## Seminars and Colloquium

#### Yong-Jung Kim (KAIST)PDE Seminar

Heterogeneous diffusion is by Stratonovich integral, not Ito integral

#### Seo Donghwi (KAIST)Ph.D. Defense

A Shape Optimization Problem of the First Mixed Steklov-Dirichlet Eigenvalue

#### Sunkwon kim (한국전기연구원)Etc.

소스 관리 툴 Git/GitHub의 사용법 및 현업 적용 사례

#### Wansu Kim (Department of Mathematical Sciences, KAIST)Colloquium

Introduction to p-adic differential equations

#### Cheuk Yu Mak (University of Cambridge)Topology Seminar

From two circles on a sphere to a Fukaya category and Khovanov homology

#### Cheuk Yu Mak (University of Cambridge)Topology Seminar

Homological mirror symmetry: overview, examples and some geometric applications

#### Hong Liu (University of Warwick)Discrete Math

A proof of Mader's conjecture on large clique subdivisions in $C_4$-free graphs

## Conferences and Workshops

## Student News

Hyukpyo Hong Chosen for Global PhD Fellowship 2019 by the National Research Foundation of Korea 2019.10

Best TA Awards for Spring 2019 2019.06

Minyoo Kim Takes 2019 KSIAM Poster Award 2019.06

2019 Spring POW (Problem of the Week) Award Winners 2019.06

KAIST Students Receive Prizes from the 2018 Simon Marias Mathematics Competition 2018.12

Winners of the 2018 Fall Semester Problem of the Week Award 2018.12

Ji, Hong-Chang Receives POSCO Science Fellowship 2019 2018.12

Kijoung Jang Wins the College Students Mathematics Competition 2017 2017.12

Seokjoo Chae receives POSCO TJ Park Science Fellowship Award 2017 2017.10

Daewook Kim Receives the 2017 Global Ph.D. Fellowships from the Korean Government 2017.08

## Bookmarks

## Bulletin Boards

고페이 수학강사 모십니다. | 08. 11 | |

중3 수학 과외 선생님 모십니다. | 04. 06 | |

여학생 과외 원합니다. | 03. 07 | |

고교2학년생입니다. 수학선생님 원해요 | 11. 11 | |

대학원 입시 설명회 자료 좀 올려주시겠어요? | 06. 22 | |

모듈 형식과 타원 방정식에 대해서 질문합니다 | 11. 13 | |

모듈 형식과 타원 방정식에 대해서 질문합니다 | 11. 13 |

## Alumni News

## Problem of the week

Let \(G = (S | R)\) be a group presentation where S is a set of generators and R is a set of relators. Given any subset S' of S, we set R' to be the subset of R which consists of words only in the elements of S'. Then the presentation \(S'|R'\) is called a sub-presentation of \(S|R\).

The presentation complex for the presentation \(S|R\) is a cell complex constructed as follows: start with a single vertex v. For each element s of S, we attach an oriented edge labelled by s to v by identifying both endpoints of the edge with v. In this way, we get a wedge of circles where the circles are in 1-1 correspondence with the generating set S. For each element r of R, we attach a closed disk to the wedge of circles we obtained so that the boundary of the disk after gluing can be read using the labels of the edges to be the word r we started with.

For instance, consider the following presentation of a group \(x, y| xyx^{-1}y^{-1}\). We get a wedge of two circles first labelled by x and y. Then we add one disk so that the boundary reads as \(xyx^{-1}y^{-1}\). It is easy to see that the resulting space is homeomorphic to the torus. As one sees from this example, the presentation complex is a cell complex whose fundamental group is the group with the given presentation. For a group presentation \((S|R)\), let \( K(S|R) \) denote the presentation complex.

Suppose we have a group presentation \((S|R)\) such that any continuous map \(f: S^2 \to K(S|R) \) is homotopic to a constant map where \(S^2\) is the 2-sphere. Prove or find a counter-example to that every sub-presentation of \((S|R)\) has the same property, i.e., for any sub-presentation \((S|R)\), every continuous map \(h: S^2 \to K(S'|R')\) is homotopic to a constant map.