남하얀 (덕성여대)

- Title: Results on numerical semigroups

- Abstract: A set S, which is a subset of the set of nonnegative integers, is called a numerical semigroup if S contains 0, S is closed under addition, and the complement of S (or the gap set of S) is finite. The genus of a numerical semigroup S is the cardinality of the complement of S. In this talk, we present results on numerical semigroups regarding their genus and gap set.

황숙정 (충북대)

- Title: Nonlinear diffusion equations

- Abstract: This talk introduces the nonlinear diffusion equation, p-Laplace and porous medium equations. Also, the existence and regularity results of the two equations are discussed.

최범준 (POSTECH)

- Title: Thom’s gradient conjecture for geometric evolution equations

- Abstract: We introduce questions regarding the asymptotic geometry of geometric objects with variational structure such as minimal surface, Einstein manifold and their parabolic equations. Originating from the study of gradient flows on Euclidean space, the uniqueness questions on limits and limiting directions have long history and many questions are still open. After an introduction, our recent result about a partial answer to the Thom/Arnold’s gradient conjecture and its possible implications in geometry will be discussed.

안병희 (경북대)

- Title: Quasi-isometric classification of graph 2-braid groups

- Abstract: For a compact (weakly) special square complex, the intersection complex which is a certain complex-of-group decomposition structure of its fundamental group is a well-defined invariant under quasi-isometry. In this talk, we use this invariant to classify quasi-isometry types of 2-braid groups of circumference 1 graphs. As an application, we also classify quasi-isometry types of 4-braid groups of trees. This is a joint work with Sangrok O.