From child prodigy to chief scientist

Xu Xiao had already anticipated this, and continued calmly:

"Senior, here's my idea. First, construct a complex X0 that is invariant to the smallest normal subgroup Z2. Since Z2 is a cyclic group, its structure is very simple, and it's not difficult to construct a perfect complex."

"Next, we will deal with the quotient group D8/Z2≅ V4, which is the three second-order isomorphisms of the Klein quaternion, twisting them one by one and gluing them together layer by layer..."

This time, Dong Yi didn't immediately refute anything. Instead, he frowned and began to think carefully.

From a conceptual standpoint, Xu Xiao's proposed method is undoubtedly somewhat unusual, as there are virtually no similar solutions for similar problems.

Logically speaking, Dong Yi felt that this method was indeed worth trying.

This hierarchical structure aligns perfectly with his recent research ideas.

As for the specific implementation strategy, Dong Yi couldn't find any problems; everything was supported by sufficient theory.

After thinking for a while, Dong Yi finally said:

"I think everything else is fine, but there's one point I'd like to mention: the mapping cones that are glued layer by layer may cause iterative divergence, which would make it impossible to guarantee compatibility."

What Dong Yi said is indeed an objective problem, but Xu Xiao has also considered this issue.

"Senior, we can use a homology algebra tool to control the homology of the group expansion, which will allow us to constrain the homology convergence of each layer of mapping cones..."

As he spoke, Xu Xiao wrote the relevant specific spectral sequences on the whiteboard.

"As long as all the differentials on page E2 are guaranteed to be zero, the spectral sequence will converge to the homology of the final complex, and the iteration will not diverge."

Seeing that Xu Xiaolian had already thought of this problem and prepared a corresponding solution, Dong Yi was speechless.

"Xu Xiao, where did you learn so many methods from?"

"Hehe, I have a wide range of knowledge. I read all kinds of papers, and some of the methods just happen to come in handy."

"Really? Looks like I'll have to read more papers in the future."

Although he said that, Dong Yi knew in his heart that this was not the most crucial point.

Often, when researchers are unable to solve a problem, it is not because they lack knowledge reserves, but because they lack the ability to apply knowledge flexibly.

Even if he saw the same paper, he might not be able to come up with this method like Xu Xiao.

This powerful mathematical intuition is the more crucial factor in determining the upper limit of a person's research ability.

By the time the two finished talking, it was almost midnight.

Although they were all eager to get started on the next task, it was not something that could be accomplished overnight. In the end, they suppressed their excitement, went back to bed, and forced themselves to fall asleep.

The next morning, both of them woke up early, each made a cup of instant noodles, and after eating, they started working according to the plan they had made the night before.

Although this was their first collaboration, they had excellent chemistry, just like longtime partners who had worked together for many years.

They can understand each other immediately through very brief exchanges.

"No problem, the homology results from Magma are exactly the same as the ones I calculated manually."

"Okay, when twisting layer by layer, remember to twist a first and then c, otherwise you might create a torsion element."

"I've finished calculating the integral of the spectral sequence. Could you double-check for any errors?"

The two spent a whole day completing the framework setup and core verification.

Next, all that's needed is to complete the final verification, and all the problems will be solved.

The final verification work is quite tedious, as they must verify all the conditions required by the Broué conjecture one by one.

If any one of these conditions cannot be met, then all their previous work will be in vain.

After resting for a night, they first made a checklist and then began to verify each item one by one.

"All terms of the complex are finitely generated transmission modes, which satisfies this condition."

"The self-dualism of the complex is satisfied."

"The perfect functor of the tensor product-induced triangular domain satisfies..."

As each condition was successfully verified, Dong Yi's hands began to tremble with tension and excitement.

Each completed verification means he is one step closer to completing his research, increasing his chances of graduating on time.

Finally, after their continuous efforts, only one property remained to be verified.

"P-advanced topological compactness... Satisfied!"

After checking the box for this last condition, Dong Yi let out a heavy sigh, closed his eyes, and leaned back in his chair.

At this moment, he did not feel much joy. Instead, he felt as if all the strength in his body had been drained away, and all he wanted to do was rest.

To be honest, although the work these past two days has been very intense, it shouldn't have exhausted him to this extent.

This is more of a psychological exhaustion. For nearly a year, Dong Yi has been on edge because of this project, and has never truly relaxed.

"It's over...it's finally over."

After resting for a while, Dong Yi finally felt some strength return to his body, and the excitement and sense of accomplishment from successfully completing the research project slowly welled up inside him.

Even among doctoral students in the Mathematics Department of Yenching University, the academic value of this topic is definitely among the top.

As long as there are no major problems with his subsequent thesis, Dong Yi will not only be able to graduate smoothly, but also has a very high chance of obtaining a position at the university.

Those decadent days are gone forever!

After the initial excitement, Dong Yi looked at Xu Xiao with some emotion.

"Without this child's help... I don't know how much longer it would have taken me to solve this problem."

Although most of the work on this project was done by Dong Yi himself.

However, if Xu Xiao hadn't appeared in time, this crucial deadlock would probably have kept Dong Yi stuck indefinitely.

Even if he were to extend his studies for another year, he might not be able to come up with the same method as Xu Xiao.

Overwhelmed with emotion, Dong Yi didn't even know how to express his gratitude to Xu Xiao.

"Xu Xiao... thank you... you're a true math genius, the most amazing math genius I've ever met!"

At this moment, Xu Xiao was still immersed in the joy of solving the problem, and when he suddenly heard Dong Yi say these things, he felt a little at a loss.

"You flatter me, senior. I'm just interested in this topic, which is why I wanted to try to solve it."