Scholar's Advanced Technological System

Chapter 429: Collatz Conjecture Report

Translator: Henyee Translations Editor: Henyee Translations

Although Lu Zhou was wasted in the afternoon, but due to his powerful metabolic function, he was able to attend the evening party.

He was one of the main attendees of this conference; if he didn’t attend, then the party wouldn’t be interesting...

The banquet went from 6 pm until 8 pm. Professor Fefferman didn’t have enough fun; therefore, he came up with the idea to use the Brazilian chocolate balls the Princeton professors got at the conference as chips for playing contract bridge.

This sounded like an interesting idea. Therefore, Lu Zhou joined in on the fun. In the beginning, he lost some of his chips because he wasn’t familiar with the rules, but after a while, he began to dominate the playing table.

Mathematicians gambling with cards was a very interesting thing.

Lu Zhou heard Fefferman said that everyone on the table except Lu Zhou was part of the contract bridge club at Princeton Institute for Advanced Study.

Prior to this, Lu Zhou, who had worked at the Institute for Advanced Study for years, never knew about this interesting club.

Professor Fefferman shuffled the cards and said, “If you’re interested in playing contract bridge, you can join our club. Unless there’s a special occasion, we play every day from 2 pm until 3 pm at the activity room of the Institute for Advanced Study. You’re welcome to join us if you like.”

Lu Zhou said, “But I’m already a consultant for the drone club at Princeton.”

“That’s fine, you can join as many clubs as you like,” Professor Fefferman said with a smile. Fefferman was a well-liked person on Princeton campus, and he said, “If I recall correctly, I’m an honorary member of more than 20 clubs.”

Lu Zhou suddenly felt like he was missing out...

They played bridge until midnight. At the end of the day, Lu Zhou had his pockets full of chocolate balls. He suddenly remembered that there was a 45-minute report tomorrow that he had to attend; therefore, he bade farewell.

Lu Zhou spent the night sleeping in his hotel room.

The next morning, Lu Zhou woke up with dark circles around his eyes. He took a shower and yawned as he walked out of his hotel room.

He took the elevator downstairs and walked into the restaurant. When he happened to see Molina, Lu Zhou immediately greeted her.

“Morning.”

“Morning.” Molina noticed Lu Zhou’s dark circles, and she teased him by saying, “Stayed up late?”

Lu Zhou yawned and said, “Nope, just a bit tired...”

Vera, who just finished her breakfast, walked out of the restaurant and bumped into Lu Zhou.

When the little girl saw Lu Zhou, she greeted him politely.

“Morning, Professor Lu.”

“Morning.” Lu Zhou smiled and encouraged her, “You got this!”

“Yes!” Vera nodded energetically. In the end, she couldn’t help but yawn as well.

Although she went to bed early last night, the thought of her reporting at the International Congress of Mathematicians caused her to stay wide awake.

She rolled around in bed and finally fell asleep around 3 am.

Her entire body felt dizzy; it was almost like she could fall asleep while standing.

Molina looked at this scene in front of her. She then looked weirdly at Lu Zhou.

“... Be honest, what did you do last night?”

When Lu Zhou heard this weird question, he asked, “What do you mean?”

Molina was about to say something, but she suddenly shook her head and said, “... Never mind, I didn’t see anything, I didn’t ask anything.”

Lu Zhou: “...?”

Molina looked like she just made a choice between ethics and her friendship with Lu Zhou. Lu Zhou felt like she had misunderstood something...

...

Vera’s report was at 10 am; she was part of the number theory division.

There was still two hours until Vera’s report, and Lu Zhou didn’t want to waste any time. Therefore, he began wandering around the conference.

Without knowing it, he arrived at the algebraic geometry division.

When he walked into the lecture hall, the person doing a one-hour report happened to be his acquaintance, Professor Schultz.

Lu Zhou was interested in the report topic written on the whiteboard. He sat down in the back row and began listening.

Simply put, Schultz’s report was based on the perfect space theory that he created which solved some of the problems in the Langlands program; many of which were closely related to the BSD conjecture.

Lu Zhou had a basic understanding of his perfect space theory; therefore, it wasn’t difficult for him to listen to Schultz’s report.

After Lu Zhou finished listening to Schultz’s report, he went to the partial differential equation lecture hall, but he didn’t see any interesting reports happening.

Apparently, some people had applied to report on the three-dimensional Navier–Stokes equation, but since Lu Zhou had defeated the Millennium Prize Problem, they had to abandon their reports...

It was soon at 10 am.

The number theory lecture hall was packed.

Lu Zhou found a seat in the back row and sat down as he quietly waited for the report to begin.

Vera’s palms were sweating as she nervously walked on stage.

Many people in the lecture hall were surprised at the presenter’s age, but since mathematics is a young scholar’s subject, they didn’t overreact.

Vera took a deep breath and remembered her professor’s encouraging words. She then patted herself on the cheeks as she tried to calm herself down.

“You got this... Vera Pulyuy, you can do it!”

She gave herself some encouragement and had a self-assuring look in her eyes.

The Collatz conjecture soon began.

Although her report was a little unsteady at first, she got the hang of it and began to smoothly articulate herself.

Lu Zhou had to admit that she was a very talented girl, both in mathematics and in public speaking.

Her only flaw was her introverted shy character.

Lu Zhou watched Vera and nodded with approval.

No wonder she’s my student, she reminds me of my presenting style.

Half an hour had gone by, the report gradually came to an end. However, Vera didn’t relax at all.

Because next up was the Q&A session; the main part of the report session.

The first question was asked by Professor Helfgott from the École Normale Supérieure. Helfgott was an analytic number theory master who proved the weak Goldbach’s conjecture; he was also one of the six peer reviewers for Lu Zhou’s Goldbach’s conjecture thesis.

Maybe Helfgott didn’t want to put Vera under too much pressure because he spoke in a non-aggressive way. He looked at the printed thesis in his hand and spoke.

“On page 9, line 7, I noticed something interesting. Φ(g) is the open subset of the complex plane f, and each of the largest connected sub-regions of Φ(g) is a branch of Φ(g)... How did you conclude this expression?”

Vera quickly turned the thesis to page nine and answered clearly.

“Φ(g) is the set of ordinary points z0 beyond the integer function g(z). On page 7, line 15, inference 1.4, I proved that the function column {gk(z)}∞/k=1 has sub-columns in the local neighborhood of point z0, which converges to the analytic function S(z)...”

When Helfgott heard Vera’s explanation, he nodded with approval.

“Thank you.”

The Q&A session continued.

After all, this was the International Congress of Mathematicians; the skill level of attendees was very high, and the questions were all sophisticated.

Of course, there were some less sophisticated questions.

A doctoral holder from the University of Montreal stood up and spoke.

“Excuse me, on page 11, line 13, any whole function h(z) gives g(z)=z/2+(1−cosπz)(z+1/2)/2+1/π(1/2−cosπz ) sinπz+h(z)sin2πz, which satisfies N⊂Φ(g). What is the derivation of this inference?”

Some people in the lecture hall chuckled.

Vera sighed and said, “For this part, please refer to the textbook by Letherman-S, Schleiche-D, Wood-R. The ‘3n+1’ problem-and-holomorphic-dynamics...], Professor Letherman has already given a complete proof, I won’t repeat it here...”

Anyone that asked this type of question obviously didn’t read Vera’s thesis at all.

When the guy realized he asked a stupid question, he blushed and sat back down.

Generally speaking, the report went quite well.

After the report finished, Vera ran to Lu Zhou excitedly.

“Professor! I did it... I did it!”

She clenched her fists tightly; her face was full of excitement.

As Lu Zhou looked at the excited little girl, he was happy that she could overcome her introverted personality.

There was nothing better than watching one’s students grow and develop.

This was one of Lu Zhou’s most rewarding days in his life.

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