Tuesday, November 10, 2020

2020-11-13 / 15:30 ~ 16:30

by 최경수()

The mean curvature flow is an evolution of hypersurfaces satisfying a geometric heat equation. The flow changes its topology through singularities, and there are infinitely many singularity models. However, the flow is a gradient flow of an entropy functional, and there are only a few linearly stable singularities. Hence, one can conjecture that some perturbations of initial hypersurfaces would make the perturbed flows avoid linearly unstable singularities. In this talk, we will discuss how to use ancient flows for the avoidance of unstable singularities, and its application to the knot theory.

2020-11-12 / 16:30 ~ 17:30

학과 세미나/콜로퀴엄 - 콜로퀴엄: Homogeneous dynamics and Diophantine approximation

by 임선희(서울대학교)

The idea of using homogeneous dynamics to Diophantine approximation has grown to an active subfield of mathematics, with numerous results on Hausdorff dimension of sets of vectors with certain Diophantine properties. In this talk, we will start from scratch, from the Gauss map of the usual continued fraction expansion for real numbers and give a "dynamical interpretation" of Diophantine properties of continued fractions in terms of the orbits of the geodesic flow on the hyperbolic plane. We will then present a series of results of the speaker with coauthors on inhomogeneous Diophantine approximation and give ideas of proofs, especially the idea related to the partial proof of Littlewood conjecture of Einsiedler-Katok-Lindenstrauss. (The latter part of the talk is based on joint works with U. Shapira-N. de Saxce, Y. Bugeaud-Donghan Kim-M. Rams, and Wooyeon Kim-Taehyung Kim.)

Events for the 취소된 행사 포함