CHAPTER 686: CHAPTER 214: PETER, YOU HAVE TO LISTEN TO ME! (PART 2)

Modular forms, modular spaces, and numerous algebraic geometry problems, all fall within this category.

Clearly, with an infinitely innovative mind in mathematics, the 17-year-old Qiao Yu has an unparalleled advantage in the research layers of the Condensed Mathematics Program.

However, Qiao Yu’s attitude during this period has truly disappointed Peter Schultz. It’s no exaggeration to say that many times Peter Schultz carefully calculates the time difference to communicate with Qiao Yu, but every time after just exchanging a few words, this guy gets busy with something else.

So he arrived in Huaxia three days earlier, just to see what exactly Qiao Yu was busy with.

For Qiao Yu, meeting Peter Schultz wasn’t because of this giant’s status in the mathematics world.

They were both Fields Medalists; as for those other math awards, it wasn’t that Qiao Yu couldn’t win them, but rather that considering his age, it wasn’t suitable for him to receive them yet.

Meeting up with Peter Schultz was mainly because of Qiao Yu’s high moral standards—he had made all sorts of promises while in Philadelphia.

After returning to Huaxia, he first went back to Star City for a week-long solid romance, and then after returning to Beijing, started getting busy with all sorts of messy stuff, indeed neglecting this giant who had helped him a lot before.

Peter Schultz arrived on the twelfth, and on the morning of the thirteenth, Qiao Yu invited him to Qiuzhai at Huaqing.

It’s not like Qiao Yu has been at Huaqing all the time; mainly, Qiao Yu cares a lot about face.

Usually, he receives family in his small room, which is no big deal; but for receiving international friends, it’s more imposing to do it at his Master’s Master’s place.

It’s not that Director Tian’s office is bad; it’s mainly because he had just cleaned out all of his master’s books not long ago. Until now it’s not completely refilled; the bookshelf behind looks empty and not very elegant.

Even his Master recently didn’t want to receive guests in his office anymore, let alone him.

Qiuzhai is different; Elder Yuan not only specially vacated a spacious and imposing office for him but also stored here the books he borrowed from Director Tian and some of Elder Yuan’s collections, making it full of the fragrance of books and quite impressive.

So early in the morning, Qiao Yu shouldered his computer and rushed to Qiuzhai; after all, time couldn’t be wasted. Strictly speaking, there were only three days left until the conference, as the fifteenth was primarily for registration, and his special report was scheduled for the morning of the sixteenth.

However, unfortunately, his paper isn’t finished yet. Or rather, his construction of the Qiao Yu Modal Space isn’t perfect, and there are some problems he hasn’t thoroughly thought through.

It was just right; when Peter Schultz arrives, they can discuss it.

Essentially, the key idea of his Qiao Yu Modal Space is to describe the state within a complex system through high-dimensional geometric space and provide a geometric framework for specific problems.

The seemingly complete space proposed by Schultz is also a kind of high-dimensional abstract geometric space aimed at connecting different fields in algebraic geometry to solve some difficult problems.

Therefore, the thought processes of both are, in some sense, aligned. Moreover, both of them have used many Category Theory tools.

After all, the person has come all this way, flying over ten thousand kilometers, not to fully utilize the resources would make Qiao Yu feel a bit embarrassed.

And indeed, the current problem he faces is quite troublesome. Mainly it’s the issue of non-uniqueness in high-dimensional mappings of modal pathways.

In Qiao Yu’s concept, one of the most important tools in simulating Quantum State evolution is the modal path Γ⊂Mmodal . Its function is to depict Quantum State evolution within the modal space.

The problem is that in a local region, the mapping of the modal path is unique, but once magnified to the entire high-dimensional modal space, the complexity of the high-dimensional topology often results in paths being unable to maintain global continuity and consistency.

And if the uniqueness of path mappings cannot be ensured, then multiple modal paths corresponding to the same evolution result will inevitably appear. Thus, in the simulation process, the real evolution trajectory of the Quantum State cannot be determined, leading to path bifurcations or loops.

This means that the entire system’s description of Quantum State evolution will no longer be reliable. Or that its robustness is insufficient; the system is quite unstable and cannot be directly used.

Qiao Yu reflected a lot over these past two days on potential solutions, such as introducing topological constraints on the modal paths to reduce possibilities or introducing path consistency corrections.

The former cannot completely solve the problem, while the latter will make the system overly elaborate, as it increases a lot of verification computations.

These are key in Quantum Computing. Without solving this, his Qiao Yu Modal Space would be a joke.

They agreed to meet at 9:30 AM, but Qiao Yu arrived at Qiuzhai an hour early.

He first settled issues on the computing side for half an hour, then opened up his paper and began pondering deeply.

Until someone knocked on the office door.

"Dr. Qiao, Professor Schultz has arrived." It was Huaqing’s Pan Jingyuan, Professor Pan, who brought Peter Schultz.

There was no choice; many guests needed receiving these two days, and as long as the mathematics research centers and the School of Mathematics hadn’t any class tasks, they were basically called upon for receiving duties.

General academics were received by the school’s graduate student volunteers. But for Fields Medalists like Peter Schultz, students were naturally not enough.

"Hi, Professor Schultz, long time no see." Qiao Yu immediately stood up and welcomed Peter Schultz into the room.

Pan Jingyuan greeted Qiao Yu with a smile, then quietly closed the door and left. In fact, he was quite interested in listening to the conversations between the globally recognized mathematical geniuses from the East and West.

"Have a seat. By the way, tea or coffee?" After Pan Jingyuan left, Qiao Yu asked.

For hospitality, he specially received a box of supposedly very good tea leaves from Director Tian.

As for coffee, it was the kind bought casually at the school supermarket, instant coffee in strips, which were somewhat brand-name.

"Coffee, please." Peter Schultz said after hesitating for two seconds.

"Haha, Peter, you have great taste,"

Qiao Yu complimented with a smile, then took a packet of instant coffee from the drawer, got up and made a cup for Peter Schultz himself, and then realized that it seemed like there was no spoon.

A bit embarrassing, it’s a small oversight, but it’s whatever; after all, this guy wasn’t here just for coffee.

As expected, seeing Qiao Yu simply handing over the coffee, Peter Schultz was taken aback but said nothing, taking it and placing it aside. Then he spoke, "Qiao, in Philadelphia, you did promise me."

"Hold on, Peter, let me tell you an idea, and once you hear it, you’ll realize it’s a very brilliant idea!"

Qiao Yu directly shifted the topic.

Just kidding, this was his home ground; how could he allow this guy to lead him around?

Peter Schultz indeed took the bait, smoothly asking, "Oh? What idea?"

Obviously, the opposite took the bait.

Qiao Yu spoke seriously, "Before I explain this idea, you need to answer me a question first. Do you also think using Hilbert Space to study quantum physics has fallen far behind the times?"

Peter Schultz looked at Qiao Yu and said, "Qiao, at most you can say that Hilbert space doesn’t intuitively describe practical measurements.

The completeness of Hilbert space is very elegant. Moreover, it can use distribution theory and Lie algebra to compensate for its shortcomings."

Qiao Yu shook his head, arguing, "Peter, you can’t say something against your will just because Hilbert is your compatriot. The fact is that Hilbert space doesn’t directly reflect the essence of physical phenomena.

For example, the process of wave function collapse is more of a mathematical abstraction rather than a real evolutionary description.

Or consider quantum state measurement, where we only obtain probability distributions, and the vector properties in Hilbert Space are of no use. Am I wrong?"

Peter Schultz looked at the animated Qiao Yu, took a deep breath, and asked, "So you’re planning to create a complete space that can be used to study quantum physics and solve all the problems of Hilbert Space?"

"You got it!" Qiao Yu snapped his fingers gleefully, his demeanor exuberant.