|Colloquium, 中央研究院數學研究所 賴俊儒研究員|
Thursday, March 3, 16:10—17:00 數學系3174
Title: Schur-Weyl Duality, Old and New
Abstract:In the beginning stage of representation theory, Schur's 1901 thesis on polynomial/rational representations of the general linear groups has played an influential role. A double centralizer property with the symmetric groups (i.e., Weyl groups of type A), now known as the Schur-Weyl duality, has been utilized to simultaneously study the representation theories of the ``holy trinity'' -- the symmetric groups, the (infinite-dimensional) general linear Lie algebras, and the finite-dimensional algebras known as the Schur algebras. Interests in Schur's ideas still continue nowadays, in a modern setting. In this talk I will focus on the quantum version of the duality, and go over the connections with the quantum groups via coordinate construction, with the Hecke algebras, and with rational Cherednik algebras.
|Colloquium, 國立成功大學數學系 劉之中助理教授|
Thursday, March 10, 15:10—16:00 數學系3174
Title: Equations in Gauge Theory
Abstract:In this talk, I will briefly introduce the vast field of gauge theory that is developed from classical electromagnetism. The theory bridges (and identifies) many theories of pure mathematic. Moreover, it unravels many longstanding mathematical mysteries, especially in differential geometry. Gauge theory is still being actively researched, and I will mention some of my past contributions and currently interested topics.
|Colloquium, 國立台灣大學數學系 陳榮凱教授|
Thursday, March 10, 16:10—17:00 數學系3174
Title: On Characterization of Extremal Varieties of General Type
Abstract: Considering varieties of general type of fixed dimension, it is interesting to study the distribution of birational invariants. For example, Miyaoka-Yau inequality, Noether inequalities forms the foundation of classification theory of surfaces. Also, Severi inequality plays the central role in the theory of irregular surfaces. Moreover, it would be interesting to understand those varieties attain the equality. In this talk, we will characterize varieties of general type on (or close to) the Noether line in dimension three.
|Colloquium, 國立高雄大學應用數學系 張惠蘭教授|
Thursday, March 17, 16:10—17:00 數學系3174
Title: Density-based Interval Group Testing
Abstract: To identify splice sites in a genome, Cicalese et al. (2005) studied interval group testing where all items in the search space are linearly ordered and each of them is either positive or negative. An interval is a set of consecutive items. The goal is to identify positive items by asking queries of the type ``does an interval contain any positive one?" A motivation for this study comes from its application in determining exon-intron boundaries within a gene. We study this group testing model by using a generalized type of queries: each query asks ``does the density of positive items in an interval exceed a given ratio? " This type of density-based queries is proposed by Gerbner et al. (2013). In this talk, I will present our sequential algorithms and nonadaptive algorithms with error-tolerance.
|Colloquium, 中央研究院數學研究所 尤釋賢特聘研究員|
Friday, March 18, 10:10—12:00 數學系3樓會議室
Title: A Computable Approach to Wave and Heat Equation
Abstract: In this talk we will give an elementary method to study wave and heat equation including various physical condition imposed.
|Colloquium, 國立台灣大學資訊工程學系 陳縕儂教授|
Thursday, March 24, 16:10—17:00 數學系3174
Title: Our Future Life - Conversational AI (我們的未來 - 對話式人工智慧)
Abstract: The current human-machine interactions still differ from human-human interactions, because machines have difficulty fully understanding natural language due to diversity of language expression, lack of human commonsense, and lack of environmental contexts. This talk provides an overview of conversational AI systems and summarizes the current challenges and potential directions towards better conversational AI.
Short Bio: Yun-Nung (Vivian) Chen (http://vivianchen.idv.tw/) is currently an associate professor in the Department of Computer Science & Information Engineering at National Taiwan University. She earned her Ph.D. degree from Carnegie Mellon University, where her research interests focus on spoken dialogue systems, language understanding, natural language processing, and multimodality. She was recognized as the Taiwan Outstanding Young Women in Science and received Google Faculty Research Awards, Amazon AWS Machine Learning Research Awards, MOST Young Scholar Fellowship, and FAOS Young Scholar Innovation Award. Prior to joining National Taiwan University, she worked in the Deep Learning Technology Center at Microsoft Research Redmond. Her course lectures are available on her YouTube channel (https://www.youtube.com/c/VivianNTUMiuLab).