Prof. Bumsig Kim in Words | Home > Prof. Bumsig Kim in Words |

MSc Seoul National University, 1989.

PhD University of California at Berkeley, 1996.

Postdoctoral Fellow at the Mittag-Leffler Institute, 1996-1997.

Visiting Research Assistant Professor at University of California at Davis, 1997-1999.

Assistant Professor at Postech, 1999-2001.

Associate Professor at Postech. 2001-2003.

Professor at KIAS, 2003-2021.

**Awards**

Korean Government Scholarship, 1990.9.1 - 1992.8.30.

Sloan Doctoral Dissertation Fellowship, 1995/1996.

Excellent Paper Award by Department of Science and Technology, 2000.

Young Scientist Award, 2003.

Invited Speaker at ICM Seoul, 2014.

POSCO TJ Park Science Prize, 2014.

Korea Science Award, 2020.

**To Make Noncommutativity Commutative, **

**in “Essays of Natural Scientists”.**

**Bumsig Kim. **

When I was in middle then high school, I preferred math over all other subjects. This is because math problems already have an answer built into the problem (otherwise they are not good problems). One of the things I realized while learning and researching new mathematics in earnest during graduate school was that the answers to questions in mathematical research were already embedded in the subjects. But since they were new to me, I felt like I was finding hidden objects. Then when several of us exchanged ideas, full pictures began to appear. As many things became clear and ordered, I often wondered, “Why didn't I know this before?” I had this experience again recently.

Last February at KIAS I met Professor Ueda, a mathematical scholar at the University of Tokyo. Prof. Ueda showed me the physics manuscript he had written a few days prior with Dr. Yutaka Yoshida, a researcher in the School of Physics at KIAS. Prof. Ueda suggested that we study his physical observations as a mathematical problem together. Ueda’s article studied non-commutative A-twisted Gauged Linear Sigma Models (GLSMs) in string theory. As an example, a formula for finding the A-twisted correlation (a kind of Gromov-Witten invariant for complex three-dimensional Calabi-Yau manifolds expressed as complete intersections in Grassmannians) was obtained using supersymmetric localization.

The field of GLSM research began with a paper published by Witten in 1993. This led to active research in the mid-1990s. More recently, new research groups have emerged in both mathematics and physics to study GLSMs again. I too have worked on GLSMs, interacting with researchers through lectures and attending international GLSM conferences for the past several years because the quasimap theory I developed can be used as a mathematical background for GLSMs. However, there is a reason I liked this particular conference. There was something unique about it. Mathematicians and physicists equally participated and took turns giving lectures. Therefore, I could do other things during the physics lectures without any remorse! It was quite the opposite at my first such conference. There, I listened intently to the physics lectures eager to do interdisciplinary research or to use original ideas from physics in mathematics. I soon found out that this was near impossible in lieu of a basic physics background. At the time, it was not easy for me to listen to physics lectures and get mathematical inspiration unless I met a very patient teacher. I learned by listening and asking questions over and over again starting at the beginning. Ultimately, I decided to just develop my strengths.

Then again, unexpected things happen in life. I recently wrote a research article with a physicist! Even when A-twisted GLSMs emerged and Professor Kimyeong Lee of our School of Physics here at KIAS published many relevant papers, I did not bother to engage. So last February when Professor Ueda informed me that the mathematization of A-twisted GLSMs is closely related to the graph quasimap invariant that I am familiar with and is a mathematically meaningful research topic I thought, “Oh my god, how can this be?”

I quietly listened to Professor Ueda's story and found out that it was also related to the problem I had asked Jeongseok Oh, a doctoral student at KAIST, to think about three years ago. My ideas on the subject at that time were as follows. Manifold changes occur according to GIT stability variation and Oh and I aimed to understand wall-crossing phenomenon for Gromov Witten invariants of these manifolds. So, I reviewed the literature to see if toric residue mirror symmetry could give me an idea of what to do. After a few months of trying, no progress was made. I stopped trying.

Professor Ueda realized that the generation function of A-twisted GLSM correlation is expressed as a toric residue when it is commutative, and had even imagined extending it to the noncommutative case. Three years ago, Jeongseok Oh and I focused on wall-crossing exclusively. It never occurred to us to generalize this to noncommutative cases. I realized once again that the direction you set is crucial no matter what you study. Why didn't I think of this?

Things moved quickly now. My student Jeongseok Oh joined the project and Professor Ueda, Dr. Yutaka Yoshida, and I all met every day of the week. Ultimately, we were lucky enough to discover a noncommutative extension of A-twisted GLSM toric residue mirror symmetry. Fortunately, Professor Ueda had a good understanding of some of the ideas from physics. Perhaps because he majored in physics in his undergraduate school, Professor Ueda was able to listen to Dr. Yutaka Yoshida's ideas and explain them to us. Jeongseok Oh and I played the role of providing a mathematical basis for how the A-twisted correlation they were discussing could be expressed as an invariant of graph quasimaps. Finally, we confirmed that this physical quantity and the mathematical invariant we constructed were exactly the same (as far as we knew). In particular in the noncommutative case, our problem could be solved by using commutative principles.

Once again, I feel that research is not much different from life. People say that KIAS is a place where ideas are exchanged openly. I think I should take more time trying to understand people and approaching others with an open mind. Yes, let's take more time to be patient. Perhaps I can do more in-depth and enjoyable research.

Transltated by David Favero and Jeongseok Oh