번역기 중 가장 좋다는 구글번역기에 '비단 골이 전부가 아니다'라는 문장을 넣으면, 'Silk is not the only goal'이라고 번역한다. 이라한 오역의 근원은, 번역을 언어의 구조, 성질, 패턴 연구가 아닌 엉뚱한 통계확률로 접근하기 때문이다. 컴퓨터가 발달하고 인간의 지능을 가진 로봇을 만드려는 인간의 노력은 인간이 사용하는 자연어를 기계언어로 번역(프로그램 용어로 compile)하는 문제를 핵심 과제로 부각시켰고 그 연구에 많은 돈과 인력이 투입되고 있다.

이 발표의 목적은 한글 고유의 조사와 서술어미 변형을 구현하는(representation) 수학적 방법론 제시 및 한글 문장의 구문분석에 응용 프로그램을 시연함으로써, 한글구문분석의 올바른 방향을 제시하고자 위함이다.

Primitive (birational) automorphisms of projective manifolds, which are irreducible au-
tomorphisms of manifolds, are natural objects in birational algebraic geometry. They are
also very closely related to complex dynamics of several variables. In fact, the dynamical
degrees of birational automorphisms (a kind of renement of a more classical notion of
topological entropy of automorphisms, tting very well with birational geometry), the relative dynamical degrees (their relative version) and the product formula (a kind of Kunneth type formula), introduced by Dinh-Sibony [DS], Dinh-Nyugen [DN], provide very powerful tools also in studying primitive birational automorphisms of manifolds.
In Lecture 1, I would like to give an overview of the basic notions (entropy, dynamical
degrees, relative dynamical degrees etc) and their basic properties with concrete applications for the study of primitive (birational) automorphisms. This lecture is, in some sense, an updated version of [Og].
In Lectures II, III, I would like to prove the well-denedness and the birational invariance
of dynamical degrees, the most basic property of the dynamical degree. The original proof ([DS]) is transcendental being based on some detailed analysis of currents. Here I explain a new purely algebro-geometric proof due to Truong ([Tr]), which is based on a precise form of Chow's moving lemma ([Ro]).
In Lectures IV, V, I would like to prove the product formula, the most fundamental
and useful property of relative dynamical degrees. Here I explain again an algebraic proof
following a guideline explained in [Tr], which is a modication of original analytic proofs
([DN], [DNT]) into an algebraic one again using a precise form of Chow's moving lemma.

References

[DS] Dinh, T.-C., Sibony, N., Une borne superieure de l'entropie topologique d'une application rationnelle, Ann. of Math., 161 (2005) 1637{1644. arXiv:math/0303271.

[DN] Dinh, T.-C., Nguyen V.-A., Comparison of dynamical degrees for semi-conjugate meromorphic maps, Comment. Math. Helv. 86 (2011) 817{840. arXiv:0903.2621.

[DNT] Dinh, T.-C., Nguyen V.-A., Truong, T.-T., On the dynamical degrees of meromorphic maps preserving a bration, Commun. Contemp. Math. 14 (2012) 18pp, arXiv: 1108.4792.

[Og] Oguiso, K., Some aspects of explicit birational geometry inspired by complex dynamics, Proceedings of the International Congress of Mathematicians, Seoul 2014 (Invited Lectures) Vol.II (2015), 695{721. arXiv:1404.2982.

[Ro] Roberts, J., Chow's moving lemma, in Algebraic geometry, Oslo 1970, F. Oort (ed.), WoltersNoordhoff, Publ. Groningnen (1972), 89{96.

[Tr] Truong, T.T., (Relative) dynamical degrees of rational maps over an algebraic closed eld, arXiv:1501.01523.