I looked at the clock hanging on the blackboard and saw that there were still a few minutes until the end of the open class.
Xu Chuan thought for a while and said, "There is still a little time before get out of class ends. If any students don't understand anything about what was just taught in class, you can ask questions now."
Hearing this, many students in the audience were eager to give it a try, but they hesitated again when they saw that no one around them responded.
Of course, there must be people who know how to seize opportunities. A Nobel Prize winner and a Philippine Prize winner personally answered the questions. I am afraid that such an opportunity is rare to come across once in a lifetime.
Xu Chuan stretched out his hand to signal a student to ask a question, and the student who was drawn stood up reflexively.
"Teach...Professor." The student who was called seemed not to have expected that he would be so lucky. When he stood up, hundreds of people in the audience were looking at him, and he immediately stuttered.
Xu Chuan smiled and did not make a sound, but quietly waited for the other party to recover.
After taking deep breaths for several times, the lucky man felt relieved and continued: "Well, well, I remember you just mentioned in class that you understood the eigenvectors and eigenvalues of square matrices from the perspective of algebraic geometry. I would like to ask
Let’s take a look at this stuff.”
"This is a very interesting question."
Xu Chuan said with a smile, picked up the chalk from the table again, turned around and wrote on the blackboard behind him: "The eigenvectors and eigenvalues of the square matrix are defined as follows from an algebraic perspective:
"Suppose an n-order matrix a, if there is a number λ and an n-dimensional non-zero column vector x→, so that the following formula is true: ax→=λx→, then λ is called the eigenvalue of the matrix, and the non-zero column vector x→ is called a matrix,
The eigenvector corresponding to the eigenvalue λ."
"To understand the eigenvectors and eigenvalues of a square matrix from a geometric point of view, the matrix can be regarded as a coordinate system transformation, such as ax→=λx→, which means that the eigenvector becomes its original value after the coordinate system transformation.
λ times, and the extension line of the direction does not change, the direction is the same or opposite..."
"At this time, the eigenvectors can be understood as those vectors that remain unchanged under the transformation of the coordinate system, but will be extended by λ times. The amplification of this length..."
"In addition, it should be noted that there is a corresponding relationship between eigenvectors and eigenvalues. A eigenvector corresponds to a eigenvalue.
When solving the eigenvectors and eigenvalues of a matrix, the eigenvalues are generally found first, and then the eigenvalues are substituted into the equation ax→=λx→ to find the eigenvectors."
In front of the blackboard, Xu Chuan wrote the last stroke, turned to look at the student who was still standing, and asked with a smile: "Do you understand?"
The student who asked the question nodded vigorously and said excitedly: "I understand! Thank you, professor."
Xu Chuan smiled and then selected students to answer questions.
With the first student taking the lead, students who had hesitated before mustered up the courage to raise their hands, but at this moment, among the hundreds of pairs of raised hands in the entire lecture theater, the probability of being selected was too small.
After answering a few questions, Xu Chuan smiled and said, "The last question is for you. That classmate wearing glasses, what doubts do you have?"
"Professor, can you tell me how you solved the Hodge conjecture?"
The student wearing glasses stood up excitedly and asked, but he did not mention the doubts in class, but asked other questions.
Hearing this question, Xu Chuan was slightly stunned. He did not expect this student to ask such a question, but it was not something that could not be answered.
Smiling, he said with some nostalgia: "Solving the Hodge conjecture was the inspiration I got from Professor Mirzakhani. At the beginning, Professor Mirzakhani once left me a manuscript. By studying that manuscript, I
I unexpectedly gained some solutions to Hodge’s conjecture.”
"As for the specific process..."
After a pause, Xu Chuan then smiled and said: "This cannot be explained in one or two sentences, and for you now, it is too early to say this."
"Based on your current foundation, I am afraid that the vast majority of people cannot even fully understand the true meaning of the difficult problem of Hodge's conjecture. As for my proof paper, there is no need to think about it, even if I am here to explain it today
I’m afraid more than 99% of the people present can’t understand the report.”
"For this kind of conjecture, which is considered top-notch in the current mathematics world, I suggest that you proceed step by step. First lay the most basic things, try to break through your own boundaries, and then move towards your goals and ideals step by step.
struggle."
"As for now, it's still a little early for you."
Xu Chuan did not talk about how he solved the Hodge conjecture. As he said, it was not contempt or contempt, but for the students sitting in this classroom, it is really too early to talk about this now.
Not everyone is a genius like Terence Tao or Schultz, who can have extremely high attainments in mathematics at the undergraduate or graduate level.
As soon as he finished speaking, someone asked: "Professor, can you tell me what you are researching after returning to China? Physics, mathematics, or astronomy? I think many people are very interested in your research direction, including
We are quite curious too.”
Xu Chuan thought for a while and said with a smile: "NS equations and particle physics, I am mainly studying these things during this time."
He did not reveal his actual research in this class, but just found a reason to talk about it. Some things can be announced after completion, but the process still needs to be kept confidential.
.......
"Ring ring ring ring..."
When the bell rang for the end of get out of class, Xu Chuan put away the textbooks he had brought and walked away without even turning off the projection equipment.
There are so many students here. If they are blocked, they will really not be able to leave for a while.
After all, it was the first time for the class to start, and these students were quite enthusiastic, so before they could react, the Thirty-Six Strategy was the best strategy.
When the classes become more frequent and students get used to it, they no longer have to worry about being stuck in a crowd.
There is a big difference between college students and those fanatical star-chasing fans. The former still have to face shame, but as for the latter, I won’t say much.
Sneaking into your idol's home to steal underwear and personal belongings, and going crazy on stage have all happened.
.......
In a hurry, Xu Chuan arrived at Chen Zhengping's office.
After knocking on the door, a voice came from inside. He opened the door and walked in. To his surprise, his mentor Chen Zhengping was not the only one in the office. Liu Gaojun, the president of Nanjing University, was also here.
"Teacher, principal." Xu Chuan greeted with a smile.
"Professor Xu is here, sit down quickly." Principal Liu greeted with a smile: "It's your first time attending class at NTU. How do you feel?"
Xu Chuan smiled and said: "It's very good. The students are very serious and enthusiastic."
"Hahahahaha, you are the only one with this charm." Liu Gaojun laughed and said: "If you are still dissatisfied with anything, or have any suggestions on teaching, you can bring it up with me, and the school will
Try your best to find a solution."
Xu Chuan nodded and said with a smile: "Of course."
On the side, Chen Zhengping interjected and asked: "The data analysis you sent to my email two days ago is the experimental data of the Alice detector?"
"Well, before and during the Chinese New Year, I analyzed the experimental data of the Alice detector. Thanks to your help, my tutor, I found some abnormal signals and data."
"It has been sent to Witten and the other side. I hope they can do a few sets of collision experiments to see if they can verify the analysis results."
Chen Zhengping pondered for a moment and then said: "Do you think that is the manifestation of sterile neutrinos?"
As soon as Xu Chuan sent the analysis data and Dalitz chart to his mailbox, he read them.
Although he was surprised at the speed of his research as a student, he still carefully studied and analyzed these Dalitz diagrams.
Judging from the images, there may indeed be a new particle in the data analyzed by Xu Chuan, and the probability is not small.
But it is just possible, and even if there is a particle, it is not necessarily a sterile neutrino.
Although his research focus has now shifted towards materials physics, he has a background in high energy physics and condensed matter physics.
Moreover, I have never stopped researching high-energy physics and particle physics. I participate in research and data analysis every year, and I also keep an eye on the cutting-edge information in these two fields.
Sterile neutrinos are not particles in the Standard Model.
In current theories in the physics world, sterile neutrinos are a type of dark matter, and no trace of dark matter has ever been found in the physics world. All theories are based on the movement of celestial bodies, the phenomenon of Newtonian gravity, and the gravitational lens effect.
Established by observations such as the formation of the large-scale structure of the universe and the microwave background radiation.
For Chen Zhengping, although he believes that dark matter exists, he does not believe that dark matter can be observed with today's technology.
Unless all aspects of the Large Strong Particle Collider are upgraded on a large scale, it will be almost impossible to detect the existence of dark matter based on the current collision energy level and the observation level of the detector.
Therefore, even if there is indeed a new particle or some undiscovered phenomenon in the experimental data of the Alice detector this time, Chen Zhengping does not think it is a sterile neutrino.
.......
In the office, Xu Chuan nodded and said, "Yes, I think it is very likely to be a sterile neutrino."
Chen Zhengping asked: "Have you ever considered the probability that this is an antineutrino?"
Judging from Xu Chuan's analysis results, he felt that this might be an unknown neutrino or an antineutrino particle.
The so-called antineutrino particles are not antimatter, they are another state of neutrinos.
The spin direction of neutrinos is opposite to the direction of motion, while the spin direction of antineutrinos is the same as the direction of motion.
The nature of their interaction with matter is different. Neutrinos only have left-hand rotation, and antineutrinos only have right-hand rotation.
It was the hypothesis of the existence of neutrinos proposed by Austrian physicist Pauli. In 1965, two physicists, Curwin and Reines, used the beta decay of nuclear reactor products to produce antineutrinos and observed them.
So theoretically, it is also possible to produce it in the Large Strong Particle Collider.
Xu Chuandao: "I have considered it, but theoretically, the probability that it is an unknown neutrino or antineutrino is much lower than the probability that it is a sterile neutrino."
Hearing this, Chen Zhengping asked quickly with interest: "How do you say it?"
He still has some understanding of this student. If there is not enough evidence, this student will generally not say such things easily.
Since he said that the probability of sterile neutrinos is higher, he must have some evidence.
If it can be confirmed that traces of sterile neutrinos are found in the experimental data of the Alice detector, it will be a huge single-volume nuclear bomb for the entire physics world, even the entire scientific community, and even the entire society!
After all, according to current theory, sterile neutrinos are one of the medium-temperature dark matter particles that constitute dark matter.
If confirmed, the discovery of dark matter will become the most sensational news in the physics and even science circles this year.
Xu Chuan pondered for a moment, collected his thoughts and then said: "From the Dalitz diagram I made, you can clearly see the energy level trajectory of this new particle, which shows a ︺-shaped arc.
, which is completely different from all regular particles."
"Even the kinetic energy trajectories of neutrinos and antineutrinos on the Dalitz diagram will not behave like this, so it is most likely a new type of particle, and its performance characteristics are not included in the conventional standard model.
in particles."
"Secondly, I don't know if you, mentor, have noticed that in all the Dalitz diagrams, the data representing this unknown new type of particle is all intermittent."
"This means that the experimental data observed by the Alice detector are actually imperfect. What it can detect and record is only a part of the resonance state structure that this unknown particle can express."
"Theoretically, sterile neutrinos are part of the warm dark matter in dark matter. Theoretically, warm dark matter does not participate in strong interactions, otherwise the process of primordial nucleosynthesis will be disturbed and the abundance of light elements will decrease.
Changes will lead to inconsistencies with current observations."
"In the Large Strong Particle Collider, the existence of primordial nuclei can be everywhere. In this case, only the residual abundance obtained from the thermal decoupling mechanism of sterile neutrinos when synthesizing warm dark matter can be
Alice detector observed it. From this point of view, there is no doubt that it meets the requirements."
"In addition, weakly interacting massive particles (wimps) are one of the most widely discussed dark matter candidates. They refer to some stable particles with mass and interaction strength near the electroweak scale, obtained through a thermal decoupling mechanism.
Known remaining abundance….”
"In the standard model of particle physics known to mankind, there are no particles that satisfy these properties at the same time, which means that the ones that produce such properties must be new physical particles that go beyond the standard model..."
"From the above points of view, the probability that this new type of particle is a sterile neutrino is quite high."