Postdoc seminar

Enumeration of quantum knot mosaics and the growth constant

홍경표 (국가수리과학연구소) | 2015-04-13 16:30~17:30 |수학원리응용센터 중형세미나실

Lomonaco and Kauman introduced knot mosaic system to give a definition of quantum knot system (2008). They proposed a question; "How many knot $(m,n)$-mosaics are there?". In this talk, we introduce an algorithm producing the precise values of them and estimate how fast the values increase.

Invitation seminar

Creating Tomorrow's Mathematics Professionals-PSM Programs in the Mathematical Sciences

Bogdan Vernescu (Worcester Polytechnic Institute) | 2015-04-03 14:00-15:30 |수학원리응용센터 중형세미나실

Considered one of the most important innovations in graduate science education in recent years, and the MBA of the 21st century, the Professional Science Master's (PSM) programs are a positive example of alignment of the higher education STEM production with the workforce demands. The fast growing number of PSM programs (331 PSM programs in 157 institutions in the United States) proves that the need to redesign the Master’s degree, to provide students with the skills needed to make them successful in jobs outside academia, responds to market needs for specialists with strong quantitative, modeling and scientific skills and that universities across the US have understood how to develop and deliver these programs.The PSM programs in the mathematical sciences have deeper roots in the applied mathematics and statistics MS programs and can be integrated well with the undergraduate and Ph.D. programs. There is evidence that shows that the programs meet the workforce needs and that graduates from these programs are successfully employed in corporations and in government.The talk will address several topics related to the development and administration of PSM programs in the mathematical sciences, such as:
Curriculum issues: courses offered, how content is related to businesses' needs, special pedagogical issues related to teaching in a PSM, etc.
Internship and research components in the PSMs.
Building effective partnerships between math PSMs and industry, business and government.
Student recruitment and retention.
Role of the PSMs in creating leaders in innovative companies in STEM fields: case studies of working mathematicians.
Start-up strategies and costs for new PSMs.

Postdoc seminar

Construction of class fields by using modular units

정호윤 (국가수리과학연구소) | 2015-03-30 16:30~17:30 |수학원리응용센터 중형세미나실

In number theory, modular units are defined to be meromorphic functions on the modular curves and they have a special property that they have no zeros and poles on the complex upper half plane. And their special values belong to a certain finite abelian extension of the corresponding imaginary quadratic field. In this talk, we introduce primitive generators of ray class fields over the given imaginary quadratic field and its applications.

Industrial Problems Seminar

이도준 상무 (LG전자) | 2015-03-11 16:30~17:30 |수학원리응용센터 중형세미나실

대한민국 전자 산업은 수십년간 국가 경제 성장의 동력이 되며 성장해 왔다. 초기 일본업체로 부터 기술을 배우며, 때로는 도 하고, 가격경쟁력을 통해 성장을 하다, 세계최고 수준에 올라섰다.
그러나 지금은 apple, Google 등 SW기반의 Platform을 강점으로 하는 기업들과, 급속하게 성장하는 중국업체들 사이에서 어려운 경쟁을 해 나가고 있다.
세계 경제가 어려워지는 최근의 상황에서 돌파구는 무엇일까? 어떻게 해결해 나갈 수 있을까?

Postdoc seminar

Stochastic convective wave equation in two space dimensions

박상현 (국가수리과학연구소) | 2015-01-26 16:30~17:30 |수학원리응용센터 중형세미나실

We briefly review stochastic partial differential equations driven by random source. We provide an overview of Walsh's stochastic integration with respect to martingale measure. We also study the convective wave equation in two space dimension driven by spatially homogeneous Gaussian noise. The existence of the real-valued solution is proved by providing necessary and sufficient condition of Gaussian noise. Holder continuity of the solution is proved.

Postdoc seminar

Model-based approach to load balancing for heterogeneous systems

추형석 (국가수리과학연구소) | 2015-01-12 16:30~17:30 |수학원리응용센터 중형세미나실

We investigated how to distribute computations among computational resources under data parallelism. A min–max model of computation times was proposed to reflect a heterogeneous computing system. Time functions for each resource were estimated with reference parameters, and sampling statistics evaluates those parameters such as effective memory bandwidths and FLOPS. Our min–max model includes those time functions as objective functions so that it suggests load balancing point for an arbitrary problem size. Several BLAS examples confirm that our model fits well comparing with real heterogeneous computing with OpenCL.

Industrial Problems Seminar

김진범 박사 (Barclays-New York, U.S.A) | 2014-10-06 16:30~17:30 |수학원리응용센터 중형세미나실

신용상품에는 크게 국가 및 회사은행개인의 신용을 거래하는 금융 상품으로 크게는 채권과 Credit Default Swap 및 옵션이
있습니다. 이 시간에는 첫번째로 각각의 상품의 개요와 미국 신용 상품 거래 시장이 어떻게 발전해 왔는지에 대해서 개략적
으로 설명하겠습니다. 두번째로는 2008년 금융 위기 이후에 새로 바뀐 제도적 규제가 신용상품 거래 시장에 어떠한 영향을
미쳤는 지를 설명하겠습니다. 마지막으로 이 규제로 인해 현재 은행 및 투자자들이 당면한 문제들과 어떻게 이것을 해결할
방법이 있는지에 대해서 알아 보는 시간을 가지겠습니다.

Industrial Problems Seminar

노건엽 박사 (보험개발원 계리 및 리스크 팀) | 2014-09-17 16:30~17:30 |수학원리응용센터 중형세미나실

보험상품은 대수의 법칙(the law of large numbers)이라는 확률론적 방법에 기반하여 만들어지는 금융상품으로 수리과학이
필수적인 역할을 합니다. 최근에는 금융공학 및 빅데이터 분석방법 등과 결합하여 다양한 적용 사례를 보여주고 있습니다.
보험상품에 내재된 옵션 평가, 현금흐름 평가를 위한 장기 이자율 시나리오 생성, 클러스터링을 이용한 보험계약 군집화 등
실제 사례를 통하여 보험에서 수리과학이 어떻게 활용되고 있는지 설명할 것입니다.
또한 보험산업에서 수리과학의 역할과 전망에 대해서 논의해 보려 합니다.

Industrial Problems Seminar

이원석 상무 (삼성전자 Software R&D Center) | 2014-08-28 11:00~12:00 |수학원리응용센터 중형세미나실

Superhyhobic micro-structured surfaces utilize a combination of chemical treatment and microscale surface
topography to increase the hyhobicity of a surface. Superhyhobic surfaces exhibit a number of interesting
properties such as dramatically decreased wettability and reduced friction in laminar flows. These characteristics make them a potential enabling technology for a variety of applications including microfluidics, lab-on-a-chip devices, self-cleaning surfaces, and reduction.
In this talk, we discuss the reduction capability of the microstructured surfaces to understand the fundamental
interfacial phenomena that allow these surfaces to exhibit such properties. Along with experimental efforts, numerical
simulations and theoretical studies have been conducted. Among those parallel efforts, in this seminar, we focus on the
analytic solution method using conformal mapping to solve pressure driven fluid flow problems under mixed boundary
conditions within microchannel.

Invitation seminar

Mechanization of Proof: From 4-Color Theorem to Compiler Verification

허충길 교수 (서울대학교 컴퓨터공학부 소프트웨어이론 연구실) | 2014-08-27 16:30~17:30 |수학원리응용센터 중형세미나실

I will give a broad introduction to how to mechanize mathematics (or proof), which will be mainly about the proof
assistant Coq. Mechanizing mathematics consists of (i) defining a set theory, (2) developing a tool that allows writing
definitions and proofs in the set theory, and (3) developing an independent proof checker that checks whether a given
proof is correct (ie, whether it is a valid combination of axioms and inference rules of the set theory). Such a system is
called proof assistant and Coq is one of the most popular ones.
In the first half of the talk, I will introduce applications of proof assistant, ranging from mechanized proof of 4-color
theorem to verification of an operating system. Also, I will talk about a project that I lead, which is to provide, using Coq,
a formally guaranteed way to completely detect all bugs from compilation results of the mainstream C compiler LLVM.
In the second half, I will discuss the set theory used in Coq, called Calculus of (Inductive and Coinductive) Construction.
It will give a very interesting view on set theory. For instance, in calculus of construction, the three apparently different
notions coincide: (i) sets and elements, (ii) propositions and proofs, and (iii) types and programs.
If time permits, I will also briefly discuss how Von Neumann Universes are handled in Coq and how Coq is used in
homotopy type theory, led by Fields medalist Vladimir Voevodsky.