalter in 2005. This model describes the boundary of the patterns. Then, under certain conditions, we can show the existence of some special solution which is corresponding to some patterns to the wave front interaction model. Later on, we use the singular limit approach to a FitzHugh–Nagumo type equation to derive a reaction-interface equations. Then, we show the existence of some special patterns to this problem. To understand the mechanism of the appearance of some special patterns, we also study the global dynamics of the solution to the reaction-interface equations with initial data. In this talk, I will show some recent results on one-dimensional space.

Some integral formulas in sub-Riemannian manifolds and their applications
Yen-Chang Huang (黃彥彰), National Taipei University of Nursing and Health Sciences (國立臺北健康護理大學)
February 27, 2:10 pm – 3:10 pm @ SC4009-1
In this talk we consider some geometric invariants with their properties in the model of sub-Riemannian manifolds. We prove that the invariants form a complete set of invariants and uniquely determine the submanifolds of co-dimension one up to a rigid motion. The structure of the group of all rigid motions can be obtained by the approach of Maurer-Cartan. We apply the above results to Integral Geometry and several integral formulas will be derived, including Blaschke-Chern-Santalo's kinematic formula and the solutions for the containment problem. Finally, we also introduce the connection of our works with that of Giovanna Citti et al. on the problems of image completion.

Spectral radius and degree sequence of a graph
Chia-An Liu (劉家安), Xiamen University Malaysia (廈門大學馬來西亞分校)
February 27, 3:20 pm – 4:10 pm @ SC4009-1
Let \(G\) be a simple graph of order \(n\). The spectral radius \(\rho(G)\) of \(G\) is the largest eigenvalue of its adjacency matrix. For each positive integer \(\ell\) at most \(n\), we give a sharp upper bound for \(\rho(G)\) by a function of the first \(\ell\) vertex degrees in \(G\), which generalizes a series of previous results. The idea of the above result further applies to bipartite graphs. Let \(k,p,q\) be positive integers with \(k < p < q+1\). We prove a conjecture stating that the maximum spectral radius of a simple bipartite graph obtained from the complete bipartite graph \(K_{p,q}\) of bipartition orders \(p\) and \(q\) by deleting \(k\) edges is attained when the deleted edges are all incident on a common vertex which is located in the partite set of order \(q\). Applications of these bounds are also provided.

Groups, Logic, and Languages
Meng-Che Ho (何孟哲), Purdue University
March 2, 3:10 pm – 4:00 pm @ SC4009-1
The interplay between group theory and logic had played a crucial role in both areas for many decades. The most famous questions in this intersection is the word problem proposed by Dehn in 1911. The word problem is shown to be unsolvable in general by Novikov in 1955. However, as a logician, the (un)solvability of a decision problem is only the beginning. For an unsolvable problem, computable structure theory gives a framework to study ``how unsolvable'' the problem is. On the other hand, for a solvable problem, formal language theory provides a way to study its complexity. We will survey various past and current results as well as some work in progress in these directions. In particular, we will study the linguistic complexity of word problems and geodesic representatives in finitely-generated groups.

Girls who fell in love with math (video watching)
April 9, 2:10 pm – 3:30 pm @ SC4009-1
This is a documentary movie featuring some woman mathematicians from Taiwan. Please refer to the official website for mode details.
(公播教育版)

Quantum colourings and derangements (video watching)
Chris Godsil, Waterloo University
April 30, 2:10 pm – 3:30 pm @ SC4009-1
The video is from the Virtual Combinatorics Colloquium hosted by Northeast Combinatorics Network. Please refer to the poster for more information.
[ Video on Northeast Combinatorics Network channel ]

Recent progress on the Erdős–Hajnal conjecture (video watching)
Maria Chudnovsky, Princeton University
May 21, 2:10 pm – 3:30 pm @ SC4009-1
The video is from the Virtual Combinatorics Colloquium hosted by Northeast Combinatorics Network. Please refer to the poster for more information.
[ Video on Northeast Combinatorics Network channel ]

The Faber–Krahn property in unweighted trees and semiregular trees
Ling-Yi Huang (黃齡誼), National Sun Yat-sen University (國立中山大學)
June 4, 2:10 pm – 2:30 pm @ SC4013
In this talk, we will explain what is the Faber-Krahn property. We will consider unweighted trees and semiregular trees. If the graph has the Faber–Krahn property in the class, the graph is unique corresponding to the shape.

Eternal vertex cover number of trees
YanWu Chen (陳彥伍), National Sun Yat-sen University (國立中山大學)
June 4, 2:40 pm – 3:00 pm @ SC4013
In this talk, I will introduce the vertex cover set of a graph \(G\). Then I will talk about the eternal problem of the vertex cover set and the least number of eternal vertex cover set of a tree \(T\).

Zero forcing and its computation
Chi Wei (魏齊), National Sun Yat-sen University (國立中山大學)
June 4, 3:10 pm – 3:30 pm @ SC4013
Let \(G(V,E)\) be a simple graph with two colors blue and white on the vertices. A zero forcing set is a subset of vertices such that it can turn all the vertices into blue by some color-change rule. Through the data type Bitset, which represents a set by a unique integer, one may speed up the computation of the minimum zero forcing set.

Characteristic set of weighted trees via Perron values
Ting-Ying Li (李庭瑩), National Sun Yat-sen University (國立中山大學)
June 11, 2:10 pm – 2:30 pm @ SC4013
In this talk, we will introduce the algebraic connectivity of a graph and the characteristic set of the tree. We will study the relation between Perron values and Perron vectors of branches at \(v\). The goal is to compared the Perron values of Type I, and TypeII tree by the Perron Frobenius theory.
(Teaching questionnaire afterward at 14:35 – 14:55.)

Second smallest eigenvalue of the Laplacian matrix for product graphs
Guan-Ying Chen (陳冠穎), National Sun Yat-sen University (國立中山大學)
June 11, 3:00 pm – 3:20 pm @ SC4013
We will discuss the Laplacian eigenvalues of corona graphs, Cartesian product graphs, and cographs. The goal is to find the graph which second smallest eigenvalue multiplicity greater than 1.

Math551 Seminar in Mathematics (I) | 數學書報討論（一）[應數碩]

Math752 Seminar in Mathematics (II) | 數學書報討論（二）[應數博]

Special Announcement regarding COVID-19

Announcements

Course Info top

Further Resources

Learning objectives

Outlines

Evaluation

Tentative Schedule top

Abstract

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Policies/Ethics top

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Grading

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