New Faculty: Professor Minju Lee
As of August 1, 2025, Professor Minju Lee joined us as a new faculty member. Received a doctoral degree in 2021 from Yale University, Professor Kim worked at School of Mathematics of IAS(Member, 2021-2022) and University of Chicago(Dickson Instructor, 2022-2025). He specializes in Homog...
New Faculty: Professor Beomjun Choi
As of July 1th, 2025, Professor Beomjun Choi was appointed as an Associate Professor. Professor Choi received his Ph.D. from Columbia University in 2019. He served as Assistant Professor at POSTECH (2021-2025). He majored in Geometric Analysis, Differential Geometry, Partial Differen...
New Faculty: Professor Donghan Kim
As of August 1, 2024, Professor Donghan Kim joined us as a new faculty member. Received a doctoral degree in 2020 from Columbia University, Professor Kim worked at University of Michigan(Assistant Research Professor, 2021-2024). He specializes in Mathematical Finance and Stochastic Anal...
Prof. Jae-Kyung Kim receives a citation from the Minister of Science and Technology and ICT
Prof. Jae-Kyung Kim of Woori Department has been awarded the 'Ministerial Citation' by the Ministry of Science and ICT. In 2017, Prof. Kim received a research grant from the Human Frontier Science Program (HFSP), an international organization known as the Nobel Prize Fund, to conduct resea...
New Faculty: Professor Jiewon Park
Received a Ph.D. degree from MIT in 2020, Dr. Jiewon Park joins the Department of Mathematical Sciences on August 1, 2023 as an assistant professor. Prior to KAIST, Dr. Park worked as Gibbs Assistant Professor at Yale University from July 2021 to June 2023. She specializes in Differenti...
New Faculty: Professor Youngjoon Hong
As of August 1, 2023, Professor Youngjoon Hong was appointed as an Associate Professor. Professor Hong received his Ph.D. from Indiana University in 2015. He served as Assistant Professor at Sungkyunkwan University (2021-2023). He majored in Scientific Computing and Machine Learning.
New Faculty: Professor Woojin Kim
As of July 1, 2023, Professor Woojin Kim joined us as a new faculty member. Received a doctoral degree in 2020 from Ohio State University, Professor Kim worked at Duke University(William W.Elliott Assistant Research Professor, 2020-2023). He specializes in Applied and Computational Topo...
2023 MWC Du-myeong Scholarships and Fellowships Award Ceremony
On Thursday, May 4, 2023, the Du-myeong (Two) Scholarships and Fellowships Awards Ceremony of MWC (Miwon Corporation) was held at the Education 4.0 Lecture Room of the Department of Mathematical Sciences at KAIST. Second-year student Kwon Dohyeong received a scholarship of KRW...
Scientists re-writes FDA-recommended equation to improve estimation of drug-drug interaction
Drugs absorbed into the body are metabolized and thus removed by enzymes from several organs like the liver. How fast a drug is cleared out of the system can be affected by other drugs that are taken together because added substance can increase the amount of enzyme secretion in the body. This dr...
Professor JungHwan Park and Dr. Sungkyung Kang’s work featured by Quanta
Professor Park and Dr. Kang’s recent article “The (2,1)-cable of the figure-eight knot is not smoothly slice” was featured in Quanta magazine. The work is joint with Irving Dai, Abhishek Mallick, and Matthew Stoffregen. Sungkyung Kang got a bachelor degree in 2014 and a master’s degree in 2015 fr...
Department Seminars and Colloquium
Jongho Park (KAUST)Computational Math Seminar
Advanced Iterative Methods as Elementary Iterations on Larger Spaces — Part I: Motivations and Preliminaries
Jongho Park (KAUST)Computational Math Seminar
Advanced Iterative Methods as Elementary Iterations on Larger Spaces — Part II: Theory
Jongho Park (KAUST)Computational Math Seminar
Advanced Iterative Methods as Elementary Iterations on Larger Spaces — Part III: Applications
Donggyu Lee (KAIST)Etc.
Introduction to Étale Cohomology and the Weil Conjectures 2/4
Peter Yi Wei (University of Arkansas)Algebraic Geometry
A Generalization of Green’s Theorem to Symmetric Products of Curves
Graduate Seminars
PDE Seminars
IBS-KAIST Seminars
Graduate School of AI for Math Seminar
MFRS Seminars
Inverse Problems Lab Seminar
Conferences and Workshops
Student News
Bookmarks
Research Highlights
Bulletin Boards
Problem of the week
Trefoil to Figure-Eight by Crossing Changes
A knot is a simple closed curve in three-dimensional space. A diagram of a knot is a projection of the knot to the plane together with over/under information at each crossing. A crossing change is the operation of switching one crossing from over to under or from under to over.
Find up to three examples of sequences of knot diagrams that begin with a diagram of the trefoil knot and end with a diagram of the figure-eight knot, where each step is obtained from the previous diagram by a crossing change.
The obvious chains trefoil → unknot → figure-eight and trefoil → trefoil # figure-eight → figure-eight are not allowed.
(3 points will be given for three correct examples, 2 points for two correct examples, and 1 point for one correct example.)
KAIST Compass Biannual Research Webzine
Trefoil to Figure-Eight by Crossing Changes
A knot is a simple closed curve in three-dimensional space. A diagram of a knot is a projection of the knot to the plane together with over/under information at each crossing. A crossing change is the operation of switching one crossing from over to under or from under to over.
Find up to three examples of sequences of knot diagrams that begin with a diagram of the trefoil knot and end with a diagram of the figure-eight knot, where each step is obtained from the previous diagram by a crossing change.
The obvious chains trefoil → unknot → figure-eight and trefoil → trefoil # figure-eight → figure-eight are not allowed.
(3 points will be given for three correct examples, 2 points for two correct examples, and 1 point for one correct example.)