From child prodigy to chief scientist
Chapter 88 A Special Case of the Broué Exchange Conjecture
"No problem, I'll definitely get all your enrollment procedures done in the next couple of days. Do you need me to arrange a dormitory room for you during this time?"
"Then I'd appreciate it if you could help me make some arrangements, Ms. Yao. Staying in the dormitory would be more convenient."
In fact, distance is only one aspect. Even if her parents move here in the future, Xu Xiao still won't live in the family compound on a regular basis.
He doesn't need his parents' care now. Now that he's in college, he should try to be as independent as possible.
…………
Over the next two days, Xu Xiao and her family of three visited several tourist attractions in Yanjing.
Under Xu Xiao's guidance, Xu Lang and Yu Guilan had a great time, and they were also very surprised by Xu Xiao's performance over the past two days.
The two adults were a bit lost in Yanjing, but Xu Xiao seemed to know the place very well, and had planned all the routes very clearly.
Even communicating with the scenic area staff was handled entirely by Xu Xiao herself, without Xu Lang and Yu Guilan having to worry about it.
Xu Xiao's level of maturity is completely unlike that of an eleven-year-old child; even college students of normal age might not be able to match him.
Meanwhile, Yao Lei had already helped Xu Xiao complete all the enrollment procedures and informed the school about the need for Xu Xiao to be assigned a dormitory room.
It just so happened that there was a PhD student in Yuan Jiyang's lab who was living alone, so they decided to let Xu Xiaoxian live in that PhD student's dormitory.
Having a roommate to help look after things a little makes everyone feel more at ease.
After a short two-day holiday, Xu Lang and Yu Guilan sent Xu Xiao back to Yenching University and then prepared to return to Gangcheng.
Xu Lang and Yu Guilan were still a little worried about Xu Xiao starting a new life on her own at Yenching University.
"Xiaoxiao, we'll finish dealing with things in Steel City as soon as possible, and then we'll come to Yanjing to be with you."
"Dad, Mom, don't worry, I'm used to living in the dorm. It's okay if you come here later."
"Parents, you can rest assured that Xu Xiao is safe with us. We will take extra care of him and ensure his safety on campus."
Yenching University even specially arranged a "life teacher" for Xu Xiao. Although it was not to the extent of taking care of Xu Xiao's daily life, the teacher would still pay attention to his situation every day and provide assistance when necessary.
After seeing Xu Lang and Yu Guilan off, Xu Xiao began to choose courses that suited her and started auditing classes at Yenching University.
Given Xu Xiao's current level of knowledge, studying university courses is more suitable, as it would make it easier for his brain to enter a state of mental brainstorming.
However, to prevent the actual course experience from being less than ideal, Xu Xiao printed out some papers in advance as a backup.
In this way, if you have already understood what the teacher is saying in class, you can switch to self-study mode at any time to maximize your learning efficiency.
At 10 p.m., Xu Xiao returned to her temporary dormitory.
His doctoral dormitory was a two-person room, and it wasn't the kind with a bunk bed and a desk underneath. Instead, the bed and desk were separated, making the room feel more spacious.
Xu Xiao has not yet met his roommate, and he is somewhat curious and looking forward to it.
the other side.
Even though it was past 10 p.m., Dong Yi was still in the lab, carrying out his research.
As a third-year doctoral student in the Department of Mathematics at Yenching University, Dong Yi is currently under a lot of pressure.
To graduate smoothly, you must publish your thesis before July this year.
It's already April, and he hasn't even finished his research project, let alone published a paper.
Dong Yi's current research topic is related to the Broué exchange conjecture.
The Broué commutative conjecture is one of the most important open conjectures in the representation theory of finite groups. Together with the Alperin weight conjecture and the Dade conjecture, it forms the three core conjectures of modular representation theory.
In simple terms, let p be a prime number, G be a finite group, b be a p-block of group G, and P be a deficient group of b.
If P is an abelian group, then the block b is derived equivalent to its Brauer counterpart in the normalizer N_G(P) of P.
This conjecture has not yet been fully confirmed, but many of its special cases have been proven.
Dong Yi's specific research topic is a special case of the Broué exchange conjecture—the verification of the Broué conjecture for blocks with a deficient group of order 8 dihedral group D8.
Dong Yi has spent nearly a year researching this topic.
During this period, Dong Yi had completed most of the proof process, but he had been stuck on a key part for a long time.
In this isomorphic construction, he needs to construct a specific bimodal M such that it induces the expected triangular equivalence.
More specifically, Dong Yi needs to prove the existence of a complex X∈D^b, which must satisfy a series of stringent homology conditions.
Before this, he had tried several classic constructions, including the Rickard complex and the Okuyama deformation, but he was never able to complete the final verification.
After yet another failure, Dong Yi sighed helplessly.
"Sigh... If I had known, I wouldn't have chosen this topic in the first place."
In fact, based on his previous grades, Dong Yi was already considered an outstanding student in the Mathematics Department of Yenching University.
During high school, Dong Yi was directly admitted to the Department of Mathematics at Yenching University based on his CMO national team performance.
After graduating with his bachelor's degree, Dong Yi continued his studies in the Department of Mathematics at Yenching University.
During his master's studies, he solved a problem concerning the finiteness of block algebras in modular representation theory. His paper was published in the Journal of Algebra, which astonished many mathematics professors.
Unexpectedly, when he reached the doctoral stage, he faced the embarrassing problem of not being able to graduate on time.
Back when he chose this topic, Yuan Jiyang specifically reminded him of its difficulty and hoped that he would choose it carefully.
Yuan Jiyang has extensive experience in mathematical research and knows that this topic has high academic value. If the research is successful, it is entirely possible to publish a paper in a top-tier journal.
However, this also exposes Dong Yi to significant risks.
If he encounters any bottlenecks in the research process and the progress of the project cannot be advanced, he may face the situation of not being able to write the paper.
However, Dong Yi was very confident in himself at the time and did not change his mind because of Yuan Jiyang's persuasion. Instead, he continued to stick to his choice.
Seeing Dong Yi's insistence, Yuan Jiyang ultimately did not directly interfere with Dong Yi's choice of topic and went along with his idea.
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