Testimonial Essay _  Yu Xaioming from Nanyang Technological University

I participated this CAMPUS ASIA program from May to the end of June this year. It is definitely an influential and enriching experience for my research.

I know this program from Prof Ng at NTU Math division. Then after searching relevant information of KAIST math, I realize that KAIST has strong faculties doing similar research area as I did over the past two years. This motivates me to apply for this program. It is of course my pleasure to be accepted by this program and continue my research in Korea.

This research program is mainly about studying research-level (i.e. beyond a standard master level) content in low-dimensional topology. To be more specific, I first learnt hyperbolic Dehn surgery. This is a process where we first drill a tubular neighbourhood of a hyperbolic 3-manifold, and then glue it back with a new identification. Then I learnt that there is a universal upper bound on the number of exceptional surgeries for manifolds with homotopically atoridal boundary. What follows next is the study of -invariant characters in  character variety. Only one of them gives a complete hyperbolic structure of the 3-manifold. But near this point, (in other words, in the same component as this complete case in the algebraic variety), we have the deformation spaces. Then we can compute the matrices relating to the generators of surface group in these deformation spaces. If we set one of the torus boundary to be cusp, then by computer software, this gives the A-polynomial. I tried to work out some details in case of my example in my undergraduate thesis. The last topic we discussed is that the example I can be degenerated with a Sol structure and be regenerated in some case to give the volume. 

Also, besides learning mathematics, I learnt some basic Korea through the weekly Korean class. After the course ends, I am able to read the words in Korean and can understand some basic phrases and vocabulary. I am looking forward to learning a bit more in my leisure time in the future.

The part I like most about this program is that I can get timely feedback from Prof Choi. He is no doubt a very nice professor. He is very patient on explaining everything I am confused with, either through email or physically. I truly appreciate his help throughout this research program.

I believe that the material I have learnt here is definitely a good preparation of my master study in Cambridge in the coming fall, and even would be beneficial for my PhD application and studies. This program also makes me more determined in pursue a career as a researcher in low-dimensional topology.