304: Chapter 304 Undergraduate Graduation Defense

He flipped open a page of paper covered in arrows, pointing to a dense area filled with norm estimates and integral boundary conditions: "The problem with the lower bound of the dimension of Kakeya sets is that the tubes in different directions overlap too densely. If you try to separate them directly using dispersion estimates from the Fourier transform, the singularity of the directional parameter space will cause the main term to spin out of control."

"But if instead of separating them, we accept these overlaps and use your set of mappings to map the singular contributions of the overlapping regions onto a structure with extra symmetry to offset them, we might be able to continue pushing down the lower bound of the dimension."

Zhao Yang took the several pages of manuscript. The derivation marks on the paper were very fresh, with several places crossed out and rewritten multiple times, showing they had been repeatedly refined. He stared at those repeatedly circled offset paths for a long time.

"Dimension reduction." Zhao Yang looked up.

"What?"

"Rely on topological mapping to compress the singular contributions into a low-dimensional subspace. It's not offsetting; it's dimension reduction. The singular points generated by the tube overlaps are bundled and mapped onto two or three main directions, while the remaining directions only retain non-singular contributions." He spoke slightly faster than usual. "Then, use different integral estimates on these subspaces to compress the overall lower bound of the dimension to the required value."

Tao Terrence didn't speak immediately after hearing this. His eyes were still on the manuscript, but his right hand slowly rose, paused for a few beats in mid-air, then pushed forward with an open palm, lightly slapping the desk as it fell. That muffled sound was exceptionally clear in the quiet office.

"Exactly. This solves both the singularity and the directional overlap problems at the same time. Zhao, I've collaborated with you several times, but this time is different."

He gathered the draft papers on the desk, rested his hand on the corner of the paper, and looked at Zhao Yang with a serious gaze. "I need your help. With the Kakeya Conjecture, I can't finish the second half of the journey alone."

Zhao Yang didn't answer immediately. He went through the several things he currently had on hand in his mind. On the chip side, Liang Mengsong was holding the front line; he only needed to look at the briefings for equipment debugging and process parameter optimization every week. Spark Technology was being managed by Chen Haifeng, with production expansion progressing quarterly, so he basically didn't need to worry. At the Biology lab, Shin-chan was responsible for daily operations; the accumulation of data from blood sample analysis and animal experiments was a long-term matter that couldn't be rushed. The P vs NP problem was indeed stuck, with no breakthrough in sight in the short term. Calculating it this way, although he had many things on hand, he really could squeeze out a block of time for the Kakeya Conjecture.

It was a pity there were no system missions. However, for a problem of the level of the Kakeya Conjecture, even if it didn't directly raise his Mathematics level, it would at least increase his Mathematics experience by a large margin. Judging from the precedents of Goldbach's Conjecture and the superconductivity model, the system was never stingy with the experience points given for solving such massive problems.

"Okay," Zhao Yang said.

Tao Terrence's eyes lit up instantly. He wasn't the type of person to shout out loud, but anyone familiar with him could see that his whole body, from his shoulders to his back, had lifted a bit. That excitement wasn't written on his face; it permeated through his physical posture.

"I knew you would definitely agree. Before I came, I told a few colleagues in the department that this trip to Yanjing wasn't mainly for the conference, but to find you for a collaboration. They even said I might not be able to invite you. I said you don't understand Zhao Yang; the things he refuses are those he finds uninteresting, but he won't refuse a problem like the Kakeya Conjecture."

"How did you know I would be interested in the Kakeya Conjecture?"

Zhao Yang looked at Tao Terrence curiously and asked.

"Because it's a hard problem! A mathematical hard problem! I feel like you are interested in almost all the hard problems in this world."

Tao Terrence looked at Zhao Yang and said with a smile.

Zhao Yang didn't respond to that. He organized the scattered manuscripts on the desk, arranged them according to the order of derivation, then wrote a few keywords in the blank spaces with a pen and began discussing them section by section with Tao Terrence.

For the next week, Zhao Yang spent most of his time with Tao Terrence. The location was sometimes in Zhao Yang's office and sometimes in the discussion room of the Peking University Mathematics Department.

The content of the discussions ranged from the choice of topological structure for the dimension reduction mapping to the comparison of error bounds for different integral estimation methods, and then to the decay rate of norm estimates in different dimensions. Every day they changed angles, and every day new things were proposed and then pushed back.

This rhythm continued until the day Zhao Yang participated in his graduation defense.

Tao Terrence heard about this from Vice President Tian. At the time, the two of them bumped into each other in the hallway of the Mathematics Department, and Vice President Tian mentioned in passing that Zhao Yang was going to Yanjing Forestry University in the afternoon to participate in his undergraduate graduation defense.

Tao Terrence first confirmed that he hadn't misheard, and then his expression became very strange. When Zhao Yang walked past him, he turned his head and looked at Zhao Yang with a strange expression, asking, "You've already proven Goldbach's Conjecture, and you still have to participate in an undergraduate graduation defense?"

"My undergraduate status is still at Yanjing Forestry University; the process has to be completed."

"This is too ridiculous." Tao Terrence shook his head and then said he wanted to go watch. Zhao Yang asked him what he was going to watch. Tao Terrence said he wanted to see someone who had won the Cole Prize being questioned by a group of undergraduate defense judges on stage; he felt this scene was worth recording. Zhao Yang said, suit yourself.

Zhao Yang's graduation defense was arranged in a lecture hall at the Yanjing Forestry University School of Life Sciences. The scale was much larger than a normal undergraduate defense. Sitting on the panel of judges were not just several professors from the School of Life Sciences, but also two teachers who had come from Peking University, and people from the Academic Affairs Office were also there.

Gu Ming sat at the very edge of the judges' panel, holding a printed copy of Zhao Yang's graduation thesis. A sticky note was attached to the cover with several key points he prepared to ask about. There were many people in the audience listening; besides Li Xin, Zhou Ting, and the others from the research group, there were also students who had come after hearing the news, filling three or four rows in the back. Tao Terrence sat in the last row by the aisle, wearing a dark blue jacket; the people next to him didn't seem to recognize him.

The defense itself went without any surprises. Zhao Yang spoke about the main framework and conclusions of the thesis for about twenty minutes, focusing on the theoretical derivation and data analysis parts of the molecular structure improvement of biological reagents. During the Q&A session, Gu Ming first asked a few questions about the choice of improvement paths, which Zhao Yang answered.

Then another professor from the School of Life Sciences who researched biochemistry asked two details about the optimization of catalyst reaction conditions, which Zhao Yang also answered. There was no making things difficult, no questioning; the entire process went very smoothly. Finally, the judges unanimously passed him. Gu Ming stood up and said, "Congratulations on graduating," and Li Xin led the applause from the audience. Tao Terrence also clapped a few times, his expression looking as if he were observing some rare animal.

After the defense ended, President Zhou came out from the nearby lounge. He had been listening in the back just now and hadn't sat on the judges' panel. He shook hands with Zhao Yang and then pulled him to a spot by the window in the hallway, saying there was something he wanted to ask in person.

"Zhao Yang, although you have already graduated with a PhD from Peking University, you are still an undergraduate graduate of Yanjing Forestry University after all. The school has benefited a lot from you these past two years, from recruitment to research evaluation to social reputation. I've also spoken with Peking University over the phone; both schools hope you can be appointed as an honorary professor at Yanjing Forestry University. You won't have to take on regular teaching duties or keep office hours; just show up if it's convenient when the school needs you to represent us. What do you think?"