From child prodigy to chief scientist

After chatting with Xu Xiao for a while, Dong Yi felt Xu Xiao's unique temperament more and more, and no longer regarded him as a child.

"You seem quite interested in my topic, how about I give you a brief overview?"

These days, apart from Yuan Jiyang, Dong Yi has hardly communicated with anyone else, and has been in a highly closed-off state.

Now that he had finally met someone he could talk to, Dong Yi's long-suppressed desire to share was awakened.

"If you don't mind, that would be great. I will definitely keep this information strictly confidential."

Xu Xiao was naturally very curious about what Dong Yi's research topic was. In addition, having the opportunity to exchange ideas on such academic issues could also help her accumulate time for brainstorming more quickly.

In the following time, Dong Yi briefly told Xu Xiao about his research topic and some problems that had not yet been solved.

Listening to Dong Yi's introduction, Xu Xiao realized that this topic was indeed very complex, much more difficult than the one she had studied before.

It is already quite remarkable that Dong Yi has been able to carry out his research to this point.

"Alright, it's getting late. Let's stop studying this now and get some rest."

Dong Yi was just using this to release his emotions; he didn't have any other intentions.

Xu Xiao, however, took this matter very seriously and was already trying to find a solution.

Although this is Dong Yi's research topic, even if Xu Xiao can find a solution, he cannot publish the results without permission.

But the process of researching this problem alone was enough for Xu Xiao to thoroughly enjoy.

He had been wanting to find another research topic, but finding a topic was not an easy task.

Although Dong Yi's topic is somewhat complex, it is not necessarily without hope of finding a solution.

Through this process, it is highly likely that the progress of the thought entry task will be advanced significantly.

The next morning, Xu Xiao did not go to the classroom as originally planned, but went directly to the computer lab.

He needs to find enough relevant information to see if he can find some methods he can refer to.

In the first batch alone, Xu Xiao downloaded more than thirty papers and printed them all out to study them slowly.

Xu Xiao can now read original English papers without much trouble. She doesn't need to translate them in her head and can read them quite naturally.

After spending several days studying these papers, Xu Xiao tried again to solve the problems in Dong Yi's research.

However, this method did not work immediately. When he actually tried to study the topic, he understood Dong Yi's feelings more and more.

"I think you've tried all the methods I can think of. It seems that solving this problem really isn't going to be easy."

Although Dong Yi's mathematical talent may not be as great as Xu Xiao's now, as a former member of the national math competition training team, Dong Yi's mathematical talent is definitely top-notch.

In addition, he has been researching this topic for nearly a year and has read at least a hundred papers, basically covering the fields related to this topic.

Despite this, Xu Xiao did not give up immediately, but instead prepared for a protracted battle.

Since some conventional methods may not be applicable, I will further expand the scope of my learning and not limit my attention to the only area that Broué conjectured.

Sometimes, two topics from different fields may have similar solutions.

This phenomenon can even exist in two different disciplines. Anyway, Xu Xiao has plenty of time, so even if he can't really solve this problem, there's no harm in learning more knowledge.

As time went by, Xu Xiao consulted a lot of materials and listened to some more advanced mathematics courses.

Although he hadn't found a way to truly solve the problem during this period, his math skills improved by more than ten points, and he accumulated fifty hours of brainstorming time.

That evening, after returning to her dormitory and washing up, Xu Xiao lay in bed, her mind wandering to all sorts of mathematical methods.

This is precisely the effect of the term "mathematical intuition." Whenever Xu Xiao thinks about mathematical problems, his brain naturally becomes more active.

Just then, an idea suddenly popped into Xu Xiao's mind.

"If we change our approach... and instead of constructing the self-dual complex in one go, we use a layered, iterative weak duality lifting method, will the result be any different?"

Xu Xiao learned about this idea from a paper, although the paper was not about the Broué conjecture, but it seemed to be very suitable for Dong Yi's research topic.

Thinking of this, Xu Xiao immediately got out of bed and went to the whiteboard to write.

Noticing Xu Xiao's somewhat unusual behavior, Dong Yi also got up and went over to look at the contents of the whiteboard with some curiosity.

Xu Xiao drew a group chain on the whiteboard; more specifically, it was a normal subgroup chain of D8.

As a researcher in group representation theory, Dong Yi is naturally very familiar with this.

For a moment, he had no idea what Xu Xiao was thinking.

It wasn't until he looked at the whiteboard and thought for a while that he finally guessed what Xu Xiao meant.

"Xu Xiao... do you want to use the normal subgroup chain of D8 in the derived equivalent complex construction?"

"That's right, senior brother, I feel we can definitely try this approach."

Even after confirming that his guess was correct, Dong Yi was still somewhat confused.

Based on his experience, no one had ever made a similar attempt before.

Strictly speaking, Xu Xiao's ideas belong to algebraic geometry and are not at all related to representation theory.

This kind of cross-disciplinary thinking can indeed seem somewhat unbelievable.

Seeing the confusion on Dong Yi's face, Xu Xiao continued to explain:

"Senior brother, I don't know if this method will definitely work, but doing automorphic distortion on the entire D8 group all at once, like before, will definitely not solve the problem."

"This way of forcibly binding together subgroups with different topologies will inevitably destroy the compactness of the group."

"We can't do the entire group's distortion all at once; we need to do it piecemeal..."

Hearing Xu Xiao's ideas, Dong Yi nodded in agreement.

"I agree with that. I realized this mistake before and tried a reductionist approach, but it didn't work in the end. We need more than just a general idea; we need more specific ideas."