Some Ideas
"Create difficulties, create difficulties... how do I create them?" Director Wu scratched his head, he was used to proceeding step by step, but he couldn't create any difficulties on the spot.
"Director Wu, our center has several researchers specializing in topology. Engineer Liang is skilled in Algebraic Topology, Engineer Wei has considerable expertise in geometric topology, and Engineer Qin's research on topological linear spaces falls under Functional Analysis, but Engineer Qin also possesses a profound foundation in topology." Shen Qi had met with all the researchers in the center over the past few days, and he remembered the academic characteristics and personality traits of each researcher.
"Homology Theory and Homotopy Theory in topology are also among my research areas," Director Wu said.
"Since that's the case, then I'll create difficulties for Director Wu." Shen Qi picked up the chalk and wrote on the blackboard:
1. Standard sphere S
2. Euclidean space R
3. Hyperbolic space H^3
4. S×S
5. H×S
6. Left-invariant Riemann metric on the universal cover of special linear groups
7. Null Power Geometry
8. Analytic Geometry
After writing these eight lines, Shen Qi patted the chalk dust off his hands.
Director Wu was very familiar with the contents on the blackboard. "These are the eight Standard Model of the Thurston's Geometrization Conjecture. Perelman proved this conjecture in 2003, and the Poincaré conjecture is a special case of it, so Perelman proved the Poincaré conjecture."
Shen Qi seemed to have an idea. "That's right, but the work we're about to undertake is different from that of Thurston, Perelman, and Poincare. We'll borrow from the successful experiences of our predecessors and innovate upon them."
"So..." Director Wu, somewhat puzzled.
"Therefore, Director Wu, we should concentrate all the topological resources of our center to derive these eight models, and the derivation direction should lean towards algebraically closed subspaces," Shen Qi suggested.
Having worked in the Mathematics Community for thirty years, the experienced Director Wu suddenly realized something, his hands trembling. "Professor Shen's intention... could it be... that most difficult mathematical problem?"
Shen Qi nodded and said, "The Hodge conjecture is considered by mathematicians to be the most difficult of the seven Millennium Prize Problem. Since the Hodge conjecture connects Algebraic Geometry, topology, and Mathematical Analysis, could we work backwards, using these three directions simultaneously, to derive and prove the Hodge conjecture? Two of my doctoral students at Princeton are currently conducting research in Algebraic Geometry. Director Wu, would you be willing to take on the task in the topology section?"
"Of course!" Director Wu trembled with excitement. He asked, "The derivation of the algebraically closed subspaces of the eight Standard Model of the Thurston's Geometrization Conjecture —this new project could easily be submitted for the 973 Program! So, Professor Shen, will you fight alongside us?"
"I won't be spending much time in China in the next year or two, maybe only National First Prize or two months a year. If the center needs me, I'm willing to provide technical support," Shen Qi stated his position.
Director Wu made a quick decision. "Okay, it's settled then. You will be the academic leader of this new project, and I will be your deputy. All the researchers in our center who specialize in topology will be at your disposal."
Shen Qi: "If there's an opportunity, the center could send a researcher to Princeton for a visit and exchange. I'll be responsible for receiving them in Princeton. While I still have some influence Princeton, I'll help as many people as I can."
Director Wu grasped Shen Qi's hands tightly, deeply moved. "Professor Shen, on behalf of the Morning Star Mathematics Center, on behalf of our young researchers, and on behalf of Chinese mathematicians, I thank you. You truly care about Chinese mathematics and are dedicated to cultivating future generations for Chinese mathematics! We have many renowned experts in our center, but only Professor Shen has truly done practical things for us! Although you are young, you have a vast and profound understanding."
The number of exchange opportunities for Chinese students to visit the Princeton Mathematics Department each year is extremely limited. The Morning Star Mathematics Center can submit applications, but the key is that a professor at Princeton must be willing to accept the visiting students.
Shen Qi spent a few days at the Morning Star Mathematics Center, where he accomplished several significant and practical tasks, earning the respect and admiration of all the mathematics workers at the center.
Shen Qi also gained something; money was a minor matter, as he inadvertently pieced together a second piece of the puzzle for Hodge conjecture.
One of the requirements for advancing from Math Level 14 is solving at least one of the two Millennium Prize Problem: the Hodge conjecture and the Black-Scholes Problem (BSD).
A few months ago, when Shen Qi was designing his doctoral thesis with Yu Lei and Ralph, he pieced together the first piece of the puzzle. Algebraic Geometry is the most important piece of the Hodge conjecture, which is generally considered a super problem in Algebraic Geometry.
Yu Lei and Ralph's doctoral research is related to Algebraic Geometry, and Shen Qi personally completed the framework design.
"The proof of the Hodge conjecture is missing one final piece: Mathematical Analysis."
Shen Qi returned to Yenching University, where he gave another lecture as Visiting Professor in the Big Mathematics Department, addressing all students.
The School of the Big Mathematics Department was very well-informed, and they quickly learned of Shen Qi's preference for the Morning Star Mathematics Center.
Lu Guozhen, Shen Qi's undergraduate math analysis teacher and now the Director of the Department of Analysis at Yenching Big Mathematics Department, invited Shen Qi for tea.
Over drinks and conversation, Lu Guozhen said, "The Morning Star Mathematics Center has a very strong background. Their funding comes from a big boss in Hong Kong, and another major backer is the Institute of Mathematics of the Chinese Academy of Sciences. To put it simply, the Hong Kong boss is responsible for funding, and the Chinese Academy of Sciences is responsible for academic support. I am very optimistic about the future development of the Morning Star Mathematics Center, especially after you, Shen Qi, became their senior advisor."
Shen Qi tapped on the table. "Hey, Director Lu, why do I feel like there's something behind your words? You've changed, you've started to enjoy making sarcastic remarks."
Lu Guozhen: "Shen Qi, you've changed too. You don't love Yanda anymore."
Shen Qi: "I just helped the Morning Star Mathematics Center solve a few math problems and incidentally helped them start a new research project. Being a senior consultant at the Morning Star Mathematics Center is just a part-time job for me. My job at Peking University is my main responsibility; I won't put the cart before the horse."
Lu Guozhen asked, "What about Princeton?"
Shen Qi took a sip of tea and said, "Princeton is just about getting an academic background and qualifications; it's standard procedure."
Lu Guozhen laughed and scolded, "You brat, if you've got the guts, go back to Princeton and say the same thing."
"Director Lu, let's skip the fluff and get down to business. How many core Mathematical Analysis do you have under you?" Shen Qi asked seriously, preparing to get down to business.
Lu Guozhen Yangyang, "There are too many to count. Half of the mathematics department is mine."
Shen Qi didn't believe it. "You're just bragging! Director Sun be the first to disagree."
Lu Guozhen was very unhappy. "Shen Qi, you're just biased! Old Sun will always be more important to you than me. Hey, waiter, what kind of tea is this? It's too bitter, please get a fresh pot!"
"Don't change the waiter, this tea is quite good." Shen Qi smiled and waved to the waiter, then said to Lu Guozhen, "Director Lu, are you interested in collaborating on the Mathematical Analysis method of the Hodge conjecture?"
Puff!
Lu Guozhen spat out a mouthful of tea, making a mess all over the floor. He wiped the tea leaves from his lips and stared at Shen Qi in surprise. "You... you're finally going to make a move against Hodge conjecture?"