|Colloquium, University of Waterloo 郭文堂教授|
Thursday, November 1, 15:10—16:00 數學系3174
Title: Prime Number Theorem and Dirichlet Series
Abstract: The Prime number theorem gives an asymptotic form for the prime counting function, which counts the number of primes less than some integer N. In 1792, when only 15 years old, Gauss proposed that the prime counting function is asymptotically equal to N/log N. Later, in 1896, Hadamard and de la Vallee Poussin independently gave proofs of this conjecture. In this talk, we will review the history of this problem and how it links to complex analysis.
|Colloquium, 臺灣科技大學資訊工程系 鮑興國教授|
Thursday, November 1, 16:10—17:00 數學系3174
Title: Machine Learning that Stands on the Shoulders of Mathematics
Abstract:We have experienced the progress of machine learning and artificial intelligence in the last few years. As a mathematician or a person who learned mathematics, how can we explain the phenomenon and leverage what we learned and contribute to the society? In machine learning, we usually sove the real-world puzzles by combinning the knowledge from both mathematical and algorithmic foundations in a community that consits of researchers from various background such as mathematics, statistics, computer science, engineering and more. That is to emphasize that we may have to deal with problems that could be ill-posed, containing solutions without their close-forms, or need some industrial-level computation to obtain their solutions. In this talk, we attempt to provide a bridge between mathematics and machine learning by domonstrating real cases about how we can take advantages of knowing mathematics to solve real problems with superior outcomes. We discuss a set of mathematical methods that are applicable to IoT data analytics, information security and computer vision to name a few. After all, we also share the thoughts on how we view the role of machines that own artificial intelligence in our future.
|Colloquium, Skywatch/行品, 英業達AI中心, 台灣人工智慧學校 陳維超博士|
Thursday, November 15, 16:10—17:00 數學系3174
Title: Abstraction or Instantiation: On Building the Internet for Smarter Place
Abstract: There are two ends of the spectrum when it comes to Internet-of-Things. On the one end, the focus is on lower level communication technology, platforms, and standards that aim to enable machine-to-machine communications. On the other end, people have been searching for the killer devices that would transform our lives. Clearly, one is the "Internet" perspective, while the other is the "Things" perspective. In this talk, instead of taking the words "Internet of Things" literally, we focus on the combined effects of devices on environments. Specifically, we discuss the conversations between devices, and how these interactions can open new frontiers of digitized spaces in the era of machine learning.
|Analysis Seminar, 北海道大學理學院 中村玄教授|
Wednesday, November 21, 10:10—13:00 數學系3樓會議室
Title: Introduction to Inverse Problems (1)(2)
|Colloquium, 清華大學數學系 吳浩平博士|
Thursday, November 22, 15:10—16:00 數學系3174
Title: Introduction to Equivariant Degree Theory
Abstract:The equivariant degree is a topological tool which allows of “counting” orbits of solutions to (symmetric) equations in the same way the Brouwer degree does, but according to their symmetric properties. In this talk, I will give an overview on Equivariant Degree Theory (EDT), which includes the following topics: Brouwer degree, axiomatic approach, group symmetry, Burnside ring and computation of equivariant degree; all of them will be supported by simple examples. After the overview, I will illustrate how one can apply EDT by considering a boundary value problem with symmetry.
|Colloquium, 南非自由省大學 Johan H Meyer教授|
Thursday, November 22, 16:10—17:00 數學系3174
Title: Unique Maximal Rings of Functions
Abstract:For several classes of groups G we characterize when the near-ring M_0(G) of 0-preserving selfmaps on G contains a unique maximal ring. Definitive results are obtained for finite abelian, finite nilpotent, and finite permutation groups.
|Analysis Seminar, 北海道大學理學院 中村玄教授|
Wednesday, November 28, 10:10—13:00 數學系3樓會議室
Title: Forward Problems for Inverse Scattering, Boundary Problems and Some Analytic Tools (1)(2)
|Colloquium, 京都大學, Prof. Takaaki Nishida|
Thursday, November 29, 16:10—17:00 數學系3174
Title: Decay of Surface Waves of Viscous Fluids
Abstract:This is based on joint works with Tom Beale and Yoshiaki Teramoto. It concerns the decay of solutions for free surface problems of Navier-Stokes equations in the horizontal strip domain. The gravity and/or surface tension act on the incompressible viscous fluids. The decay properties of the solutions with respect to time depends on those forces. Those algebraic decay rates can apply also to small solutions for the nonlinear system and give global in time results.
|Algebraic Geometry Seminar, Universita degli Studi di Padova, Prof. Stefano Urbinati|
Friday, November 30, 14:00—15:30 數學系3樓會議室
Title: Finite Generation of Valuation Semigroups Via Tropical Compactifications
Abstract: In this talk I will discuss some recent work in progress with Alex Kuronya. The aim is twofold. First of all I will give a local description of the theorem of Hu-Keel on the embedding of Mori Dream Spaces in toric varietis, extending it to the case of ample families.