The continued fraction is a formal expression of the iterated fraction which is investigated in various perspectives; metrical number theory, hyperbolic geometry, and combinatorics on words. In this talk, we consider three topics related to continued fractions. One of the important properties of continued fraction is that the classical continued fraction gives an algorithm to generate the best approximation of every irrational as the principal convergents. We define a continued fraction which gives best-approximations among the rationals whose denominators and numerators are both odd. We call the continued fraction the odd-odd continued fraction. The second topic is Lévy constants of real numbers whose continued fraction expansions are Sturmian words. Lévy constant is the exponential growth rate of denominators of principal convergents of a continued fraction. We examine the existence and the spectrum of the Lévy constants of Sturmian continued fractions. The last topic is about quasi-Sturmian colorings of trees. We characterize quasi-Sturmian colorings of regular trees by its quotient graph and its recurrence functions. We find an induction algorithm of quasi-Sturmian colorings which is similar to the continued fraction algorithm of Sturmian words. 발표시간:17:00~18:00 온라인 심사로 진행합니다. Zoom 링크 https://snu-ac-kr.zoom.us/j/2254272974