數 學 年 會

D e c . 8 & 9 國 立 臺 灣 師 範 大 學 數 學 系

Department of Mathematics, National Taiwan Normal University

TMS Annual Meeting 數 學 年 會

2 0 1 8

數 學 年 會

大 會 手 冊

A b s t r a c t B o o k

Ь ᒤ ൂ Տ ڐ ᒤ ൂ Տ

2018年中華民國數學年會

2018 Taiwan Mathematical Society Annual Meeting

會議時間：2018年 12 月8日 (星期六) 至9日 (星期日) 會議地點：國立臺灣師範大學公館校區

主辦單位：中華民國數學會

承辦單位：國立臺灣師範大學數學系

協辦單位：台灣數學教育學會、科技部數學研究推動中心、

國立臺灣師範大學、李梅樹紀念館 贊助廠商：昊青公司

學術委員會Scientific Committee

淡江大學數學系 郭忠勝 召集人 國立臺灣師範大學數學系 林俊吉

國立臺灣大學數學系 王偉仲 國立中央大學數學系 洪盟凱 國立中興大學應用數學系 施因澤 國立政治大學應用數學系 陳隆奇 國立清華大學數學系 蔡志強

承辦單位籌備人員(組織委員會Organizing Committee)

國立臺灣師範大學數學系 林俊吉

國立臺灣師範大學數學系 王婷瑩

國立臺灣師範大學數學系 呂翠珊

國立臺灣師範大學數學系 林延輯

國立臺灣師範大學數學系 張毓麟

國立臺灣師範大學數學系 郭君逸

國立臺灣師範大學數學系 郭庭榕

國立臺灣師範大學數學系 陳賢修

國立臺灣師範大學數學系 黃聰明

國立臺灣師範大學數學系 楊青育

國立臺灣師範大學數學系 楊凱琳

國立臺灣師範大學數學系 劉容真

國立臺灣師範大學數學系 樂美亨

國立臺灣師範大學數學系 謝世峰

國立臺灣師範大學數學系 謝豐瑞

國立臺灣師範大學數學系 朱啓台

國立臺灣師範大學數學系 李小慧

國立臺灣師範大學數學系 李君柔

國立臺灣師範大學數學系 張珈華

國立臺灣師範大學數學系 莊雲閔

國立臺灣師範大學數學系 陳秉君

國立臺灣師範大學數學系 游珮詩

國立臺灣師範大學數學系 黃鴻霖

國立臺灣師範大學數學系 劉欣怡

Sessions

數論與代數 Number Theory and

Algebra

幾何 Geometry

偏微分方程 Partial Differential

Equations

離散數學 Discrete Mathematics

計算數學

Mathematics

機率 Probability

最佳化 Optimization

動態系統與 生物數學

Dynamical Systems and Biomathematics

分析 Analysis

統計 Statistics

數學科普 Popular Mathematics

數學教育 Mathematics

Education

Room G003

圖書館

B102 理學院

M210 數學館

G001 圖書館

M212 數學館

B103 理學院

M310 數學館

M417 數學館

G002 圖書館

M211 數學館

H301 綜合館

B101 理學院 8:30-

9:30 9:30- 10:00

10:00- 10:50

10:50- 11:05 11:05- 11:20

11:20- 12:05

主持人:夏良忠 演講者:王姿月

主持人: 江孟蓉 演講者: 崔茂培

主持人:吳恭儉 演講者:劉太平

主持人: 董立大 演講者: 李渭天

主持人:鄧君豪 演講者:吳金典

主持人:黃啟瑞 演講者:許順吉

主持人:陳界山 演講者:

Yongdo Lim

主持人:陳國璋 演講者:吳昌鴻

主持人:沈俊嚴 演講者:林欽誠

主持人:蔡碧紋 演講者:姚怡慶

主持人:賴以威 演講者:秋山仁

主持人:劉柏宏

演講者:單維彰 *** *** ***

12:05- 13:30

13:30- 13:55

主持人:劉家新 演講者:劉承楷

主持人: 何南國 演講者: 王業凱

主持人:李志豪 演講者:江金城

主持人: 張薰文 演講者: 林晉宏

主持人:李勇達 演講者:嚴健彰

主持人:陳冠宇 演講者:須上苑

主持人: 張毓麟

演講者:黃淑琴 ***

14:00- 14:25

主持人:劉家新 演講者:彭勇寧

主持人: 何南國 演講者: 蔡忠潤

主持人:李志豪 演講者:林英杰

主持人: 張薰文 演講者: 鄭硯仁

主持人:李勇達 演講者:游承書

主持人:陳冠宇 演講者:洪芷漪

主持人: 張毓麟

演講者: 胡承方 ***

14:30- 14:55

主持人:劉家新 演講者:姚為成

主持人: 何南國

演講者: 邱聖夫 *** 主持人: 張薰文

演講者: 商珍綾

主持人:吳金典

演講者:黃杰森 *** 主持人: 張毓麟

演講者: 杜威仕 ***

14:55- 15:20 15:20- 15:45

主持人:劉承楷

演講者:陳光武 *** *** 主持人: 郭君逸

演講者: 黃鵬瑞 *** *** 主持人: 杜威仕

演講者: 蔡豐聲

主持人: 張志鴻 演講者: 張覺心

15:10-15:50 主持人:沈俊嚴 演講者:蔡明誠

主持人: 蔡碧紋

演講者: 李百靈 *** *** *** *** ***

16:00- 16:50 16:50- 18:10 18:30- 21:00

2018年中華民國數學年會

2018 Taiwan Mathematical Society Annual Meeting 2018年12月8日(星期六)

中正堂

H301, 綜合館 H301, 綜合館 Registration

Opening Ceremony

Chair：President Jong-Shenq Guo Plenary Lecture by Professor Fang-Hua Lin

Chair ：Professor Jenn-Nan Wang

報到註冊

年會開幕式 主持人 郭忠勝 理事長 大會演講 林芳華 教授 主持人 王振男 教授

遊戲,思考,學習 數學普及特展

中正堂

2018年中華民國數學年會晚宴

H301, 綜合館 中正堂 H301, 綜合館 13:30-14:15

主持人:沈俊嚴 演講者:黃毅青 14:15-14:55 主持人:沈俊嚴 演講者:王雅書 13:30-14:15

主持人:陳賢修 演講者:

Eliot Fried

14:30-14:55 主持人: 鄭昌源 演講者: 王埄彬

13:30-15:00 Fun學奠數 1. 國中組 2. 國小組 Group Photo

Coffee Break

茶會 Coffee Break

14:00-16:00 數學會是您 的好夥伴!

Plenary Lecture by Professor Motoko Kotani Chair：Professor Jung-Kai Chen

大會演講 Motoko Kotani 教授 主持人 陳榮凱 教授

團體照 H301, 綜合館

中華民國數學會會員大會暨頒獎典禮

13:30-14:15 主持人:姚怡慶 演講者:王維菁 14:20-14:45 主持人: 呂翠珊 演講者: 陳春樹 14:45-15:10 主持人: 呂翠珊 演講者: 黃世豪 茶會

午餐 Lunch

與韓國數學會雙邊會談 Bilateral Talk between KMS & TMS

13:30-15:00 論壇：

因應AI 時代學生該 具備哪些數學能力 主持人兼與談人：

李華倫 其他與談人：

樂美亨 曾俊雄 魏澤人

13:30-14:15 秘數淘學 真實秘數遊戲

14:15-15:00 秘數淘學 真實秘數遊戲 更新日期: 2018年12月6日

Sessions

數論與代數 Number Theory and

Algebra

幾何 Geometry

偏微分方程 Partial Differential

Equations

離散數學 Discrete Mathematics

計算數學

Mathematics

機率 Probability

最佳化 Optimization

動態系統與 生物數學

Dynamical Systems and Biomathematics

分析 Analysis

統計 Statistics

數學科普 Popular Mathematics

數學教育 Mathematics

Education

Room G003

圖書館

B102 理學院

M210 數學館

G001 圖書館

M212 數學館

B103 理學院

M310 數學館

M417 數學館

G002 圖書館

M211 數學館

H301 綜合館

上午: B101 下午:B101(主場), B102, B103(分場)

理學院 8:30-

9:00

9:00- 9:50

9:50- 10:20

10:20- 11:05

主持人:王姿月 演講者:粘珠鳳

主持人: 林俊吉 演講者:

Eliot Fried

主持人: 游森棚 演講者: 周文賢

主持人:鄧君豪 演講者:吳宗信

主持人:許順吉 演講者:陳冠宇

主持人: 許瑞麟 演講者: 孫德鋒

主持人: 陳賢修

演講者: 班榮超 *** *** *** *** ***

11:10- 11:35

主持人:王姿月 演講者:魏福村

主持人: 崔茂培 演講者: 陳志偉

主持人: 林延輯 演講者: 俞韋亘

主持人:鄧君豪 演講者:李勇達

主持人:陳隆奇 演講者:劉聚仁

主持人:孫德鋒 演講者: 許瑞麟

主持人: 陳賢修

演講者: 林得勝 *** *** ***

11:40- 12:05

主持人:王姿月

演講者:康明軒 *** 主持人: 林延輯

演講者: 徐祥峻

主持人:鄧君豪 演講者:許佳璵

主持人:陳隆奇 演講者:黃建豪

主持人:孫德鋒 演講者: 陳鵬文

主持人:陳賢修

演講者:王琪仁 *** *** ***

12:05- 13:30 13:30-

13:55 *** *** *** *** *** *** 主持人: 黃建豪

演講者: 許為明

主持人:曾睿彬

演講者:李俊憲 *** ***

14:00-

14:25 *** *** *** *** *** ***

主持人:黃建豪 演講者:

Chieu Thanh Nguyen

主持人:曾睿彬

演講者:梁育豪 *** ***

14:30-

14:55 *** *** *** *** *** ***

主持人: 黃建豪 演講者:

Jan Harold Mercado Alcantara

*** *** ***

11:10-11:55 主持人:左台益 演講者:郭伯臣

賦歸

中正堂

14:00-16:00 數學會是您 的好夥伴!

13:30-15:00 工作坊：

數學素養評量 主持人:楊凱琳

帶領人：

洪有情 謝豐瑞 林素微 13:30-14:10

主持人:沈俊嚴 演講者:莊智升 14:15-14:55 主持人:沈俊嚴 演講者:吳希淳

10:20-10:45 主持人: 蔡碧紋 演講者: 呂翠珊 10:45-11:10 主持人: 蔡碧紋 演講者: 趙維雄 11:10-11:35 主持人: 蔡碧紋 演講者: 邱詠惠 11:35-12:00 主持人: 蔡碧紋 演講者:楊洪鼎 10:20-11:05

主持人:沈俊嚴 演講者:王昆湶 11:10-11:55 主持人:沈俊嚴 演講者:簡茂丁

13:30-14:15 秘數淘學 1. 真實秘數遊

戲 2. 賽局理論教

你思考

14:15-15:00 秘數淘學 1. 真實秘數遊

戲 2. 賽局理論教

你思考

Plenary Lecture by Professor Wen-Ching Winnie Li Chair：Professor Shun-Jen Cheng

大會演講 李文卿 教授 主持人 程舜仁 教授

13:30-15:00 Fun學奠數 1. 國中組 2. 國小組 午餐 Lunch

茶會 Coffee Break

H301, 綜合館

11:10-11:55 主持人:陳宏賓 演講者:施宣光 10:20-10:45

主持人:郭鴻文 演講者:陳逸昆 10:55-11:20 主持人:郭鴻文 演講者:張覺心

遊戲,思考,學習 數學普及特展

Registration 報到註冊 中正堂

2018 Taiwan Mathematical Society Annual Meeting 2018年12月9日(星期日)

2018年中華民國數學年會

更新日期: 2018年12月6日

Sessions

Number Theory and

Algebra

Geometry

Partial Differential

Equations

Discrete Mathematics

Computational

Mathematics Probability Optimization

Dynamical Systems and Biomathematics

Analysis Statistics Popular Mathematics

Mathematics Education

Room G003

Library

B102 College of Science

M210 Math Building

G001 Library

M212 Math Building

B101 College of Science

M310 Math Building

M417 Math Building

G002 Library

M211 Math Building

H301 General Hall

B101 College of Science 8:30-

9:30

9:30- 10:00

10:00- 10:50

10:50- 11:05 11:05-

11:20

11:20- 12:05

Chair:

Liang-Chung Hsia Speaker:

Tzu-Yueh Wang

Chair:

River Chiang Speaker:

Mao-Pei Tsui

Chair:

Kung-Chien Wu Speaker:

Tai-Ping Liu

Chair:

Li-Da Tong Speaker:

Wei-Tien Li

Chair:

Chun-Hao Teng Speaker:

Chin-Tien Wu

Chair:

Chii-Ruey Hwang Speaker:

Shun-Chi Hsu

Chair:

Jein-Shan Chen Speaker:

Yongdo Lim

Chair:

Kuo-Chang Chen Speaker:

Chang-Hong Wu

Chair:

Chun-Yen Shen Speaker:

Chin-Cheng Lin

Chair:

Pi-Wen Tsai Speaker:

Yi-Ching Yao

Chair:

I-Wei Lai Speaker:

Jin Akiyama

Chair:

Po-hung Liu Speaker:

Wei-Chang Shann

*** *** ***

12:05- 13:30

13:30- 13:55

Chair:

Chia-Hsin Liu Speaker:

Cheng-Kai Liu

Chair:

Nan-Kuo Ho Speaker:

Ye-Kai Wang

Chair:

Jyh-Hao Lee Speaker:

Chin-Cheng Chiang

Chair:

Hsun-Wen Chang Speaker:

Jephian C.-H. Lin

Chair:

Yung-Ta Li Speaker:

Chien-Chang Yen

Chair:

Guan-Yu Chen Speaker:

Shang-Yuan Hsu

Chair:

Yu-Lin Chang Speaker:

Shu-Chin Huang

***

14:00- 14:25

Chair:

Chia-Hsin Liu Speaker:

Yung-Ning Peng

Chair:

Nan-Kuo Ho Speaker:

Chung-Jun Tsai

Chair:

Jyh-Hao Lee Speaker:

Ying-Chieh Lin

Chair:

Hsun-Wen Chang Speaker:

Yen-Jen Cheng

Chair:

Yung-Ta Li Speaker:

Cheng-Shu You

Chair:

Guan-Yu Chen Speaker:

Jyy-I Hong

Chair:

Yu-Lin Chang Speaker:

Cheng-Feng Hu

***

14:30- 14:55

Chair:

Chia-Hsin Liu Speaker:

Wei-Chen Yao

Chair:

Nan-Kuo Ho Speaker:

Sheng-Fu Chiu

***

Chair:

Hsun-Wen Chang Speaker:

Jen-Ling Shang

Chair:

Chin-Tien Wu Speaker:

Chieh-Sen Huang

***

Chair:

Yu-Lin Chang Speaker:

Wei-Shih Du

***

14:55- 15:20

15:20- 15:45

Chair:

Cheng-Kai Liu Speaker:

Kwang-Wu Chen

*** ***

Chair:

Junyi Guo Speaker:

Peng-Ruei Huang

*** ***

Chair:

Wei-Shih Du Speaker:

Feng-Sheng Tsai

Chair:

Chih-Hung Chang Speaker:

Chueh-Hsin Chang

15:10-15:50 Chair:

Chun-Yen Shen Speaker:

Ming-Cheng Tsai

Chair: Pi-Wen Tsai Speaker:

Pai-Ling Li

*** *** *** *** ***

16:00- 16:50

16:50- 18:10 18:30-

21:00

Group Photo

Plenary Lecture by Professor Motoko Kotani Chair：Professor Jung-Kai Chen

Lunch

Bilateral Talk between KMS & TMS

13:30-14:15 Chair:Yi-Ching Yao

Speaker:

Wei-Jing Wang

14:20-14:45 Chair:Tsui-Shan Lu

Speaker:

Chun-Shu Chen

14:45-15:10 Chair:Tsui-Shan Lu

Speaker:

Shih-Hao Huang 13:30-14:15

Chair:

Chun-Yen Shen Speaker:

Ngai-Ching Wong

14:15-14:55 Chair:

Chun-Yen Shen Speaker:

Ya-Shu Wang 13:30-14:15

Chair:

Shyan-Shiou Chen Speaker:

Eliot Fried

14:30-14:55 Chair:

Chang-yuan Cheng Speaker:

Feng-Bin Wang

Coffee Break

H301, General Hall

14:00-16:00 Join Your

Math World!!

13:30-15:00 Forum:

What mathematical competences should we prepare for AI

generations?

Chair and Panelist:

Hua-Lun Li

other Panelists:

Mei-Heng Yueh Chun-Hsiung Tseng

Tzer-jen Wei

13:30-14:15 Mathemagic Escape Authentic Mathemagic

Games

14:15-15:00 Mathemagic Escape (2nd round) 13:30-15:00

Just Fun Math

(1) Junior high

level (2) Elementary

level Coffee Break

2018 Taiwan Mathematical Society Annual Meeting 8 Dec. 2018(Saturday)

Jhong-Jheng Hall

H301, General Hall H301, General Hall

Math Museum

Jhong-Jheng Hall

Registration

Opening Ceremony

Chair：President Jong-Shenq Guo

Plenary Lecture by Professor Fang-Hua Lin Chair ：Professor Jenn-Nan Wang

H301, General Hall

Jhong-Jheng Hall H301, General Hall

TMS Meeting & Award Ceremony Banquet

6 Dec. 2018 Updated

Sessions

Number Theory and

Algebra

Geometry

Partial Differential

Equations

Discrete Mathematics

Computational

Mathematics Probability Optimization

Dynamical Systems and Biomathematics

Analysis Statistics Popular Mathematics

Mathematics Education

Room G003

Library

B102 College of Science

M210 Math Building

G001 Library

M212 Math Building

B101 College of Science

M310 Math Building

M417 Math Building

G002 Library

M211 Math Building

H301 General Hall

Morning: B101 Afternoon:

B101(Main) B102, B103(parallel)

College of Science 8:30-

9:00

9:00- 9:50

9:50- 10:20

10:20- 11:05

Chair:

Tzu-Yueh Wang Speaker:

Chu-Feng Nien

Chair:

Chun-Chi Lin Speaker:

Eliot Fried

Chair:

Sen-Peng Eu Speaker:

Wun-Seng Chou

Chair:

Chun-Hao Teng Speaker:

Jong-Shinn Wu

Chair:

Shun-Chi Hsu Speaker:

Guan-Yu Chen

Chair:

Ruey-Lin Sheu Speaker:

Defeng Sun

Chair:

Shyan-Shiou Chen Speaker:

Jung-Chao Ban

*** *** *** *** ***

11:10- 11:35

Chair:

Tzu-Yueh Wang Speaker:

Fu-Tsun Wei

Chair:

Mao-Pei Tsui Speaker:

Chih-Wei Chen

Chair:

Yen-chi Roger Lin Speaker:

Wei-Hsuan Yu

Chair:

Chun-Hao Teng Speaker:

Yung-Ta Li

Chair:

Lung-Chi Chen Speaker:

Gi-Ren Liu

Chair:

Defeng Sun Speaker:

Ruey-Lin Sheu

Chair:

Shyan-Shiou Chen Speaker:

Jung-Chao Ban

*** *** ***

11:40- 12:05

Chair:

Tzu-Yueh Wang Speaker:

Ming-Hsuan Kang

***

Chair:

Yen-chi Roger Lin Speaker:

Hsiang-Chun Hsu

Chair:

Chun-Hao Teng Speaker:

Chia-Yu Hsu

Chair:

Lung-Chi Chen Speaker:

Chien-Hao Huang

Chair:

Defeng Sun Speaker:

Peng-Wen Chen

Chair:

Shyan-Shiou Chen Speaker:

Chi-Jen Wang

*** *** ***

12:05- 13:30

13:30-

13:55 *** *** *** *** *** ***

Chair:

Chien-Hao Huang Speaker:

Wei-Ming Hsu

Chair:

Jui-Pin Tseng Speaker:

Chun-Hsieh Li

*** ***

14:00-

14:25 *** *** *** *** *** ***

Chair:

Chien-Hao Huang Speaker:

Chieu Thanh Nguyen

Chair:

Jui-Pin Tseng Speaker:

Yu-Hao Liang

*** ***

14:30-

14:55 *** *** *** *** *** ***

Chair:

Chien-Hao Huang Speaker:

Jan Harold Mercado Alcantara

*** *** ***

Plenary Lecture by Professor Wen-Ching Winnie Li Chair：Professor Shun-Jen Cheng

Registration

H301, General Hall

Coffee Break

Closing

Math Musium

14:00-16:00 Join Your

Math World!!

13:30-15:00 Workshop:

Assessing Mathematics

Literacy

Chair:

Kai-Lin Yang

Facilitators:

Yu-Ching Hung Feng-Jui Hsieh

Su-Wei Lin 13:30-14:10

Chair:

Chun-Yen Shen Speaker:

Chih-Sheng Chuang

14:15-14:55 Chair:

Chun-Yen Shen Speaker:

Hsi-Chun Wu

10:20-10:45 Chair: Pi-Wen Tsai

Speaker:

Tsui-Shan Lu

10:45-11:10 Chair: Pi-Wen Tsai

Speaker:

Wei-Hsiung Chao

11:10-11:35 Chair: Pi-Wen Tsai

Speaker:

Yung-Huei Chiou

11:35-12:00 Chair: Pi-Wen Tsai

Speaker:

Hong-Ding Yang 10:20-11:05

Chair:

Chun-Yen Shen Speaker:

Kun-Chuan Wang

11:10-11:55 Chair:

Chun-Yen Shen Speaker:

Mao-Ting Chien

13:30-14:15 Mathemagic Escape (1) Authentic

Mathemagic Games (2) Game Theory Inspired

Thinking

14:15-15:00 Mathemagic Escape (2nd round) Lunch

Jhong-Jheng Hall

13:30-15:00 Just Fun

Math (1) Junior high

level (2) Elementary

level 11:10-11:55

Chair:

Hong-Bin Chen Speaker:

Hsuan-Kuang Shih 10:20-10:45

Chair:

Hung-Wen Kuo Speaker:

I-Kun Chen

10:55-11:20 Chair:

Hung-Wen Kuo Speaker:

Chueh-Hsin Chang

11:10-11:55 Chair:

Tai-Yih Tso Speaker:

Bor-Chen Kuo

Jhong-Jheng Hall

2018 Taiwan Mathematical Society Annual Meeting

9 Dec. 2018(Sunday)

目錄 Table of Contents

【邀請演講 Plenary Speeches】 ... 1

【研究群論文發表 Sessions and Abstracts】 ... 4

01. 數論與代數 Number Theory and Algebra ... 4

02. 分析 Analysis ... 14

03. 幾何 Geometry ... 25

04. 動態系統與生物數學 Dynamical Systems and Biomathematics ... 32

05. 偏微分方程 Partial Differential Equations ... 42

06. 離散數學 Discrete Mathematics ... 49

07. 計算數學 Computational Mathematics ... 61

08. 機率 Probability ... 69

09. 最佳化 Optimization ... 76

10. 統計 Statistics ... 95

11. 數學科普 Popular Mathematics ... 105

12. 數學教育 Mathematics Education ... 109

【附錄】 1. 論文發表注意事項 Guidelines for the speakers ... 112

2. 大會會場示意圖 Site Map ... 113

Plenary Speech

Fang-Hua Lin

Silver Professor, Courant Institute of Mathematical Sciences New York University

E-mail: linf@cims.nyu.edu

Extremum Problems for Laplacian Eigenvalues

Eigenvalue Problems for Laplacians are among most studied ones in classical analysis, partial differential equations, calculus of variations and mathematical physics. In this lecture I shall discuss some recent progress on a couple extremum problems involving Dirichlet eigenvalues of the Laplacian.

These problems have origins in shape optimization, pattern formation,..., and even the data science. We will show how they are related to harmonic maps into singular spaces and some recent works on free boundary value problems involving vector valued functions.

Prof. Lin is currently a Silver Professor of Mathematics at Courant Institute of Mathematical Sciences. He is a world-renowned mathematician in the field of nonlinear analysis and partial differential equations, making important contributions in geometric measure theory, mathematical theory of liquid crystal, homogenization theory, unique continuation property, etc.

Prof Lin graduated from Zhejiang University, China in 1981 and obtained

his PhD from University of Minnesota in 1985. His research output includes more than 160 research papers and three books of lecture notes.

Prof Lin received numerous honors and awards, notably the Alfred P. Sloan Research Fellowship, the Presidential Young Investigator Award, AMS Bôcher Prize, a member of American Academy of Arts and Sciences, and S.S. Chern Prize at ICCM.

1

Plenary Speech

Motoko Kotani

Professor, Mathematical Institute, Tohoku University

E-mail: kotani@math.tohoku.ac.jp

Mathematical challenge to understand Materials structure

Materials is a complex system with hierarchical structure; namely materials consists of atoms, atoms form atomic clusters, atomic clusters from their networks, entangled networks form nano-structures. Therefore it is a challenge to understand relations between structures and functions of materials.

I would like to discuss how mathematics, discrete geometric analysis,

contributes in the challenges. Non-equilibrium materials, topological materials, carbon materials are our targets.

Prof. Kotani got her degree from Tokyo Metropolitan University. After several years as a researcher and lecturer, she joined the Tohoku University in 1999.

Kotani's research is in geometry, mainly on discrete geometry and symmetry of figures.

Her research on discrete geometric analysis, aiming to understand micro-scale structures and macro-scale properties of materials, finds interesting connection of geometry with crystal lattices.

In 2005, she was awarded Saruhashi Prize, awarded to a Japanese female researcher in natural science. In 2012, she was appointed as director of Advanced Institute for Materials Research (AIMR) of Tohoku University. She was President of Math. Soc. of Japan during 2015-2016.

2

Plenary Speech

Wen-Ching Winnie Li

Professor, Department of Mathematics, Pennsylvania State University E-mail: wli@math.psu.edu

The Riemann Hypothesis, Ramanujan conjecture and applications

The Riemann Hypothesis and Ramanujan conjecture are two celebrated open problems in number theory which have important and far reaching consequences. They also appear in different settings. In this talk we discuss their relations and show some applications derived from the occasions where the conjectures hold. This is a survey talk highlighting the interplay between number theory and combinatorics.

Prof. Winnie Li is currently a Distinguished Professor of

Mathematics at the Pennsylvania State University. She is highly recognized for her works in

number theory, where, in particular, she has made outstanding

contributions to automorphic forms.

She is also known for her influential works in applying number theory to areas such as

coding theory and spectral graph theory.

Li graduated from the National Taiwan University in 1970. She received her Ph.D. in mathematics from the University of California, Berkeley, in 1974, and joined the PSU faculty in 1979. She was appointed director of the National Center of

Theoretical Sciences in Taiwan from 2009 to 2014.

Li was awarded the Chern Prize at the International Congress of Chinese

Mathematicians in 2010. She became a fellow of the American Mathematical Society in 2010 and was chosen to give the 2015 Noether Lecture.

3

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4

Diophantine Approximation for Subvarieties and GCD problems

Tzu-Yueh Wang Institute of Mathematics

Academia Sinica

E-mail: jwang@math.sinica.edu.tw

A fundamental problem in Diophantine approximation is to study how well an algebraic number can be approximated by rational numbers. The celebrated Roth’s theorem states that for a fixed algebraic number α, ϵ > 0, and C > 0, there are only finitely many p/q∈ Q, where p and q are relatively prime integers, such that|α −^p_q| ≤_|b|^C2+ϵ.

There are two kinds of generalization of Roth’s theorem. One is to approx- imate an algebraic point by rational points in an arbitrary projective varieties which is done in a recent work of McKinnon and Roth. Another is in the di- rection of Schmidt’s subspace theorem to study Diophantine approximation of rational points to a set of hyperplanes in projective spaces, or more generally a set of divisors in an arbitrary projective variety.

I will discuss a Diophantine inequality in terms of subschemes which is a joint work with Min Ru. In the case of points, it recovers a result of McKinnon and Roth. In the case of divisors, it connects Schmidt’s subspace theorem and the recent Diophantine approximation results obtained by Autissier, Corvarja, Evertse, Faltings, Ferretti, Levin, Ru, W ustholz, Vojta, Zannier, and etc. I will then discuss possible application of the above result to the study of gcd problem which is a joint work with Ji Gou.

5

The structure of triple homomorphisms onto prime algebras

Cheng-Kai Liu

Department of Mathematics

National Changhua University of Education E-mail: ckliu@cc.ncue.edu.tw

A well-known result of Kaup states that a linear bijection between two JB^∗- triples is an isometry if and only if it is a triple isomorphism. Fundamental examples of JB^∗-triples are C^∗-algebras and JB^∗-algebras. From the viewpoint of associative algebras, we characterize the structure of triple homomorphisms from an arbitrary ⋆-algebra onto a prime ∗-algebra. The analogous results for prime C^∗-algebras factor von Neumann algebras and standard operator ∗- algebras on Hilbert spaces are also described. As an application, we show that every triple homomorphism from a Banach ⋆-algebra onto a prime semisimple idempotent Banach ∗-algebra or a prime C^∗-algebra is automatically continuous.

Keywords: Triple homomorphism, prime algebra, Banach algebra, C^∗- algebra, standard operator algebra.

6

Schur-Weyl duality and its variations

Yung-Ning Peng Department of Mathematics

National Central University E-mail: ynp@math.ncu.edu.tw

Let V =Cⁿ be the standard representation of the general linear Lie algebra G = gl(C). Then for any positive integer d, the tensor space V = V^⊗d is naturally aG-module and hence a U(G) is the universal enveloping algebra of G. On the other hand, the symmetric group Sd also acts naturally on V by permuting the tensor factors. As a result,V, can be viewed as a C[Sd]-module as well, whereC[Sd] means the group algebra of Sd. The celebrated Schur-Weyl duality implies that the images of these two actions in the endomorphism space EndV actually form a full centralizer of each other.

In this short talk, we will try to introduce a few variations of the Schur-Weyl duality by replacing the role ofG by other structure (in particular, the periplec- tic Lie superalgebra pn) and suitably modifyingV. In particular, an interesting algebra Ad and it’s affine version, called the affine pereplectic Brauer algebra Pˆ_d⁻, will show up. If time permitted, we will give a diagrammatic realization of ˆP_d⁻ together with a PBW basis which is very similar to that of the Brauer algebras and that of the Nazarov-Wenzl algebras. This talk is based on a joint work with Prof. Chih-Whi Chen (Xiamen University).

Keywords: Schur-Weyl duality, Brauer algebra, pereplectice Lie superal- gebra.

References

[1] Richard Brauer, On algebras which are connected with the semisimple continuous groups, Annals of Mathematics, 38 (1937) 857-872.

[2] Chih-Whi Chen, Yung-Ning Peng, Ane periplectic Brauer algebras, Journal of Algebra, 501 (2018), 345-372.

[3] Dongho Moon, Tensor product representations of the Lie superalgebra p(n) and their centralizers, Communications in Algebra, 31 (2003), 2095-2140.

[4] Maxim Nazarov, Youngs orthogonal form for Brauers centralizer algebra, Journal of Algebra, 182 (1996), 664-693.

7

Representations Functions of Definite Binary Quadratic Forms over F ^q [t]

Wei-Chen Yao

Department of Mathematics University of Taipei E-mail: yao@Utaipei.edu.tw

LetFq be a finite field of odd characteristic. For A, B, C ∈ Fq[t], a binary quadratic form f (x, y) = Ax²+ Bxy + Cy²is called definite if the discriminant mathcalD = B²−4AC has either odd degree or has even degree and non-square leading coefficient in Fq. For m ∈ Fq[t] and f is a definite binary quadratic form, we define N (f, m) by the number of representations of m in f . Let {f1,· · · , fh,· · · , fH} be a representative set of properly equivalent classes of definite binary quadratic forms for given discriminant D and f1,· · · , fh are primitive. We define

R(D, m) = 1 2

∑H i=1

N (f_i, m) and r(D, m) = 1 2

∑h i=1

N (f_i, m).

In this talk, we will discuss properties of these functions and present formulas for these functions.

8

Generalized Harmonic Number Sums and Symmetric Functions

Kwang-Wu Chen Department of Mathematics

University of Taipei E-mail: kwchen@utaipei.edu.tw

We express some general type of infinite series such as

∑∞ n=1

F (Hn⁽¹⁾(z), Hn⁽²⁾(z), . . . , Hn^(ℓ)(z)) (n + z)^s1(n + 1 + z)^s2· · · (n + k − 1 + z)^sk, where F (x1, . . . , x_ℓ)∈ Q[x1, . . . , x_ℓ], Hn^(m)(z) =∑n

j=11/(j + z)^m, and s1, . . . , s_k are nonnegative integers with s1+· · ·+sk≥ 2, as a linear combination of multiple Hurwitz zeta functions and harmonic functions.

Keywords: Symmetric functions, multiple Hurwitz zeta functions

References

[1] S. Akiyama, H. Ishikawa, On analytic continuation of multiple L-functions and related zeta-functions, Analytic Number Theory, C. Jia and K. Mat- sumoto (eds.), Developments in Math. Vol. 6, Kluwer, 2002, pp. 1–16. DOI:

10.1007/978-1-4757-3621-2 1.

[2] K.-W. Chen, Generalized Harmonic Numbers and Euler Sums, Int. J. Num- ber Theory, 13 (2) (2017), 513–528. DOI:10.1142/S1793042116500883.

[3] K.-W. Chen, C.-L. Chung, M. Eie, Sum formulas of multiple zeta values with arguments multiples of a common positive integer, J. Number Theory, 177 (2016), 479–496.

[4] M.-A. Coppo, B. Candelpergher, The Arakawa-Kaneko zeta function, Ra- manujan J., 22.2 (2010), 153–162.

[5] R. L. Graham, D. E. Knuth, O. Patashnik, Concrete Mathematics, second edition, Addison-Wesley, 1994.

[6] M. E. Hoffman, On multiple zeta values of even arguments, arXiv:

1205.7051v4 (2016).

9

[7] M. E. Hoffman, Harmonic-number summation identities, symmetric func- tions, and multiple zeta values, Ramanujan J., 42 (2) (2017), 501–526.

[8] J. P. Kelliher, R. Masri, Analytic continuation of multiple Hurwitz zeta functions, Math. Proc. Camb. Phil. Soc., 145 (2008), 605–617.

[9] I. G. MacDonald, Symmetric Functions and Hall Polynomials, 2nd edition, Claredon Press, 1995.

[10] J. Mehta, G. K. Viswanadham, Analytic continuation of multiple Hurwitz zeta functions, J. Math. Soc. Janpan, 69 (4) (2017), 1431–1442.

[11] A. Sofo, Harmonic number sums in higher powers, J. Math. Anal., 2 (2) (2011), 15–22.

[12] A. Sofo, M. Hassani, Quadratic harmonic number sums, Appl. Math. E- Notes, 12 (2012), 110–117.

[13] R. P. Stanley, Enumerative Combinatorics, vol. 2, Cambridge University Press, 1999.

[14] J. Zhao, Sum formula of multiple Hurwitz-zeta values, Forum Mathe- maticum, 27 (2) (2015), 929-936.

10

Converse theorem on gamma factors

Chu-Feng Nien

College of Mathematics and Statistics Hunan Normal University E-mail: nienpig@hotmail.com

The talk is about converse theorem of gamma factors. After Jacquet’s con- jecture (n× [ⁿ₂] converse theorem) is confirmed, we wonder what information about representations is encoded in n× 1 gamma factors in finite field case and its counterpart of level zero cuspidal representations in p-adic case. In a joint work with Lei Zhang, we use number-theoretic result of Gauss sums to verify n× 1 Local Converse Theorem of cuspidal representations of GLn(Fp), for prime p and n≤ 5. After the communication with Zhiwei Yun, he applied geometric method and established n× 1 Local Converse Theorem for generic representations of GLn(Fq), when n < ^q₂⁻¹√q + 1 and q is a prime power.

11

Green’s functions on Mumford curves

Fu-Tsun Wei

Department of Mathematics National Tsing Hua University E-mail: ftwei@math.nthu.edu.tw

In this talk, we shall introduce an analogue of Green’s function on Mumford curves. The special value of Green’s function at s = 0 interprets the volume of the corresponding curve. Using harmonic analysis on Bruhat-Tits trees, we connect the derivative of Green’s functions at s = 0 with the Manin-Drinfeld theta functions, which enables us to show that the special derivative here is equal to twice of the N`eron’s local height with sign changed.

12

Geometric Decomposition of Affine Weyl Groups

Ming-Hsuan Kang

Department of Applied Mathematics National Chiao-Tung University

E-mail: kmsming@gmail.com

We will introduce a geometric decomposition of affine Weyl groups aris- ing from their actions on Coxeter complexes. This decomposition is length- preserving and gives some new results on invariant theory of affine Weyl groups.

13

分析 Analysis 地 點 ： G 0 0 2 圖 書 館

TMS Annual Meeting

數 學 年 會

2018 ^{數 學 年 會}

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D e c . 9 / 0 9 : 3 0 - 1 5 : 5 0

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Hardy spaces associated with Monge-Ampe`re equation

Chin-Cheng Lin Department of Mathematics

National Central University E-mail: clin@math.ncu.edu.tw

We study the boundedness of singular integrals related to the Monge-Ampe`re equation established by Caffarelli and G utie´rrez. They obtained the L<sup>2</sup>bound- edness. Since then the L<sup>p</sup>, 1 < p < ∞, weak (1, 1) and the boundedness for these operators on atomic Hardy space were obtained by several authors. It was well known that the geometric conditions on measures play a crucial role in the theory of the Hardy space. In this talk, we establish the Hardy space H via the Littlewood-Paley theory with the Monge-Ampe`re measure satisfying the^F doubling property together with the noncollapsing condition, and show the H boundedness of Monge-Ampe`re singular integrals. The approach is based on^F the L² theory and the main tool is the discrete Caldero´n reproducing formula associated with the doubling property only.

15

The No Trade Principle and the Characterization of Compact Beliefs

Ngai-Ching Wong

Department of Applied Mathematics National Chung Hsing University E-mail: wong@math.nsysu.edu.tw

We establish the no trade principle, i.e., the no trade theorem and its con- verse, for any dual pair of bet and extended belief spaces, defined on a given measurable space. A key condition is that, except perhaps one of the agents, everyone else has (weak^∗) compact sets of beliefs. We find out that in most of the models of uncertainty adopted in the economic literature, roughly speaking, the epistemic statement that an agent has a compact set of beliefs is equiv- alent to the economic statement that he has an open cone of positive bets.

This improves our understanding of what compactness actually means within an economic context.

This is a joint work with Man-Chung Ng.

16

2-local isometries on vector-valued Lipschitz function spaces

Ya-Shu Wang

Department of Applied Mathematics National Chung Hsing University

E-mail: clin@math.ncu.edu.tw

Let E and F be Banach spaces. Let S be a subset of the space L(E, F ) of all continuous linear maps from E into F . A (non-necessarily linear nor continuous) mapping ∆ : E→ F is a 2-local S-map if for any x, y ∈ E, there exists Tx,y∈ S, depending on x and y, such that

∆(x) = Tx,y(x) and ∆(y) = Tx,y(y).

In this talk, I will present a description of the 2-local isometries on the Ba- nach space Lip(X, E) of vector-valued Lipschitz functions from compact metric space X to Banach space E in terms of a generalized composition operator.

Also, I will show when every 2-local (standard) isometry on Lip(X, E) is both linear and surjective.

Co-author(s): Jim´enez-Vargas, L. Li, A. M. Peralta and L. Wang.

17

Maps between different matrix spaces preserving disjoint matrix pairs

Ming-Cheng Tsai General Education Center

National Taipei University of Technology E-mail: mctsai2@mail.ntut.edu.tw

In this talk, the structure of the linear maps between two different matrix spaces preserving disjointness is characterized. Moreover, some related results for zero product preservers between matrix algebras are obtained. This is a join work with Chi-Kwong Li, Ya-Shu Wang, Ngai-Ching Wong.

Keywords: disjointness preserver, zero product, matrix spaces, matrix al- gebras

18

The Convergence of Calderón Reproducing Formulae of Two Parameters on Some Classical

Function Spaces

Kun-chuan Wang

Department of Applied Mathematics National Dong Hwa University E-mail: kcwang@gms.ndhu.edu.tw

The Calderón reproducing formula is the most important in the study of harmonic analysis, which has the same property as the one of approximate identity in many special function spaces. In this talk, we use the idea of sep- aration variables and molecular decomposition to extend single parameter into two-parameters and discuss the convergence of Calderón reproducing formula of two-parameters in some generalized function spaces of two parameters. Mainly, we focus on Besov spaces in two-parameter and show that these spaces are well- defined by Plancherel-Pôlya inequalities. Consequently, we obtain the norm equivalence between Besov spaces and corresponding sequence space in two- parameter. Also we show the convergence of Calderón reproducing formula in Besov space.

Keywords: atomic decomposition, Calderón reproducing formula, Littlewood- Paley, Plancherel-Pôlya inequality

References

[1] Bui, H.-Q., Paluszyński M. and Taibleson M.H., A maximal function char- acterization of weighted Besov-Lipschitz and Triebel-Lizorkin spaces, Stu- dia Math. 119 (1996), 219-246.

[2] Deng, D.G., Han, Y.-S. and Yang, D.C., Besov spaces with non-doubling measures. Trans. Amer. Math. Soc., 358 (2006), 2965-3001.

[3] Frazier, M., Jawerth, B., Decomposition of Besov spaces, Indiana Math.

J. 34 (1985), 777-799.

[4] Frazier, M. and Jawerth, B., A discrete transform and decompositions of distribution spaces, J. Funct. Anal, 93 (1990), 34-170.

19

[5] Han, Y.-S., Lee, M.-Y., Lin, C.-C. and Lin, Y.-C., Calderón-Zygmund operators on product Hardy spaces, J. Funct. Anal. 258 (2010), 2834- 2861.

[6] Han, Y.-S., Lu, S.Z., Yang, D.C., Inhomogeneous Besov and Triebel- Lizorkin spaces on spaces of homogeneous type, Approx. Theory Appl (N.S.), 15 (1999), no. 3, 37-65.

[7] Han, Y., Yang, D.C., New characterizations and applications of inhomoge- neous Besov and Triebel-Lizorkin spaces on homogeneous type spaces and fractals, Dissertationes Math. (Rozprawy Mat.) 403 (2002), 102 pp.

[8] Johnson, R., Temperatures, Riesz potentials, and the Lipschitz spaces of Herz, Proc. Lond. Math. Soc. 27 (1973), 290-316.

[9] Peetre, J., New thoughts on Besov spaces, Duke University Mathematics Series, No. 1. Mathematics Department, Duke University, Durham, NC, 1976.

[10] Taibleson, M. H., On the Theory of Lipschitz Spaces of Distributions on Euclidean n-Space: I. Principal Properties, J. Math. Mech., 13 (1964), 407-479.

[11] Triebel, H., Theory of Function Spaces, Monographs in Mathematics, 78 Birkh¨auser Verlag, Basel, 1983.

[12] Weisz, F., On duality problems of two-parameter martingale Hardy spaces, Bull. Sci. Math. 114 (1990), no. 4, 395-410.

[13] Weisz, F., Interpolation between two-parameter martingale Hardy spaces, the real method, Bull. Sci. Math. 115 (1991), no. 3, 253-264.

[14] Weisz, F. The boundedness of the two-parameter Sunouchi operators on Hardy spaces, Acta Math. Hungar. 72 (1996), no. 1-2, 121-152.

[15] Yuan, W., Sawano, Y. and Yang, D.C., Decompositions of Besov-Hausdorff and Triebel-Lizorkin-Hausdorff spaces and their applications, J. Math.

Anal. Appl. 369 (2010), no. 2, 736-757.

20

Linear matrix representations of ternary forms

Mao-Ting Chien Department of Mathematics

Soochow University mtchien@scu.edu.tw

Peter Lax (1958) conjectured that every hyperbolic ternary form F (t, x, y) of degree n admits a determinantal linear matrix representation, i.e., there exist n× n real symmetric matrices H and K satisfying F (t, x, y) = det(tIn+ xH + yK). Helton and Vinnikov confirmed in 2007 the Lax conjecture is true. In this talk, we study the linear matrix representations of the hyperbolic ternary forms associated to some matrices.

Keywords: Hyperbolic ternary form, determinantal representation, Lax conjecture.

References

[1] Mao-Ting Chien, Hiroshi Nakazato, Unitary similarity of the determinan- tal representation of unitary bordering matrices, Linear Algebra Appl., 541(2018), 13-35.

[2] Mao-Ting Chien, Hiroshi Nakazato, Symmetric representation of ternary forms associated to some Toeplitz matrices, Symmetry, 10(2018), 55;

doi:10.3390/sym10030055

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Douglas-Rachford Algorithm for The Generalized DC Programming in Hilbert Spaces

Chih-Sheng Chuang

Department of Applied Mathematics National Chiayi University

E-mail: cschuang@mail.ncyu.edu.tw, cschuang1977@gmail.com

In this paper, we first study the generalized DC programming in real Hilbert space:

(GDCP) argminx∈H{f(x) = φ(x) + g(x) − h(x)},

where H is a real Hilbert space, φ, g : H → (−∞, ∞] are proper, strongly con- vex, and lower semicontinuous functions, and h : H → (−∞, ∞] is a Fréchet dif- ferentiable with the gradient ∇f(x). Next, we give the Douglas-Rachford algo- rithm and Peaceman-Rachford algorithm to study the generalized DC program- ming. Next, we also study the split generalized DC programming by proposing a split Douglas-Rachford algorithm.

Keywords: Douglas-Rachford algorithm, Peaceman-Rachford algorithm, DC programming, strongly convexity, strongly monotonicity.

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Poincaré Lemma on Some SubRiemannian Manifolds

Hsi-Chun Wu

Department of Mathematics National Central University E-mail: flyinmoon0217@yahoo.com.tw

Let X ={X1, X2, . . . , Xm} be m linearly independent vector fields defined on an n-dimensional manifoldMnwith m≤ n, and assume that X satisfies the bracket generating property: the vector fields X and finitely many steps of their Lie brackets span TMn. Therefore,Mn can be recognized as a subRiemannian manifold by Chow’s theorem [6] and the Carnot-Carathéodory distance. Let V = (a1, a2, . . . , am) be a vector-valued function defined on Mn where aj, j = 1, . . . , m are smooth functions. The function V is said to be conservative if there exists a function f , called the potential function, that satisfies the following system

X₁f = a₁, X₂f = a₂, · · · Xmf = a_m.

It is known that in [2], in virtue of the curl operator [7], a characterization of conservative vector fields, called the integrability condition, on the Heisenberg groupH¹is provided as

{ X₁²b = (X1X2+ [X1, X2])a, X₂²a = (X2X1+ [X2, X1])b,

where X1 = ∂x− 2y∂z, X2 = ∂y+ 2x∂z, a, b are smooth functions, and [·, ·] is the Lie bracket. In [3], a potential function onH¹ is given by

f (x, y, z) =

∫ 1 0

⟨U(γ(t)), ˙γ(t)⟩dt,

where ⟨·, ·⟩ is a subRiemannian metric, U = aX1+ bX2, and γ is a geodesic connecting (x, y, z) and the origin.

In this talk, I will discuss integrability conditions and potential functions on two important examples in subRiemannian manifolds: the Heisenberg groups Hⁿand the quaternion Heisenberg group qH¹[4, 5]. The integrability conditions can be found by using the curl tensor [1]

(curl U)(X, Y ) = Y g(U, X) − Xg(U, Y ) + g(U, [X, Y ]),

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where U, X, Y are vector fields and g is a Riemannian metric. The potential functions related to conservative vector fields are able to be solved explicitly in integral forms.

Keywords: Bracket generating property, Heisenberg group, Curl, Integra- bility condition, Poincaré lemma

References

[1] O. Calin and D. C. Chang, Geometric mechanics on Riemannian manifolds:

applications to partial differential equations, Birkhäuser Boston, 2005. doi:

https://doi.org/10.1007/b138771

[2] O. Calin, D. C. Chang, and M. Eastwood, Integrability conditions for Heisenberg and Grushin-type distributions, Anal. Math. Phys., 4 (2014), 99-114. doi: 10.1007/s13324-014-0073-1

[3] O. Calin, D. C. Chang, and J. Hu, Poincaré’s lemma on the Heisenberg group, Adv. in Appl. Math., 60 (2014), 90-102.

http://dx.doi.org/10.1016/j.aam.2014.08.003

[4] D. C. Chang, Y. S. Lin, H. C. Wu, and N. Yang, Poincaré lemma on Heisenberg groups, Applied Analysis and Optimization, 1 (2017), 283-300.

[5] D. C. Chang, N. Yang, and H. C. Wu, Poincaré lemma on quaternion- like Heisenberg groups, Canad. Math. Bull., 61 (2018), 495-508.

http://dx.doi.org/10.4153/CMB-2017-027-4

[6] W. L. Chow, Uber Systeme van Linearen partiellen Differentialgleichungen erster Ordnung, Math. Ann., 117 (1939), 98-105.

[7] B. Franchi, N. Tchou, and M. C. Tesi, Div-curl type theorem, H-convergence and Stokes formula in the Heisenberg group, Comm. Contemp. Math., 8 (2006), 67-99.

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幾何 Geometry 地 點 ： B 1 0 2 理 學 院

TMS Annual Meeting

數 學 年 會

2018 ^{數 學 年 會}

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Deformation of area decreasing maps by mean curvature flow

Mao-Pei Tsui

Department of Mathematics National Taiwan University E-mail: maopei@math.ntu.edu.tw

In this talk, I will present some recent results about the the evolution of an area decreasing map induced by its mean curvature. I will explain the key esti- mates in proving the longtime existence and convergence results under suitable curvature conditions.

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Revisit the small sphere limits of Wang-Yau quasi-local mass

Ye-Kai Wang

Department of Mathematics National Cheng Kung University E-mail: ykwang@mail.ncku.edu.tw

A fundamental problem in general relativity is to measure the energy of gravitational field in an extended but finite region. The Wang-Yau quasi-local mass is proposed in 2008 to tackle the problem. Besides positivity, theWang-Yau quasi-local mass verifies various classical limits: It recovers ADM mass, Bondi- Sachs energy-momentum for large spheres at spatial infinity and null infinity, and Bel-Robinson tensor for small spheres in vacuum spacetimes. In this talk, we present another approach to the small sphere limits using the idea from the proof of positive mass theorem. This is a joint work with Po-Ning Chen, Mu-Tao Wang, and Shing-Tung Yau.

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Global uniqueness of the minimal sphere in the Atiyah–Hitchin manifold

Chung-Jun Tsai Department of Mathematics

National Taiwan University E-mail: cjtsai@ntu.edu.tw

In a hyper-Kahler 4-manifold, holomorphic curves are stable minimal sur- faces. One may wonder whether those are all the stable minimal surfaces.

Micallef gave an affirmative answer in many cases. However, this cannot be true in general. Micallef and Wolfson found that the minimal sphere in the Atiyah–Hitchin manifold is strictly stable, but cannot be holomorphic with respect to any compatible complex structure. The minimal sphere in the Atiyah–

Hitchin manifold is conjectured to be quite rigid.

In this talk, we will first review the construction of the Atiyah–Hitchin man- ifold, and then explain the uniqueness of that minimal sphere. This is based on a joint work with Mu-Tao Wang.

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Introduction to Hochschild (co)homology

Sheng-Fu Chiu Institute of Mathematics

Academia Sinica

E-mail: ykwang@mail.ncku.edu.tw

In this talk I will introduce the notion of Hochschild (co)homology of cate- gories satisfying certain microlocal conditions. If time permits, I will discuss its application to symplectic geometric quantities such as displacement energy.

Keywords: Hochschild cohomology, displacement energy, microlocal con- dition.

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Möbius Kaleidocycles:

A New Class of Everting Ring Lnkages

Eliot Fried

Mathematics, Mechanics, and Materials Unit

Okinawa Institute of Science and Technology Graduate University E-mail: eliot.fried@oist.jp

Many mechanical devices from scissors to robotic arms are characterizable as ‘linkages’ or sets of rigid links connected by moving joints. Known linkages displaying a single degree-of-freedom, which facilitates control, have hitherto consisted of six or fewer links. In this talk, we will introduce a new class of one- degree-of-freedom ring linkages: ‘Möbius kaleidocycles’. These objects consist of seven or more identical hinge-joined links and might thus serve as build- ing blocks in positioning, extrusion, and pultrusion systems, to instance a few among many promising applications in engineering, architecture, robotics, and chemistry. They also pose a myriad of intriguing fundamental geometrical and topological questions, some of which will be touched upon in this talk. This is joint work with postdoctoral scholar Johannes Schönke.

Keywords: spatial mechanisms, nonorientability, single degree-of-freedom

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Geometry in Big Data

Chih-Wei Chen

Department of Applied Mathematics National Sun Yet-sen University E-mail: chencw@math.nsysu.edu.tw

I will talk about the interactions between geometry and data analysis, espe- cially nonlinear dimensionality reductions.

Keywords: dimensionality reduction, manifold learning

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動態系統與生物數學

Dynamical Systems and Biomathematics

地 點 ： M 4 1 7 數 學 館

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