最新消息
【TWSIAM DIGEST】2020年10月
TWSIAM Digest
發行日期：2020年10月07日
期別：2020年10月
本期主題：
[研討會訊息]第十一屆臺灣無網格法與邊界元素法學術研討會, 2020/10/17
[研討會訊息] Quantum Information Science (QIS) and Mathematics, 2020/10/17
[演講公告] Nonlinear Phenomena in Evolutionary Partial Differential Equations, 2020/10/06
[演講公告] On The Newform Problem for Split SO(2n+1), 2020/10/07
[演講公告] Curves on K3 Surfaces, 2020/10/09, Zoom, Online seminar
[演講公告] Counting Richelot Isogenies of Superspecial Curves of Genus 2, 2020/10/09, Zoom, Online seminar
[工作機會]國立中興大學應用數學系誠徵專任助理教授以上2名(收件截止日期：109/11/08，隨到隨審)
[工作機會]國立臺北商業大學財經學院徵聘專案教師(自2020/09/17-2020/10/30)
[工作機會] Advanced Algorithm Developer at TSMC
[其他]力成科技教育基金會【2020AI人才訓練營】
台灣工業與應用數學會將於每月定期發行TWSIAM Digest。
如您有最新的研究議題或重要的研究成果，個人動態，研討會訊息、工作機會、文章與書籍的推廣與分享、計劃徵求、學會的贊助等，歡迎您踴躍分享第一手的相關資訊與此平台的會員們！
我們會在每月初發行TWSIAM Digest，期望藉由您提供的資訊分享，能夠促成更多台灣工業界、科技界與數學界的交流與發展！
投稿TWSIAM Digest：https://bit.ly/2CmHon6
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From：國立臺灣海洋大學河海工程學系<This email address is being protected from spambots. You need JavaScript enabled to view it.>
日期：2020/10/17
類別：研討會訊息
主旨：第十一屆臺灣無網格法與邊界元素法學術研討會
活動網址：http://alumni.hre.ntou.edu.tw/?page_id=80
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From：NCTS
日期：2020/10/17
類別：研討會訊息
主旨：Quantum Information Science (QIS) and Mathematics
內容：Quantum Information Science (QIS) has emerged in many disciplines among physical sciences, materials science, computer science, mathematics, and engineering, for the demands for novel computers, secure communication, and higher resolution sensors to go beyond the scaling limits of classical technologies. As the mother of all the sciences, mathematics definitely is involved everywhere in QIS. This activity aims to initiate the dialogue between researchers in QIS and mathematicians in Taiwan. In our first contact, theorists from the foundation of quantum mechanics, quantum error-correcting codes, quantum communication protocols/channel capacity theory, and quantum cryptography/quantum complexity theory will introduce the terminologies, mathematical structures, unsolved problems, and the application targets to mathematicians. Concepts and paradigms will be stressed from scratch, in order to provide the fundamental knowledge and tools necessary for any possible exploration and collaboration.
活動網址：http://www.ncts.ntu.edu.tw/events_2_detail.php?nid=286
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From：NCTS
日期：2020/10/06
類別：演講公告
主旨：Nonlinear Phenomena in Evolutionary Partial Differential Equations
內容：The prediction and measurement of ecological niche are fundamental part of modern ecology in both practical and theoretical aspects. It has strong relationship with competitive Lotka-Volterra system and can be served as an intuitive approach to study competition interaction. I will introduce some basic idea of niche theory in the first few parts and talk about my recent study of the connection between niche theory and traveling wave theory in 2 component DLV ＆ evolutionary game theory in the last parts of this speech.
活動網址：http://www.ncts.ntu.edu.tw/events_1_detail.php?nid=1806
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From：NCTS
日期：2020/10/07
類別：演講公告
主旨：On The Newform Problem for Split SO(2n+1)
內容：https://tinyurl.com/yyvgbrc6
活動網址：http://www.ncts.ntu.edu.tw/events_1_detail.php?nid=1808
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From：NCTS
日期：2020/10/09, Zoom, Online seminar
類別：演講公告
主旨：Curves on K3 Surfaces
內容：I will survey the recent completion (joint with Chen-Liedtke) of the remaining cases of the conjecture that a projective K3 surface contains infinitely many rational curves. As a consequence of this along with the Bogomolov-Miyaoka-Yau inequality and the deformation theory of stable maps, I will explain (joint with Chen) how in characteristic zero one can deduce the existence of infinitely many curves of any geometric genus moving with maximal variation in moduli on a K3 surface. In particular this leads to an algebraic proof of a theorem of Kobayashi on vanishing of global symmetric differentials and applications to 0-cycles.
活動網址：http://www.ncts.ntu.edu.tw/events_1_detail.php?nid=1757
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From：NCTS
日期：2020/10/09, Zoom, Online seminar
類別：演講公告
主旨：Counting Richelot Isogenies of Superspecial Curves of Genus 2
內容：Recently, supersingular elliptic curve isogeny cryptography has been extended to the genus-2 case by using superspecial curves of genus 2 and their Richelot isogeny graphs. In view of this situation, we examine the structure of Richelot isogenies of superspecial curves of genus 2, and give a characterization of decomposed Richelot isogenies. We also give a concrete formula of the number of such decomposed Richelot isogenies up to isomorphism between superspecial principally polarized abelian surfaces. This is a joint work with Katsuyuki Takashima (Mitsubishi Electic Co.).
活動網址：http://www.ncts.ntu.edu.tw/events_1_detail.php?nid=1758
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From：國立中興大學應用數學系< This email address is being protected from spambots. You need JavaScript enabled to view it.>
日期：收件截止日為109/11/08，隨到隨審
類別：工作機會
主旨：國立中興大學應用數學系誠徵專任助理教授以上2名
詳細資訊：http://www.amath.nchu.edu.tw/
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From：國立臺北商業大學財經學院<This email address is being protected from spambots. You need JavaScript enabled to view it.>
日期：自2020/09/17至2020/10/30止
類別：工作機會
主旨：國立臺北商業大學財經學院徵聘專案教師
詳細資訊：https://cob.ntub.edu.tw/p/406-1016-79787,r247.php?Lang=zh-tw
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From：王偉仲<This email address is being protected from spambots. You need JavaScript enabled to view it.>
類別：工作機會
主旨：Advanced Algorithm Developer at TSMC
內容：The candidate will have responsibility to develop & implement synergetic Image/GDS/Simulation co-processing algorithms, as well as to sustain production line - with continuous improvement of yield and productivity of advanced technology nodes.
Requirements:
(1) Master or Ph.D. degree in EE, CS, Physics, Applied Math or related engineering fields.
(2) Demonstrable > 2+ year hands-on experiences in advanced algorithm code development:
Expertise in Matlab, Python, Linux, Optimization, Machine Learning & EDA/GDS SW are must;
C++ & Optics Simulation experiences are plus.
(3) Good problem solving ability and creative thinking
(4) Positive & Can-Do working attitude with strong ambition to accept challenges
(5) Fluent English communication
Location：Hsinchu
Contact Window：Alice Chuang <This email address is being protected from spambots. You need JavaScript enabled to view it.>
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From：王偉仲<This email address is being protected from spambots. You need JavaScript enabled to view it.>
日期：2020/11/21起
類別：其他
主旨：力成科技教育基金會【2020AI人才訓練營】
內容：力成科技體認人工智慧是未來產業發展趨勢，為普及AI基礎知識並培養AI人才，力成科技教育基金會於11/21起與人工智慧科技基金會合作開辦【2020AI人才訓練營】，合計4天共5堂AI概念課程。
活動時間 : 2020/11/21(六)9:00-16:00、2020/11/28(六)9:00-12:00、2020/12/05(六)9:00-12:00、2020/12/12(六)9:00-17:00
報名費用 : 全程免費
上課地點 : 力成科技總部第三廠區(3D)
地址：新竹縣湖口鄉新竹工業區大同路15號(新豐火車站步行三分鐘)
任何課程相關問題請洽力成科技：(03)5980300#338636 陳瑩娜/Chole、#338619 李怡萱/Annie
活動網址：https://infonews.nctu.edu.tw/files/20200900052/AI人才培訓營-招生海報.jpg
【TWSIAM DIGEST】2020年09月
TWSIAM Digest
發行日期：2020年09月02日
期別：2020年09月
本期主題：
[研討會訊息] 2020 Workshop for Young Scholars on Applied Mathematics, 2020/09/03
[研討會訊息] The Taiwan Number Theory Symposium, 2020/09/09-09/11
[研討會訊息] NCTS Data Sciences Forum, 2020/09/08
[研討會訊息] Seminar of Algebraic Geometry in East Asia-Counting Sheaves on Calabi-Yau 4-folds (線上seminar Zoom), 2020/09/11
[研討會訊息] Seminar of Algebraic Geometry in East Asia-Birationality Centers and Cremona Groups (線上seminar Zoom) , 2020/09/11
[工作機會]國立彰化師範大學科學教育研究所誠徵專任教師, 109年09月30日截止(以郵戳為憑)
[工作機會]淡江大學數學系109學年度延攬師資, 至109 年9 月13日截止
台灣工業與應用數學會將於每月定期發行TWSIAM Digest。
如您有最新的研究議題或重要的研究成果，個人動態，研討會訊息、工作機會、文章與書籍的推廣與分享、計劃徵求、學會的贊助等，歡迎您踴躍分享第一手的相關資訊與此平台的會員們！
我們會在每月初發行TWSIAM Digest，期望藉由您提供的資訊分享，能夠促成更多台灣工業界、科技界與數學界的交流與發展！
投稿TWSIAM Digest：https://bit.ly/2CmHon6
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From：交通大學丘成桐中心<This email address is being protected from spambots. You need JavaScript enabled to view it.>
日期：2020/09/03
類別：研討會訊息
主旨：2020 Workshop for Young Scholars on Applied Mathematics
Invited Speakers:
陳孟豁教授(中正大學)
樂美亨教授(台灣師範大學)
葉均承教授(高雄師範大學數學系)
陳宏銘教授(東海大學)
曾仲麟博士(清華大學)
張俊偉博士(國家理論科學研究中心)
梁長雯女士(中央大學)
林佳威先生(交通大學)
活動網址：https://yaucenter.web.nctu.edu.tw/?p=3497&lang=tw
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From：NCTS
日期：2020/09/09-09/11
類別：研討會訊息
主旨：The Taiwan Number Theory Symposium
內容：
The goal of the Taiwan Number Theory Symposium is twofold. We bring together the number theory community in Taiwan to share their recent research progress, and meanwhile, take this opportunity to provide an orientation to applying various research resources for our graduate students and young scholars in number theory.
We in particular encourage graduate students, postdoctoral fellows and young faculty to take part in the symposium.
活動網址：http://www.ncts.ntu.edu.tw/events_2_detail.php?nid=278
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From：NCTS
日期：2020/09/08
類別：研討會訊息
主旨：NCTS Data Sciences Forum
內容：
Airflow signal encodes rich information about the respiratory system. While the gold standard for measuring airflow is to use a spirometer with an occlusive seal, this is not practical for ambulatory monitoring of patients. Advances in sensor technology have made measurement of motion of the thorax and abdomen feasible with small inexpensive devices, but estimation of airflow from these time series is challenging. We propose to use the nonlinear-type time-frequency analysis tool, synchrosqueezing transform, to properly represent the thoracic and abdominal movement signals as the features, which are used to recover the airflow by a locally stationary Gaussian process. We show that, using a dataset that contains respiratory signals under normal sleep conditions, an accurate prediction can be achieved by fitting the proposed model in the feature space both in the intra- and inter-subject setups. We also apply our method to a more challenging case, where subjects under general anesthesia underwent transitions from pressure support to unassisted ventilation to further demonstrate the utility of the proposed method.
This is joint work with Yu-Min Chung (Math and Stat, UNC-Greensboro), Yu-Bo Wang (Math and Stat Clemson), Jeff Mandel (Anesthesiology & Critical Care, UPenn), and Hau-Tieng Wu (Math and Stat, Duke & NCTS).
活動網址：http://www.ncts.ntu.edu.tw/events_1_detail.php?nid=1764
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From：NCTS
日期：2020/09/11
類別：研討會訊息
主旨：Seminar of Algebraic Geometry in East Asia-Counting Sheaves on Calabi-Yau 4-folds (線上seminar Zoom)
內容：
We define a localised Euler class for isotropic sections, and isotropic cones, in SO(N) bundles. We use this to give an algebraic definition of Borisov-Joyce sheaf counting invariants on Calabi-Yau 4-folds. When a torus acts, we prove a localisation result. This talk is based on the joint work with Richard. P. Thomas.
活動網址：http://www.ncts.ntu.edu.tw/events_1_detail.php?nid=1754
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From：NCTS
日期：2020/09/11
類別：研討會訊息
主旨：Seminar of Algebraic Geometry in East Asia-Birationality Centers and Cremona Groups (線上seminar Zoom)
內容：
I will introduce a framework to account for the ambiguity of stable birational types of a sequence of centers for birational transformations. I will explain in which settings the introduced invariants are nonvanishing, and give applications to the structure of Cremona groups over various fields (based on joint work in progress with H.-Y. Lin and S. Zimmermann).
活動網址：http://www.ncts.ntu.edu.tw/events_1_detail.php?nid=1753
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From：國立彰化師範大學科學教育研究所<This email address is being protected from spambots. You need JavaScript enabled to view it.>
日期：截止日期至109年09月30日(以郵戳為憑)
類別：工作機會
主旨：國立彰化師範大學科學教育研究所誠徵專任教師
內容：
職級：助理教授（含）以上。
名額：專任教師二名。
聘期：110年2月1日起聘。
資格：具數學教育、科學教育、工程教育(資工、機電...等)或跨領域之博士學位者。
網址：http://gise.ncue.edu.tw/2020/08/17/科教所徵聘教師/
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From：淡江大學數學系
日期：至109 年9 月13日截止
類別：工作機會
主旨：淡江大學數學系109學年度延攬師資
內容：
擬聘職級為助理教授(含)以上，新聘專任講師及助理教授均以約聘方式聘任，聘任第二年通過教師評鑑及三級教師評審委員會者，得改聘為編制內專任教師，改聘後敍薪及升等均採計約聘期間年資。
應徵教師請於109 年8 月27日至109 年9 月13日於「淡江大學教職員招募系統」登錄並上傳相關資料。
【TWSIAM DIGEST】2020年08月
TWSIAM Digest
發行日期：2020年08月03日
期別：2020年08月
本期主題：
[TWSIAM]第八屆台灣工業與應用數學會年會暨第三屆第三次會員大會(含理監事改選)已於2020/07/24假國立成功大學圓滿結束
[研討會訊息] Meet physicians, mathematicians and statistcians, 2020/08/01
[研討會訊息] Second NCTS PDE Symposium, 2020/08/27
[工作機會]國立中正大學數學系誠徵專任教師(申請截止日至2020年9月15日截止)
[工作機會]中央研究院統計科學研究所誠徵助研究員、副研究員、研究員(收件截止日期為2020年12月27日)
[其他] 2020 NCTS Summer Course on Mathematical Biology, 2020/07/27-2020/08/05
[其他] 2020 NCTS Summer Course on Dynamical Systems: Dynamics and Thermodynamics on Expanding Maps, 2020/08/07-2020/09/04
台灣工業與應用數學會將於每月定期發行TWSIAM Digest。
如您有最新的研究議題或重要的研究成果，個人動態，研討會訊息、工作機會、文章與書籍的推廣與分享、計劃徵求、學會的贊助等，歡迎您踴躍分享第一手的相關資訊與此平台的會員們！
我們會在每月初發行TWSIAM Digest，期望藉由您提供的資訊分享，能夠促成更多台灣工業界、科技界與數學界的交流與發展！
投稿TWSIAM Digest：https://bit.ly/2CmHon6
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From：NCTS
日期：2020/08/01
類別：研討會訊息
主旨：Meet physicians, mathematicians and statistcians
內容：We will gather physicians and mathematicians/statisticians that have common interest in biomedical signal processing in this event. Several speakers will give briefs talks to introduce physicians why math is important and how math can help, and to let mathematicians/statisticians know why there are a lot of opportunities from medicine.
活動網址：http://www.ncts.ntu.edu.tw/events_2_detail.php?nid=281
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From：NCTS
日期：2020/08/27
類別：研討會訊息
主旨：Second NCTS PDE Symposium
內容：This is the second NCTS PDE symposium. We aim to bring experts and young researchers in PDEs and related disciplines together to introduce their current works and explore new ideas. We expect by joining this series of symposium, our researchers can have chances to talk to each other often to inspire each other.
活動網址：http://www.ncts.ntu.edu.tw/events_2_detail.php?nid=282
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From：國立中正大學數學系<This email address is being protected from spambots. You need JavaScript enabled to view it.>
日期：申請截止日至2020年9月15日截止
類別：工作機會
主旨：國立中正大學數學系誠徵專任教師
資格：具國內外數學及統計相關領域之博士學位
應徵方式：意者請將完整的個人資料(含著作目錄、五年內之重要著作、研究成果自述及未來三年之研究構想）、三封推薦信、學歷證書或證明文件及成績單（申請者依需要程度，自我評估是否提供）寄至621嘉義縣民雄鄉大學路168 號國立中正大學數學系卓建宏主任收
活動網址：http://www.math.ccu.edu.tw/math/?p=4125
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From：中央研究院統計科學研究所< This email address is being protected from spambots. You need JavaScript enabled to view it.>
日期：截止日期為2020年12月27日
類別：工作機會
主旨：中央研究院統計科學研究所誠徵助研究員、副研究員、研究員
內容：有意申請者需要具備統計、生物統計、資訊工程、資料科學或相關領域的博士學位，並請附上以下申請資料：(1)求職信、(2)最新的個人履歷、 (3)詳細的著作目錄、(4)研究計畫、(5)三封推薦信、(6)代表性著作或技術報告、和(7)碩博士論文指導教授姓名。應屆博士生申請者建議附上成績單。
申請資料建議以e-mail電子檔案方式提供（郵寄方式也可）。
請e-mail至 This email address is being protected from spambots. You need JavaScript enabled to view it.
或郵寄至 11529 台北市南港區研究院路二段128號 中央研究院統計科學研究所 新聘小組召集人 蔡恆修博士收
申請資料及推薦信收件截止日期為2020年12月27日，有意願者敬請儘早提出申請。
活動網址：http://www.stat.sinica.edu.tw/statnewsite/job/show/1789/
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From：NCTS
日期：2020/07/27-2020/08/05
類別：其他
主旨：2020 NCTS Summer Course on Mathematical Biology
內容：Mathematical modeling can play an important role in the understanding of mechanisms in biological systems. Motivated by this, we intend to introduce mathematical models of HIV infection, spatial segregation, and ecological systems with internal storage. Recently, Ergodic Theory has been successfully used to investigate the weakly repelling property of a compact and invariant set on the boundary, which is crucial when we utilize persistence theory to establish the possibility of coexistence for an ecosystem. Thus, we will also provide a brief introduction of Ergodic Theory in this course.
活動網址：http://www.ncts.ntu.edu.tw/events_3_detail.php?nid=212
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From：NCTS
日期：2020/08/07-2020/09/04
類別：其他
主旨：2020 NCTS Summer Course on Dynamical Systems: Dynamics and Thermodynamics on Expanding Maps
內容：The aim of this summer course is to provide the knowledge of the transformations (on manifolds and on metric spaces) which expand the distance between nearby points. There are many reasons why this transformation has an important role in ergodic theory. On the one hand, expanding maps exhibit very rich dynamical behaviors, from the metric and topological point of view (e.g., topological exact property, shadowing property and growth rate of periodic points) as well as from the ergodic point of view (e.g., thermodynamics and fractal geometry). On the other hand, the study of the expanding map leads to paradigms that are useful for understanding other systems (e.g., partially and non-uniformly hyperbolic systems). After introducing the classical results of the expanding maps, we will touch some interesting research topics which include the weighted thermodynamics, multifractal analysis of the Gibbs measure and multiple ergodic theory.
【TWSIAM DIGEST】2020年07月
TWSIAM Digest
發行日期：2020年07月01日
期別：2020年07月
本期主題：
[TWSIAM]第八屆台灣工業與應用數學會年會暨第三屆第三次會員大會(含理監事改選), 2020/07/24@國立成功大學
[TWSIAM]第八屆台灣工業與應用數學會學生海報論文競賽
[TWSIAM]109年第1期數學應用活動計畫申請(至2020年7月31日截止)；第一類：開放軟體之學習與推廣活動補助/第二類：學生社團推廣數學應用活動補助
[其他] 2020 NCTS Summer Course on Random Walk and Parabolic Partial Differential Equations, 2020/07/20-2020/08/28
[其他] NCTS Mini Course on Manifold Learning, 2020/07/23-2020/07/24
[其他] 2020 NCTS Summer Course on Mathematical Biology, 2020/07/27-2020/08/05
台灣工業與應用數學會將於每月定期發行TWSIAM Digest。
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投稿TWSIAM Digest：https://bit.ly/2CmHon6
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From：台灣工業與應用數學會<This email address is being protected from spambots. You need JavaScript enabled to view it.>
日期：2020/07/24
類別：研討會訊息
主旨：第八屆台灣工業與應用數學會年會暨第三屆第三次會員大會(含理監事改選)
內容：第八屆台灣工業與應用數學會年會暨第三屆第三次會員大會訂於109年7月24日(星期五)假國立成功大學舉行，會議邀請國立臺灣大學資訊工程學系林智仁教授擔任大會主講，另規劃六場領域論壇，邀請各位會員共襄盛舉。
報名日期 : 2020年6月8日(一)至7月23日(四)，線上報名。
會議註冊：https://twsiam2020.emath.tw/registration/info/
年會官網：https://twsiam2020.emath.tw/
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From：台灣工業與應用數學會<This email address is being protected from spambots. You need JavaScript enabled to view it.>
類別：研討會訊息
主旨：第八屆台灣工業與應用數學會學生海報論文競賽
內容：因新型冠狀病毒肺炎疫情，第八屆台灣工業與應用數學會年會已延期至109年7月24日（星期五）舉辦，本次會議之海報論文展(poster paper)亦改由線上方式進行。歡迎工業與應用數學領域相關之學術及工程應用論文投稿。海報論文投稿經大會初步審查通過後，將以線上方式於年會官網發表，會場不張貼海報。2020年07月02、03日將進行線上問答。線上會議之連結方式將於網頁提供(若未在指定時間出席，視同放棄參賽資格)。
海報論文徵稿專區：https://twsiam2020.emath.tw/registration/poster/
年會官網：https://twsiam2020.emath.tw/
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From：<TWSIAM>
日期：2020/07/01-2020/07/31
主旨：109年第1期數學應用活動計畫申請
內容：本會為推廣數學應用之活動，自即日起徵求109年第1期數學應用活動計畫。
申請期別：109年第1期
申請截止：109/07/31前
活動執行：109/09/01-110/02/28
單據核銷：110/03/31前
申請類別共分兩類，第一類屬於開放軟體之學習與推廣活動補助，第二類屬於學生社團為推廣數學應用的活動補助，學生可自組以推廣數學應用為宗旨並在學校立案的學生社團，由學生社團負責人提出申請。補助項目為活動所需之材料費(壁報)、演講費及雜支等，並優先受理本會永久會員、普通會員及學生會員且其所屬單位加入本會團體會員者提出之申請案。
凡獲第二類補助之學生社團，應報名參加2021年台灣工業與應用數學會年會之學生海報論文展，展示成果，並請於核銷時提供至少一張活動照片至本會信箱。
如欲申請請至本會網站下載申請表格，並請於109年7月31日前將申請表email至本會信箱。
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From：NCTS
日期：2020/07/20-2020/08/28
類別：其他
主旨：2020 NCTS Summer Course on Random Walk and Parabolic Partial Differential Equations
課程背景與目的：The intended audience for this mini-course is advanced undergraduates. We do not assume the students to have had a course on measure theory or real analysis. But we do hope that the topics will be interesting enough to attract some of the students to go further for graduate studies on Probability, Parabolic PDE and related fields.
活動網址：http://www.ncts.ntu.edu.tw/events_3_detail.php?nid=210
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From：NCTS
日期：2020/07/23-2020/07/24
類別：其他
主旨：NCTS Mini Course on Manifold Learning
課程背景與目的：Manifold learning encompasses much of the disciplines of geometry, computation, and statistics, and has become an important research topic in data mining and statistical learning. The simplest description of manifold learning is that it is a class of algorithms for recovering a low-dimensional manifold embedded in a high-dimensional ambient space.
The goal of this mini-course is to introduce three of the important topics in manifold learning theory: PCA ( Principal Component Analysis), diffusion map and MDS (Multidimensional Scaling). We will introduce the theory and implementation of these topics. The prerequisite of this mini-course is linear algebra.
活動網址：http://www.ncts.ntu.edu.tw/events_3_detail.php?nid=214
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From：NCTS
日期：2020/07/27-2020/08/05
類別：其他
主旨：2020 NCTS Summer Course on Mathematical Biology
課程背景與目的：Mathematical modeling can play an important role in the understanding of mechanisms in biological systems. Motivated by this, we intend to introduce mathematical models of HIV infection, spatial segregation, and ecological systems with internal storage. Recently, Ergodic Theory has been successfully used to investigate the weakly repelling property of a compact and invariant set on the boundary, which is crucial when we utilize persistence theory to establish the possibility of coexistence for an ecosystem. Thus, we will also provide a brief introduction of Ergodic Theory in this course.
課程大綱與講者：
Lecture 1
Lecturer: Professor Chih-Hung Chang (張志鴻) , National University of Kaohsiung
Title: A Short Course for Ergodic Theory
Abstract:Ergodic theory studies the long time behaviour of dynamical systems. This line of investigation has its origin in Poincare's investigations in statistical physics more than one hundred years ago. However, in the meantime ergodic theory has found many remarkable applications in various branches of mathematics. In this short course, I will give an introduction to some classical results, such as Poincare's recurrence theorem, Birkhoff ergodic theorem, and Furstenberg's multiple recurrence theorem. Meanwhile, some applications like the ergodic viewpoint of Borel's normal number theorem will also be covered.
Lecture 2
Lecturer: Professor Chang-Yuan Cheng (鄭昌源), National Pingtung University
Title: Mathematical Studies for HIV infection
Abstract:Human immunodeficiency virus type 1 (HIV-1) is one of the most and intensely studied viral pathogens in the history of science. Mathematical modeling has helped to improve our understanding of the infection as well as the pharmacodynamics within the host under a drug therapy. However, from recent reports, the spacial heterogeneity related to either the virus environments or the pharmacodynamics is a significant issue that deserves more attentions. We begin the sequel from introducing the routes of infection and virus environments, then formulating the drug efficacy, and studying its critical effect on viral dynamics via a perturbation technique. The lecture will include four parts:
(1) Basic viral dynamics in ODE/DDE/aged models
(2) Multi-compartmental virus models
(3) Pharmacodynamics within the host under a drug therapy
(4) A perturbation technique to determine viral extinction/persistence
Lecture 3
Lecturer: Professor Chang-Hong Wu (吳昌鴻), National Chiao Tung University
Title: Spatial Segregation in Competition Models
Abstract:The understanding of the spatial behavior of the interacting species is one fundamental issue in mathematical ecology. In particular, spatial segregation of species is a commonly observed phenomenon.This phenomenon has been studied widely in the literature. Generally speaking, it may occur when the competition between species is very strong. We will introduce some reaction-diffusion systems to approximate such a phenomenon. Furthermore, the limiting problems may help us understand the formation of spreading front from the modeling viewpoint and bring some mathematical models that may describe the invasion of species. In this lecture, we plan to divide the discussion into three parts:
(1) A brief introduction regarding the spatial segregation phenomenon
(2) The Fisher-Stefan model and some competition models
(3) Some applications.
Lecture 4
Lecturer: Professor Feng-Bin Wang (王埄彬), Chang Gung University
Title: Applications of Theory of Monotone Dynamical System and Uniform Persistence to Ecological Models with Internal Storage
Abstract:Competition for resources is a fundamental interaction between species and there has been a lot of experimental and theoretical analyses of nutrient-limited phytoplankton growth and competition studies. The simplest competition models use one ordinary differential equation to govern the dynamics of each species. These population dynamics are coupled to dynamics of one or more resources by assuming a constant quota of nutrient per individual, or equivalently, a constant yield of individuals from consumption of a unit of resource. In fact, quotas may vary, leading to variable-internal-stores models. In this talk, I shall introduce several systems modeling nutrient consumption, storage, and population growth in temporally homogeneous/varying environments (ODEs system involved in constant/time-periodic coefficients). In order to obtain the analytical analysis of the models, I shall further introduce the theory of monotone dynamical system and uniform persistence.
