- Development of a model for the relationship between power consumption prediction and

  power production (Jeju City Hall)

This biannual conference, EACAT, has been held since 2007 at Seoul. Before then there had been annual China-Japan-Korea(CJK) Conference on Algebraic Topology for a few years. The conference was expanded to East Asia as Singapore, Taiwan, Vietnam topologists began to participate in 2007. Although this is a regional conference, a few European and American topologists also particiapted every year. The EACAT was held in 2008 at Singapore, 2009 at Hanoi, 2011 at Tokyo and 2013 at Beijing.

● 주 관: 국가수리과학연구소, 경북대학교 그라스만다양체연구단 (공동주관)
● 조직위원회: 서영진(경북대학교, 교수), J. Berndt(Kings College London, 교수), Y. Ohnita(Osaka City Univ. 교수), 이현진(포항공과대학교, 박사후연구원)

최근 미분기하학과 관련분야 연구발전 동향에 대해 폭넓게 회의하고 첨부 명기한 강연자들의 강연을 중심으로 학술 연구에 관해 발표하고 토론하고자 한다. 본 미분기하학관련 국제워크셥을 통해 발표된 연구결과는 후진 교육과 국가과학기술 발전을 위해 매년 Proceedings를 편집하였으나 이번 회차부터는 그 방법을 달리 하여 온라인상에서 자료를 제공할 예정이다.

특히, S.S. Chern conjecture, S.T. Yau conjecture and its counter example, symmetric submanifolds, convex and integral geometry, complex two plane Grasmmannians, non-compact Grassmannians, homogeneous hypersurface and foliations on symmetric space, E. Cartans's structural equations for cosmology and differential geometry 및 Riemannian, conformal, projective, concircular and conharmonic curvature 2-form등의 Riemannian 다양체상의 generalized curvature 2-form 등을 중점적으로 연구회의 한다.

본 학술대회에서는 Ginzburg-Landau, Phase Field 이론과 관련된 내용과 관련된 저명한 학자들을 초청하여 연구의 세계적인 추이를 알아보고 최신 이론을 접할 기회를 제공하고자 한다. Ginzburg-Landau이론은 다양한 분야에 응용되며 혼합체의 수학적 연구에도 많은 기여를 하고 있는 분야입니다. 본 학회에 큰 세계적인 석학인 미국 뉴욕대학교 수학과 Fanghua LIn교수, 퍼듀대학교의 Patricia Bauman과 Daniel Phillips, 중국 East China Normal 대학교의 Xingbin Pan교수, 북경대학교의 Pingwen Zhang및 영국 Univeristy of Bath의 Apala Majumdar을 초청하여 Ginzburg-Landau이론과 Navier-Stokes방정식과의 coupling에서 나타나는 방정식의 해의 대한 연구와 액정과 관련된 Landau-de Gennes과의 연계에 의한 학문 분야에 대한 세계적인 연구 방향을 알아 볼 계획입니다.

The International Conferences on Domain Decomposition Methods, which ed on 1987, gave a great influence to the development of scientific computing and computational science.
The purpose of the meeting is to discuss recent developments in various aspects of domain decomposition methods bringing together mathematicians, computational scientists, and engineers who are working on numerical analysis, scientific computing, and computational science with industrial applications.

이번 학술대회에서는 여러 명의 국제적 저명 학자들을 초청하여 강연을 듣는 시간을 갖는다. 초청강연자들은 다음과 같다.
Algebraic geometry, commutative algebra, algebraic statatics, computational biology, tropical geometry의 전문가인 Bernd Sturmfels (UC Berkeley, 미국), Combinatorics, Discrete probability의 전문가인 Igor Pak (UCLA, 미국),Algebraic Combinatorics, Ordered Algebraic Structures and Probabilistic Methods의 전문가인 Catherine Yan (Texas A&M University, 미국), Operads, tree algebras, quivers, polytopes의 전문가인 Fr&eae;d&eae;ric Chapoton (Universit&eae; Claude Bernard Lyon 1, 프랑스), Graph theory, probabilistic combinatorics의 전문가인 Mihyun Kang (Graz University of Technology, 오스트리아), Enumerative combinatorics, discrete geometry의 전문가인 Christos Athanasiadis (University of Athens, 그리스), Algebraic combinatorics, representation theory의 전문가인 Stephanie Van Willigenburg (University of British Columbia, 캐나다), Representation theory, Hecke algebra의 전문가인 Susumu Ariki (Osaka University, 일본), Algebraic combinatorics, symmetric functions의 전문가인 Valentin F&eae;ray (Universität Zürich, 스위스) 또한 30여개의 일반강연과 40여개의 포스터발표가 있을 예정이다. 세계 최고 수준의 국제저명학자들과 함께 토의하는 기회가 되어, 국내에서는 활발하지 않은 연구와 분야를 소개하여 교육적 효과를 증대시키고, 조합수학 분야에서 새로운 협력과 발전이 이루어지는 계기가 되게 한다.

▪주 관: 국가수리과학연구소
▪조직위원회: 아주대학교 고계원 교수, 아주대학교 이중섭 교수, 아주대학교 정의진 교수, 동국대학교 김동한 교수 외

본 학술대회는 기 개최되었던 2009년 (아주대학교) 2011년 (University of Science and Technology of China), 2013년 (Keio University) 학술대회의 연장선으로, 동력학계 전반에 걸친 다양한 분야의 참석자들이 연구결과를 강연할 예정입니다.
전통적으로 연구가 깊은 측도론적 동력학계(measurable dynamics, ergodic theory) 와 위상동력학계(topological dynamics)를 중심으로 동력학계의 응용에 관한 발표들도 섭외할 예정으로, 학술대회에서 주로 다루어질 큰 주제들은 다음과 같습니다.
- 동력학계의 동형문제(isomorphism problem)
- 다차원 동력학계의 불변량 및 thermodynamic formalism
- amenable 작용의 특성과 구조
- 미분동력학계(Differentiable dynamics)의 분기(bifurcation) 및 포괄적인(generic) 성질
- 동력학계의 응용
보다 효율적인 학술대회가 되도록 동력학계 분야의 넓은 스펙트럼의 학자들을 초청할 예정이며 국내 학자들에게도 발표기회를 넓힐 예정으로, 이 분야를 이끌고 있는 해외 동력학계 연구자와 국내 연구자들 사이의 활발하고 폭넓은 교류가 목적입니다.

The research on nonlinear elliptic and parabolic equations is one of the most developed in Mathematics, and mightily important because of its intimate connection with other areas within Mathematics and for its wide applications in many scientific research areas such as Mathematical Physics, Mathematical Physics Chemistry, Mathematical Biology, Fluid Dynamics, Phase Transitions, and Mathematical Finance.
Recently there has been a great quantity of research works regarding regularity theory for nonlinear elliptic and parabolic equations such as Calderon-Zygmund type estimates, Holder estimates, obstacle problems, homogenization, and curvature flows.
This conference will concentrate on regularity theory for nonlinear elliptic and parabolic equations for the purpose of bringing together people working on this research area, discussing the current progress of development, encouraging interactions with each other, and drawing up future projects.

Feynman introduced a famuous heuristic formula which is known as "Feynman path integral" for the evolution of a nonrelavistic quantum system. The integral has been approached from many different point of view by mathematicians and physicists with varied backgound and interests. The resulting diversity has led to many different definitions of the Feynman integral. One of these approaches is to define the integral using a stochactis process, the Wiener process. Wiener process also plays an important role in stochastic calculus, applied and financial calculus and in theoretical physics such as quantum physics, statistical physics and condensed matter physics, etc. In particular, the Wiener measure can be widely applicable to the mathematical physics including quantum mechanics. The followings are shortcomings of many of the mathematical theories of the Feynman integral which are often pointed out:
(1) The existence theories are not sufficiently general. In particular, many of the standard realvalued time indepent potentials which are used in modeling quantum sysytems are singlular (ex.the attractive Coulomb potenial) and do not fit within the theories.
(2) No much information is given about how the various approaches to the Feynman integral are related to one another or to the unitary group which gives the evolution of the quantum systems in the standard approach to quantum dynamics.
(3) There is a shortage of satisfactory limiting theorems. Indeed, in some cases, no such theorems are available, while in others, the results do not seem natural from a physical point of wiew.
The goal of this workshop is that we discuss quite satisfactory responses to all three objections,especially for the approaches to the Feynman integral which are developed using Wiener integral or path integral without measures.

We plan to bring international researchers together to discuss recent developments in the theory of equations that arise as models for fluid motion. A particular focus of the conversation will be on models that feature non-local operators. The discussion is envisioned to deal with fundamental issues of local existence and regularity, but interest will devolve more to issues of singularity formation. Issues of this sort have seen sustained effort in the last decade or so, both by theoretical means and using numerical simulations. The research in this area has been carried on by groups that have largely focused upon only one type of equation. Considering the progress that has been made as well as the recalcitrance of some of the open issues, it seems timely to bring together successful workers on the various equations of fluid motion for an extended discussion of issues and methods. Especially mixing people who are numerically based with theoreticians seems propitious. More detailed commentary concerning the various perspectives we intend to embrace now follows.