Chapter 381 Challenges from Neighboring Countries "I'm lucky too." Xu Qingzhou said modestly. The Fourier integral operator is indeed involved in many fields and is an important tool in partial differential equations. In physics, it can convert the wave function from one representation to another, such as converting the spatial representation to the momentum representation, so as to display the frequency and momentum distribution of particles. This is also the reason why he chose this direction. "In March, according to the plan, you will go to MIT to study abroad on a government scholarship. You can start thinking about your supervisor. Several senior fellows have contacted me, but you still have to choose for yourself." "Well, I'll think about it seriously." Xu Qingzhou nodded. He had not really thought about the issue of supervisor. He would consider it after he finished writing the thesis. Chu Jiangfeng nodded, and the topic turned to mathematical calculations. He asked, "How do you solve the problem of the lack of estimates for the variable coefficient Kakeya maximum function L^p-L^p?" “I focused on the geometric properties of Kakeya sets.”
Xu Qingzhou took out a piece of manuscript paper and did the calculations on the spot. “Well, this is a good idea.” "Junior brother, you are awesome. This function can be changed like this." After staying with Chu Jiangfeng for half an hour, Xu Qingzhou stood up and said goodbye, going back to work on his paper. Yang Yongze couldn't help but sigh: "Junior brother is so amazing." "You should have some sense of crisis. It would be embarrassing if you were surpassed by your junior brother." Chu Jiangfeng said unhappily. "It would be abnormal if I wasn't crushed by my junior brother." Yang Yongze muttered. Chu Jiangfeng paused. He wanted to scold Yang Yongze for having no ambition, but then he felt that there seemed to be some truth in his words. This kid Xu Qingzhou was really too talented. Yang Yongze pondered and said, "It's time to recruit a few graduate students to guide us." "Figured out?" Chu Jiangfeng took a sip of tea and asked with a smile. "Well, I've thought it through." Yang Yongze nodded, paused, and said, "There must be one thing that is better than my junior brother. It's a bit difficult to compare research, so the only thing is the number of students." "." Are students compared in quantity? Chu Jiangfeng blew his beard and glared, feeling that this account was useless. During the Qingming Festival, the air was filled with the fresh scent of earth. It had just stopped in the morning, but a drizzle began again in the evening, falling on the balcony handrails and then dripping down the windowsill. Xu Qingzhou was still calculating, and after more than half a month of hard work, he successfully completed the improvement of the local smoothness research. The local smoothness conjecture attempts to describe how the output function of the Fourier integral operator will maintain or improve this smoothness when the input function has a certain smoothness. After proving this smoothness, the next step is to extend it to local smoothness. Song Yao came out of the bedroom lazily, leaned on the sofa, wanted to play with Xu Qingzhou's hair, and then went to rest on the sofa.
Xu Qingzhou also stood up and followed. School Beauty Song was mad again when she was sleeping, her long hair scattered on her shoulders, her black eyes staring at the ceiling in a daze, and her bare face, which looked a little haggard compared to usual, gave people a familiar sense of brokenness. Xu Qingzhou couldn't help but pinch her fair and delicate little face, like a porcelain doll that could be ravaged by anyone. Song Yao remained motionless, staring at Xu Qingzhou expressionlessly. He was thinking about taking revenge after he got better, and the feeling of having no strength, not wanting to move, and having to let Xu Qingzhou bully him made him inexplicably enjoyable. But, it's a bit strange. Sometimes she actually expected Xu Qingzhou to try harder. Something is wrong. Something is wrong. Song Yao's face froze and her expression was solemn. This kind of thinking was abnormal. How could she hope that Xu Qingzhou would torture her? How perverted. Just like Xu Qingzhou likes to be beaten. Some strange property. Song Yao sighed inwardly, she was about to die, she seemed to be becoming more and more weird. Why is this happening? because because She simply put the blame on Xu Qingzhou. It’s all because of Xu Qingzhou. Song Yao came back to her senses, blinked, and stared at Xu Qingzhou, "Teacher Xu, please be stronger." Hmm? Xu Qingzhou increased his strength. He had never heard of such a request. However, he found a hand on his waist. not good. "Sigh~" Xu Qingzhou's voice begging for mercy was heard in the living room. Song Yao was satisfied. Seeing Xu Qingzhou staring at her resentfully, she drove him away: "You disturbed me." "." Xu Qingzhou shook his head, realizing that Song Yao was fishing just now. He returned to the table and continued his calculations. If ε is sufficiently small, it can be replaced by fψ, where ψ is a smooth function supported on B(e, 1\5) and equal to 1 on B(e, 100\1). When an inequality uses the Feffennan-Stein estimator, an additional factor e^ε appears. "Here, we need to construct an inequality." Time flies, and it is already late April.
After being busy for two weeks in a row, Xu Qingzhou finally had some free time, and Song Yao also took a short vacation. The two of them didn't go anywhere and just stayed at home and played badly. In the evening, golden sunlight fell on a corner of the sofa. After Xu Qingzhou finished washing the dishes and came out of the kitchen, he went to the sofa and pulled the legs of the school beauty Song. Song Yao said without even looking up, "Academician Chu just sent me a message saying that your graduation defense will be held on April 4. Academician Wang and the others will be here by then." Xu Qingzhou finished his thesis on the afternoon of April 4th. It was a uneventful day, so he went out with Song Yao to have a nice meal to celebrate. Then he translated the manuscript and gave a copy to Chu Jiangfeng. Chu Jiangfeng didn’t even want to be a corresponding author. In Chu Jiangfeng's words: "I can't afford to lose this person." He said that all the projects were completed by Xu Qingzhou, and they usually went to the office mainly for communication, which was considered as mutual learning. If he still wanted the position of corresponding author, where would he put his face? "Number 22. Not bad." Xu Qingzhou nodded. Actually, he didn’t have much to prepare. He had been studying this for more than a year and was very familiar with the content of each part. Song Yao seemed to see it, frowned, and hooked Xu Qingzhou's clothes with her feet. “Someone is challenging you online.” "challenge?" Xu Qingzhou found it curious and went over to read the news with Song Yao. The number of private messages on Weibo is still 99+. There were advertisers, people asking for advice on math problems, people with papers to present, people who claimed to have proved a math conjecture and wanted Xu Qingzhou to take a look, and there was even an agency. "God Xu, Third Brother challenges you." After commenting, the netizen also attached a video of the interview. When I clicked on the video, a familiar person appeared on the screen. Reporter: "Mr. Amir, I heard that you are studying the local smoothness conjecture. Do you have any good news for us?" "Of course, we have made gratifying progress now. I am confident that within half a year, we will be able to solve the problem raised by the master of harmonic analysis Christopher D. Sogge in 1991." "Can you tell me what your next work arrangements are?" "Xu Qingzhou from Xia Country seems to be conducting similar research, or in other words, research on the local smoothness conjecture, just like your topic. What do you think about this?" The reporter paused and asked with a smile: "After all, you have always regarded this Xia countryman who has repeatedly created miracles as a competitor." “Excuse me, but not every research requires a miracle. As a scientific researcher, I believe more in carefulness and my own strength. I have absolute confidence in coordination and analysis.” Amir smiled. "Can I take that as a challenge?"
“I’d love to,” Amir said. The video is only two minutes long. Song Yao sat up straight and interviewed her boyfriend, "What do you think?" "he" Xu Qingzhou paused, his face serious, and slowly said: "It's darker than the last time I saw it." (End of this chapter)