Princeton University, belongs to a laboratory of graduate student Mathematics Department.
"Ahahaha, I'm done! I'm done!"
At a certain workstation, someone suddenly threw away the pen in his hand, picked up the draft paper on the table, waved it, and shouted excitedly.
For a moment, the other graduate students in the laboratory looked sideways at this person.
Could he be another person who went crazy studying mathematics?
Then I took a closer look, okay, this person is the PhD senior brother of their laboratory, a Chinese, named Wen Chenghua.
Their senior brother has been studying for a doctorate for four years, but has not yet graduated because his doctoral thesis has not been completed.
Of course, for a PhD student in mathematics, it is not too late to study for four years, but who doesn't want to graduate this morning?
"Wen, what are you excited about! Calm down!"
Their mentor, Andre Okounkov, was also in the laboratory at this time, sitting at the front, studying his things.
Compared with other professors who may prefer to sit in the office, Okounkov prefers to sit in a laboratory with his students, so that if his students have questions, they can ask him at any time.
Of course, it is also convenient for him to monitor whether his students are studying seriously.
Hearing the instructor's scolding, Wen Chenghua immediately shrank his head and apologized quickly, "Sorry, professor, I was wrong."
Their tutor from Russia has a very bad temper. Once these students make any mistakes, whether they are big or small, or academic or daily performance, they will be severely criticized, so they are all afraid of this tutor.
However, the other party's ability and the academic help he provided them also made them have to maintain respect for this tutor.
After all, Okounkov is the Fields Medal winner in 2006. It is their luck to be a student who is the Fields Medal winner.
He put away his voice, but Wen Chenghua still brought his scratch paper to the instructor and said, "Professor, I have completed that question!"
Okounkov frowned, "That question? Is it about the problem of p entering Galois representation in a non-Archimedes local domain under the residual feature p?"
Wen Chenghua was surprised that his professor could still remember the problem he had just told him a few months ago, and then he nodded. "Yes, professor! I have solved it!"
"Aren't you kidding?"
Seeing his disciple's happy look, Okounkov raised his brows and was a little surprised. He knew the difficulty of this question very well, otherwise he wouldn't have been stuck for so long as a student.
He remembered that the topic of Wen Chenghua's thesis was observability of Galois representations, which involved part 2 of Tate Conjecture. It can be said to be a very difficult problem, no less than what most mathematics professors are studying.
If this problem is solved, more refined results of previous research will be achieved, which will be particularly important for any scholars who are studying this aspect.
Well, all in all, there is definitely a chance to publish to the top four publications. Although it may take a long time to queue up, it is definitely more than enough to publish to the second-highest journal.
But obviously, it is difficult.
The place where Wen Chenghua was stuck before was about the Gavarro representation problem in p-adic Hodge theory.
Okounkov himself has not solved this problem yet, otherwise Wen Chenghua would not have been stuck for so long.
Surprised, Okounkov said, "Please show me how to solve it."
"Okay!"
When the instructor asked, Wen Chenghua immediately puffed up his chest, walked to the blackboard, and started writing.
Soon, Okounkov was surprised. "Wait! What method are you using here? Is it the automorphic theory of etale algebraic varieties created by YiXiao?"
"Professor, you also know?" Wen Chenghua asked in surprise.
"You're just kidding, you know it, can I know it?" Okounkov glared at him, "I've been studying this thing recently."
Wen Chenghua I suddenly realized that I had said the wrong thing.
However, Okounkov didn't say much, and continued, "Don't stop, keep writing. I also want to know how useful this theory can be."
"Okay professor!"
Wen Chenghua nodded quickly and then continued writing on the blackboard.
Soon, with the help of Xiao Yi's etale algebraic variety automorphic theory, the problem that had stumped him and Okounkov, the winner of Fields Medal, for a long time was easily solved.
This means that Wen Chenghua's graduation thesis has finally been completed, and it is also a top journal-level paper. He has become the first batch of biggest beneficiaries after the birth of Xiao Yi's etale algebraic variety automorphic theory.
Even in the end, Okounkov took the initiative to ask Wen Chenghua about something about this theory. Even though he is Wen Chenghua's mentor and the winner of Fields Medal, due to subtle differences in research directions, he sometimes needs to ask his students some questions that he may not understand yet.
This is also the characteristic of the subject of mathematics.
For a moment, Wen Chenghua seemed to be able to feel the admiring looks from his junior brothers.
Installed!
That night, after returning to the dormitory, Wen Chenghua, whose graduation thesis was no longer a problem, lay on the bed relaxedly, turned on his mobile phone, and browsed the foreign version of Zhihu's Quora.
As soon as he entered, he saw a problem in the field of mathematics recommended to him.
[Chinese mathematics genius Xiao Yi created a theory called etale algebraic variety automorphism in his last two papers. What role does this theory play in mathematics?]
There are already more than 20 people who have answered this question. After clicking on it, Wen Chenghua was surprised to find that the great master Terence Tao also appeared among the respondents.
[This theory has many uses! Looking forward, it will be of great help to us in any number theory problem. In fact, I have already planned to discuss the x^2+1 prime number problem with J·Maynard.
Looking back, we will be able to use the Automorphic Forms and trace formula methods to study any issues related to etale's basic group, and thus extend to all aspects of Algebraic Geometry, such as p-adic Hodge theory, Tate Conjecture, of course Far Abelian Geometry is indispensable. Maybe Shinichi Mochizuki, after reading this paper by Xiao Yi, will also have more inspiration on the abc conjecture?]
Seeing Terence Tao's comment, Wen Chenghua immediately exclaimed in his heart, "You are truly a master. You can see at a glance that this theory can have an effect on Tate Conjecture."
Looking at other comments, there are no shortage of doctors and professors from various prestigious universities, all of whom have expressed great recognition of etale's algebraic variety automorphic theory.
Finally, as a beneficiary of this theory, Wen Chenghua feels that it is necessary to also praise it.
[Princeton University is about to graduate and get a PhD in mathematics uninvited. I don't know what effect this theory of Xiao Yi has on mathematics, but what I know is that it helped me complete my doctoral thesis that I have been stuck on for a long time. My supervisor is Andre Okounkov. Even he said that this theory is a major achievement in our mathematics community this year.
Finally, please allow me to express my most sincere respect to God Xiao! salute!]
[PS: It should be on the shelves on May 1st. It is ready to be updated. I hope all readers will support it.]