We first started with orientation on 31 May 2017. Prof.Lazaros, Kelly and Parker introduced us about DIMACS and Rutgers. I met my mentor, Prof.Anders Buch, in that afternoon. We discussed about our project related to Grassmannian and quantum cohomology rings. We also attended workshop about creating website for updating our profile on DIMACS' website. On Friday, I met my mentor again. We discussed about first presentation. I worried about this presentation because I did not understand his paper. However, I finished my presentation and my mentor liked it (?). Before I came here, I had been nervous because I had done research aboard last year and I had no friends there! (nobody speaks English.. what a boring life!) My father told me that I should come to USA because people living here are really friendly. Fortunately, I have many friends now. :) They are very kind and they try to understand what I was saying. lol
We gave a first presentation on Monday. I think it was a good chance to see brief work concepts from my friends. On Tuesday, there was a seminar presented by Nelli Sloane. I had spent this week to study in algebraic variety, projective space, Schubert variety and so on. I have read many lecture notes on internet and also study via youtube. It was very difficult for me to learn everything myself, especially defining groups/rings/functions which I have never seen before. I cannot imagine what they are and why this definition is natural. Anyway, Prof.Anders is very kind. I could send him email whenever I was struck.
I had discussed with Prof.Anders Buch on Monday. He explained some points that I did not understand from his paper. He said I should write down some examples using the definitions. I really appreciate his help, but sorry Anders, I cannot. ￼ However, I will try to do my best (Promise!). I spent this week to read some points related to Schubert variety that I still did not get any idea about them. I started to read homology groups and cohomology groups, how to define them and what their property is. I attended a seminar by Sorelle Friedler. It was great! Now I know how to use a fake name on facebook without getting flagged (Just kidding). There was a Culture day on Friday. I gave a presentation about Thailand. We really had fun today. We danced and played a game by Czech students. Finally, cake was awesome!
On Monday, I had discussed about homology and cohomology with Prof. Anders. He introduced some functions and a brief concept in geometry ideas for these groups. We attended a seminar given by David Pennock on Tuesday. I spent this week to study the Littlewood-Richardson rule, the Pieri formula, Jen de taquin slides and using the sage program for checking my answers.
Prof.Anders introduced me his conjecture. It is related to some properties of small quantum cohomology which is determined by the fact that Gromov-Witten invariants are non negative integer. He also proved that this conjecture is true for Gr(2,n). Moreover, he introduced this problem with quantum k-theory. We went to IBM on Friday. It was really nice! I got an inspiration to study in quantum physics in future.
I had spent this week for solving the conjecture. I tried to use maple with my mentor's instruction. I computed the product of quantum cohomology rings and compare with the results using the program. We attended graduated school panel on Friday. I have learned useful things to improve my graduated school plan.
I tried to prove the conjecture again and again. Everytime I have done my proof, I always find the incorrect things later. Anyway, there is two weeks left! I did my presentation and present it on Thusday. Everyone did a good job. After we finished our presentation, we had lunch together and sang HBD song to Prof.Lazaros.