From child prodigy to chief scientist

At the beginning, Dong Yi's research did indeed proceed quite smoothly.

He quickly completed all the previous proofs one by one.

However, as the research progressed, he gradually realized that the topic was much more complicated than he had imagined.

But by this point, it was too late for him to change his research topic, so he had no choice but to grit his teeth and keep going.

"If all else fails... we'll have to choose to publish a sub-topic."

This was a difficult outcome for Dong Yi to accept, since publishing only a sub-project would greatly diminish the value of the entire research.

However, the delayed graduation is also very difficult. Recently, he has often doubted himself and wondered if he is really suited to do scientific research, which makes him very anxious every day.

"Never mind, let's go back to the dorm first."

Seeing that it was getting late, Dong Yi didn't want to dwell on the matter any longer, so he packed his things and prepared to go back to his dormitory.

On the way, Dong Yi remembered something Yuan Jiyang had told him during the day.

"Oh right, Ms. Yuan said I'll have a new roommate coming over today... Oh well, whatever."

Since the beginning of last semester, Dong Yi has been living alone and has become somewhat accustomed to living alone.

Anyway, I don't usually stay in my dorm room much; I spend most of my time in the lab.

For him, having one more roommate wouldn't make much difference.

After a brief moment of thought, Dong Yi's attention inevitably returned to his own research topic.

Back at the dormitory entrance, Dong Yi habitually took out his key to open the door, only to find that it was unlocked, and then he remembered that he had a new roommate.

But when he opened the door and saw Xu Xiao in the dormitory, he froze on the spot.

"This...is my new roommate?"

He had subconsciously assumed that his roommate must also be a PhD student.

But the person in front of me was clearly a child, who looked to be only eleven or twelve years old.

At this moment, Dong Yi was completely baffled as to what was going on.

Upon seeing Dong Yi enter, Xu Xiao politely stood up and greeted him.

"Hello, senior brother, my name is Xu Xiao."

"Ah, hello."

Dong Yi had no recollection of the name Xu Xiao, and naturally had no idea who Xu Xiao was.

In this era, there are no things like Weibo trending topics. Apart from checking academic papers online, Dong Yi doesn't pay much attention to news on the internet.

Furthermore, since Yuan Jiyang hadn't given him a detailed introduction to Xu Xiao before, Dong Yi had no idea that Xu Xiao had already secured a place at Peking University through the guaranteed admission program.

After a quick thought, Dong Yi had a vague guess in his mind.

Perhaps Xu Xiao is the child of a relative or friend of Yuan Jiyang, and is using this connection to come to Yenching University for a period of time.

To be honest, Dong Yi was somewhat unhappy with this arrangement; he might even have to babysit someone else's child.

Now I'm even having trouble graduating on time, how can I possibly have the mood to play with my child every day!

This made his already anxious mood even worse, and he no longer wanted to communicate with Xu Xiao, so he went to the bathroom to wash up on his own.

Xu Xiao noticed that Dong Yi seemed to be in a bad mood, and knew that it was probably because her arrival had disturbed his peaceful life.

He could only try his best to be a decent roommate; he didn't expect others to like him, but at least he didn't want to be disliked.

…………

In the days that followed, Xu Xiao continued to attend classes in the classroom every day.

Just as he had predicted, he did find it easier to enter a brainstorming state while listening to university lectures, and the progress of the task was significantly faster than before.

However, when listening to courses such as mathematical analysis and higher algebra, Xu Xiao would often take out his own materials to study on his own.

After all, he had already learned most of these courses when he was preparing for the math competition, and he had already mastered a lot of the content that the teacher taught.

This made Xu Xiao realize that she could skip many basic math courses in her first and second years and go directly to advanced courses in her third year and beyond.

On the other hand, after a few days of adjustment, Dong Yi has gradually gotten used to having an extra roommate.

Contrary to his expectations, Xu Xiao's arrival did not have any impact on him.

Every night, Xu Xiao is very quiet in the dormitory. She goes to bed on time when the lights go out, so it doesn't affect her at all.

He would even take the initiative to do some of the dormitory cleaning work, making the dormitory environment much cleaner than when Dong Yi lived alone.

This gradually changed Dong Yi's attitude towards Xu Xiao, and he seemed less anxious every day.

That evening, Dong Yi returned to his dormitory after finishing his work for the day.

Recently, he tried to use some new methods to prove his conjecture. Although he has not made any progress yet, at least he can still see a glimmer of hope.

While washing up, Dong Yi was still thinking about the research project, and he almost forgot to rinse his mouth after brushing his teeth.

"Wait a minute... If we can use Green's approach to reduce the subgroups, first solve the derived equivalence of the subgroups, and then promote them back to the original group, it seems possible to solve this problem..."

Thinking of this, Dong Yi didn't bother to wash up properly anymore. He just grabbed a towel and wiped his face before going to the whiteboard to start deriving the code.

Previously, Dong Yi had bought a whiteboard and hung it on the wall so that he could easily record his thoughts at any time.

That way, if he suddenly has a new idea while in the dormitory, he can write it down on the whiteboard.

Dong Yi's approach makes some sense, because the Broué conjecture requires constructing derived equivalences between large groups of blocks, but the block structure of large groups is itself very complex.

The structure of defective groups is relatively simple, making it easier to construct equivalences.

Following this line of thought, Dong Yi began the work of simplification on the whiteboard.

It must be said that his reduction path is very clear: first, he splits the group structure, then constructs it at the subgroup level, and then tries to pull back the original group.

However, before he could finish writing down all the steps, Dong Yi suddenly stopped, and his expression, which had been somewhat radiant, suddenly dimmed.

"No...this method won't work either..."

Dong Yi did not continue the derivation because he realized that this method was not applicable to his research topic.

In Green's correspondence, there is a rather hidden boundary of applicability—it can only preserve the properties of a single module and cannot preserve the improvement of derived equivalence.