歷史演講 PAST TALKS

Abstract：

The study of the birational automorphisms of the plane has a history of more than a hundred years. These automorphisms are invertible maps defined by polynomials, and several significant results have been established over the field of complex numbers, or more generally over perfect fields. Over a finite field, we call such a map a birational permutation if it induces a bijection on the points defined over the ground field. Given an abstract permutation, can we always realize it via a birational permutation? In this talk, I will give an almost full answer to this question. This is joint work with Shamil Asgarli, Masahiro Nakahara, and Susanna Zimmermann.

20200109演講_賴冠文教授 ( UMass Amherst)

Abstract：

The interplay between group theory and logic had played a crucial role in both areas for many decades. One of 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. We will also give some special attention to Gromov's model of random groups, and study the logical properties of them.

20191226演講_何孟哲教授 (Purdue University)

Abstract：

The resurgence of neural networks has revolutionized artificial intelligence since 2010. Luckily for mathematicians and statistical physicists, the study of large random network scaling limits, which can be thought of as *nonlinear* random matrix theory, is both practically important and mathematically interesting. We describe several problems in this setting and develop a new comprehensive framework, called “tensor programs”, for solving these problems. This framework can be thought of as an automatic tool to derive the behavior of computation graphs with large matrices, as used in neural network computation. It is very general, and from it we also obtain new proofs of the semicircle and the Marchenko-Pastur laws. From this framework follows many insights on neural networks, such as the limit of wide neural networks to Gaussian processes. This talk presents the works arXiv:1902.04760 and arXiv:1910.12478.

20191226演講_Greg Yang (Microsoft Research Lab - AI)

20191224演講_ 賴馨華博士 (國立中央大學數學系)

Abstract

The disordered system has been studied broadly in biology, chemistry, physics and mathematics. In the study of the disordered system we consider stochastic processes (or dynamical system is also possible) in the random environments. We are mainly interested in how much and how the random environment affects the system.

In the beginning of this talk I will introduce one of the basic models: one-dimensional Random Walk in Random Environment (RWRE), which has rich of results. And then we compare another model of the disordered system: Self-Avoiding Walk in Random Conductors (SAWRC), which has different way of import the random environment. In the last part of my talk, I will introduce the application of RWRE called Random Walk in Cooling Random Environment (RWCRE), which has a time evolution in the environment and show some results we obtained.

20191220Yuki Chino演講1000_1130

Abstract：

In this talk, we aim to have a glance of the spark between dynamics and geometry. I will start from “what are dynamical systems” and try to answer “how could dynamics tell us about geometry.” Along the way, I will introduce works of Sinai (2014 Abel Prize winner), Margulis (1978 Fields medalist), Thurston (1982 Fields medalist), McMullen (1998 Fields medalist), Mirzakhani (2014 Fields medalist), and some of my recent works on entropy rigidity and pressure metrics.

20191219演講_⾼連庸教授 (芝加哥大學)

Abstract：

Homomorphic encryption is a form of encryption that allows specific types of computations to be carried out on ciphertext and generate an encrypted result that, when decrypted, matches the result of operations performed on the plaintext. This is a desirable feature in modern communication system. Therefore, homomorphic encryption has been studied extensively in recent years. In this talk, we will introduce linear homomorphic encryption studied by Guilhem Castagnos and Fabien Laguillaumie and some possible applications.

20191219演講_莊治耘博士 (AMIS帳聯網路科技 密碼學工程師)

Abstract：

The asymptotic distribution theory for coefficients of a polynomial is an active topic in asymptotic analysis. In 1967, Harper proposed a criterion to measure the asymptotic normality of a series of numbers, when he researched the asymptotic behavior of Stirling numbers of the second kind. In this paper, we aim to develop some further asymptotic normality criteria of coefficients of a polynomial with all real roots or purely imaginary roots (including 0). These new asymptotic normality criteria turn out to be very efficient and have abundant applications in combinatorics, mainly including the coefficients of a series of characteristic polynomials of adjacency matrix, Laplacian matrix, signless Laplacian matrix, skew-adjacency matrix, chromatic polynomial, and some graph numbers, such as matching numbers, independence numbers, clique numbers. Among which, we generalize and verify some conjectures about asymptotic normality in combinatorics, e.g., the matching numbers proposed by Godsil and Kahn , the (signless) Laplacian coefficients claimed by Wang et al.

20191213演講_葉永南教授 (中央研究院數學研究所)

Abstract：

The bombing of airliners has been a tactic used by terrorists during the past 40 years. It become a big issue for homeland security. To investigation of such bombings, this talk provides the results of the development of mathematical modeling and computer simulation for the study of aircraft bombings and associated forensics.

The speaker will discuss some photographic evidence, introduce mathematical modeling and do computational modeling regarding a  particular case --- Daallo Airline's bombing case on February 2, 2016, in which only a small amount of explosives was used to demonstrate the event reconstruction can be accomplished for the purpose of forensic investigations. Most of our supercomputer results are visualized by video animations in order to show the dynamic effects and phenomena of explosives and the associated event reconstruction.

20191213演講_葉均承教授 (高雄師範大學)

Abstract：

Precision medicine initiative is to overcome the “averaged” medical paradigm that has been practiced for decades. To illuminate meaningful translational information out of the intrinsically complicated of a biological system created an unprecedented demand for an ultrahigh throughput biosensor with capability of providing big data information. The developments of microarray and NGS, with the help of systems biology and bioinformatics, steps closer to a more precise translational approach for diseases, including cancers. Further development of a next generation biosensor is indeed needed. With the help from semiconductor's dimension (compatible with target bio-molecules makes it possible to measure what could not be easily measured in the past), we could mitigate the gap we have to realize precision medicine and companion diagnosis. In this talk, I will try to explain what's the ecosystem and infrastructure available out there from consumer electronics companies and pharmaceutical companies, who are also working on the mobile health care and bench-to-bedside diagnostics to achieve precision medicine - as well as what's the bottlenecks limitations of the current technologies, i.e. sensitivity and resolution of conventional CMOS process.Given the above information, I wish to draw the attention from semiconductor and pharmaceutical companies and elucidate how they can work together and the economics that they can generate.

Keywords: precision medicine; biosensor; field effect transistors

20191212演講_陳文逸教授 (國立中央大學化材系)

Abstract：

This talk introduces the Hardy space, and more generally,  the Nevanlinna class  over the unit disk of the complex plane. The main goal is to prove the Canonical Factorization Theorem for Nevanlinna functions. Their zero distribution is also discussed.

20191203演講_ 黎懷仁博士生 (國立中央大學數學系)

Abstract：

這場演講是個科普性質的演講，我將介紹兩個離散幾何的經典問題：球體最密堆積問題(Sphere packing problem) 與親吻數問題 (kissing number problem). 三維的球體最密堆積問題也叫做克普勒猜想(Kepler Conjecture)，此問題懸疑了將近四百年才解決並發表在 Annals of Math (05')長達一百多頁。我也會談談離散幾何的相關問題的最新發展。本演講適合大學部學生參加。

20191126演講_俞韋亘教授 (國立中央大學數學系)

Abstract:

本演講我將分享 從數學領域跨足資訊、金融的過程。金融交易最重要的一個環節為資金管理，此領域起源於凱利法則，Kelly藉由部位大小控制風險與利潤。然而理論的凱利法則該如何套用於實務的金融交易，並不是一件容易的事。本演講將針對這個問題進行探討。從傳統銅板賭局出發，到複雜的骰子賭局、賽馬賭局。最後套用理論於實務的金融交易策略，投資組合..等實務議題。最後，我們探討槓桿空間模型與馬可維茲現代投資組合理論的差異。到底理論與實務之間有怎樣的鴻溝？ 機器學習機制該如何運用於交易策略研發? 深度學習技術是否能帶來金融交易的AlphaGo? 本演講我將分享這些問題的觀點。

20191122演講

Abstract：
Let G be a semisimple Lie group with Lie algebra \g and maximal compact subgroup K. The philosophy of coadjoint orbits suggests a way to study unitary representations of G by their close relations to the coadjoint G-orbits on \g*. In this talk, we study a special part of the orbit philosophy. We provide a comparison between the K-structure of unipotent representations and regular functions of bundles on nilpotent orbits for complex and real groups of type D. More precisely, we provide a list of genuine unipotent representations for a Spin group; separately we compute the K-spectra of the regular functions on certain small nilpotent orbits, and then match them with the K-types of the genuine unipotent representations.This is joint work with Dan Barbasch.

20191121演講_蔡宛育教授 (清華大學數學系)

20191112演講_陳正傑教授 (國立中央大學數學系)

摘要如附件

20191107演講_林剛玄博士 (中央研究院資訊科學研究所)

20191105演講_黃榮宗教授 (國立中央大學數學系)

Abstract：
Deep learning is part of a broader family of machine learning methods based on artificial neural networks. In this talk, we will first introduce what is machine learning and different types of learning. Further, we will talk about the artificial neural network and how it works.

20191101陳靖玟演講1000_1130

Abstract：

The surface morphology and lateral ordering of micellar assemblies on a substrate are generally addressed with direct imaging techniques involving a scanning electron microscope (SEM) and an atomic force microscope (AFM), but these techniques provide a localized view of the structural information with limited statistics and lack the ability to probe buried and inner structures within a film. In contrast to use of an AFM or SEM, Grazing-incidence small-angle X-ray scattering (GISAXS) is a powerful tool to probe a surface or interface and buried nanostructures in thin films, such as islands on a substrate or buried nanoparticles within a film. The detectable length with X-ray scattering in a grazing-incidence geometry covers a range from less than 1 nm to hundreds of nanometers. Measurement of relief islands on a substrate or objects buried within a film near the critical angle of the substrate decreases the bulk scattering from the substrate. Through GISAXS modeling analysis with IsGISAXS software, experimental scattering data provide quantitative nanostructure information in and out of the plane of objects deposited on a substrate. By combining an AFM, GISAXS, and modeling of the scattering data, we quantitatively examined four types of block copolymer (BCP) thin films, polystyrene-block-poly(methyl methacrylate), polystyrene-block-poly(2vinylpyridine), and polystyrene-block-poly(4-vinylpydine), and polystyrene-block-poly(ethylene oxide), in reciprocal space and real space. The GISAXS technique provides much insight into not only spatial ordering but also the orientations of mesophase-separated nanostructures on a substrate, the roughness replication, the thickness of a film and the faceting of microscale-dewetted terraces in the thin films.

20191031演講_孫亞賢教授 (國立中央大學化學工程與材料工程學系)

Abstract：

Nowadays, Machine learning performs astonishingly in many different fields. The more data we have, our machine learning methods show better results. However, in some cases, the data owners may not want to share the information they have, because those materials contain privacy issues. On the other hand, sometimes we encounter a very large dataset, which are difficult to store in a single machine. To deal with these two problems, we propose the distributed consensus reduced support vector machine (DCRSVM) for binary classification. Imagine that we have many local working units and a central master, and each working unit owns its data. The DCRSVM includes the following two merits. First, our method keeps the privacy of data, so we are not going to disclose local data to the central master. Besides, when we confront a large dataset, which is hard to store in a single server, the central master can still derive a good machine learning model even if the data stores only in local devices. Our method successfully solves the problems we mentioned above, and it generates a competitive result.

20191024演講_李育杰教授 (國立交通大學)

20191022演講_李明憶教授 (國立中央大學數學系)

20191015演講_李明憶教授 (國立中央大學數學系)

Abstract：

In this talk I will first give an overview of the known bounds for cliques in strongly regular graph. Then I will present a new bound. This is based on joint  work with Gary Greaves and Jongyook Park.

20191003演講_Prof. Jack H. Koolen (University of Science and Technology of China)

Abstract：

Optimal investment and reinsurance of insurers are treated on a market with a bank account and a risky stock. An economic factor process is formulated as a geometric Brownian motion, and affects the return of the risky stock. The aim of an insurer is to maximize the exponential utility.

The problem becomes a jump-diffusion control problem. We derive the Hamilton-Jacobi-Bellman equations and study these solutions. Using solutions, we construct optimal strategies and optimal values.

This talk is based on joint work with Li-Hsien Sun (National Central University).

20190912演講_Prof. Hiroaki Hata (Shizuoka University)