Chapter 463

The words that Gu Lu said with a smile when he stood on the stage were like a stone thrown into a calm lake, causing ripples.

None of the mathematicians on the scene could have a calm look on their faces at this time.

They've just recovered from the shock they had had come from, and now they were in the middle of another shock.

Looking at the high-spirited Gu Lu on the stage, many people had a feeling of looking up to the mountains.

Such a Gu Lu ......

I'm afraid it's an existence that they can't catch up with in their lifetime!

On the stage of the auditorium.

Gu Lu ignored the people who were still in a sluggish state, but directly turned his head and continued to write the formula on the blackboard, and talked while writing.

"In topological geometry, one of our ultimate goals is to compute the canonical conformal mapping of topological complex surfaces to obtain the full system of conformal invariants. ”

"However, it is relatively difficult to calculate the map directly, so we tend to calculate the derivative of the map in a roundabout way. ”

"My new discovery is related to the derivative of this conformal map. ”

After a few seconds of silence, there was a whispered discussion.

The conformal mapping of complex surfaces is one of the major problems that have always existed in the topological geometry direction, and even in the entire geometry field.

This problem has been raised for a long time in the last century, but it has never been completely and effectively solved.

The reason is simple.

The derivative of a conformal map can be simply understood as a pure differential on a surface.

The integration of the holopure differential is the canonical conformal map, and the integral of the holopure differential on the canonical basis of the homotopy group gives the conformal invariant, periodic matrix.

But following this path, mathematicians need to build up difficult concepts and derive obscure lemmas.

This is quite unfriendly to most mathematicians at an intermediate level.

When a theory is only mastered and understood by a very small number of mathematicians, it is not a successful theory.

This is exactly the case with conformal mapping of complex surfaces.

Among mathematicians, only a very small group of mathematicians have a sufficient level to calculate the conformal mapping problem of complex surfaces by computing this form of the derivative on the conformal map.

But it's still horribly inefficient.

Rather than this, it is better to directly calculate the common invariants of topological complex surfaces in the most reckless way.

This is computationally intensive, but it doesn't require complex reasoning.

It's just a foolish repetitive operation.

Therefore.

In today's mathematicians, even those who have the ability to solve the conformal mapping problem by the conformal mapping derivative of the conformal map, still take the kind of brainless foolish direct operation operation.

However, listening to the meaning of Gu Lu's words just now, it seems that he has found another way to make simple calculations by using the narrow Hodge conjecture.

…………

The crowd was right.

Gu Lu has indeed found a shortcut to solve the problem of complex surface conformal mapping.

This discovery was a fortuitous one.

In the beginning, Gu Lu did not relate the special Hodge conjecture to the complex surface conformal mapping.

Until......

When Gu Lu was preparing for the speech of the report meeting, a series of formulas in the proof process made Gu Lu inexplicably familiar.

After searching in his mind, Gu Lu recalled that it was the manifestation of a multi-dimensional surface of a complex surface conformal mapping problem.

This accidental discovery surprised Gu Lu.

So, Gu Lu used half a day or so to deduce the theorem that he will talk about today.

…………

Gu Lu drew a simple concept map on the blackboard.

Then tap on the blackboard to keep everyone's eyes on you.

"Everyone, look at this picture, there are a lot of surfaces on the picture, and there are some unspired, non-scattered fields on the surface!"

"These real-world models of spin-free fields are electrostatic fields, but you can also think of them as vector fields that are too smooth to be smoother on a surface. For the sake of clarity, let's think of it as an electrostatic field for the time being. ”

Gu Lu used different chalks to add a few simple strokes to the concept map.

"Then, we use red tracks for contour lines and blue tracks for power lines. The tangent vector field of electric field intensity on the surface is a harmonic field with no rotation and no dispersion. ”

"Next, we can assume that given a surface (S,g) with a Riemann metric, take the ......"

Gu Lu told in detail step by step.

Because Gu Lu transformed the complex surface problem of no rotation and no dispersion into a simple electrostatic field problem, everyone in the audience understood it very easily.

However, the more easily the crowd understood, the more frightened they became.

They simply can't imagine.

What kind of smart brain Gu Lu has to think of these contents.

Put yourself in their shoes.

If they were Gu Lu, just preparing the manuscript of the report meeting in a week would be enough to be busy, not to mention taking time to derive a new theorem.

However, Gu Lu has only just spoken about the beginning, and everyone is still unclear about the significance of Gu Lu's new discovery.

But since Gu Lu dares to take it out, the level will definitely not be low.

Although everyone was deeply puzzled by the output rate of Gu Lu's miraculous skills.

However, Gu Lu's production must be a high-quality product!

Everyone still believes in these eight words.

"Next, let's introduce the concept of the special Hodge conjecture, and more specifically, the harmonic differential form of nonsingular projective algebraic clusters!"

On stage, Gu Lu's narration continued.

After filling the formula on a quarter of a blackboard, Gu Lu formally introduced the concept of the narrow Hodge conjecture.

This means that the derivation process of Gu Lu has officially entered the main topic.

The mathematicians in the room sat up straight, cheered up, and listened attentively.

What's more, he wrote down every formula that Gu Lu wrote on the blackboard, for fear of missing any details.

Everyone had a premonition in their hearts.

Gu Lu's new discovery will definitely leave a bright mark in the annals of mathematics.

“…… In this way, we can get a preliminary conclusion that all harmonic k-forms constitute groups, and harmonic k-form groups and manifolds are isomorphic to cohomology groups on the k-order. ”

What does this mean? This means that the dimension of the solution space of an elliptic partial differential equation on a manifold is constrained by the manifold topology. After that, we use the external calculus method to get the ......"

Under Gu Lu's dry mouth, the entire derivation process entered the final stage.

After writing down a few lines of formulas, Gu Lu presented a brand new theorem to everyone on the blackboard.

And the content of the theorem is only a simple sentence:

All the unspirated and non-scattered vector fields on the surface are grouped, and this group is isomorphic to the upper cohomology group of the surface!

"Professor Gu, what's the name of this theorem?" asked a mathematician who couldn't wait to stand up.

Gu Lu smiled slightly, "You can call it the conformal isomorphism theorem!"

At this point, the comorphic isomorphism theorem that has been passed down in history was born.

However, compared to the conformal isomorphism theorem, later generations prefer to call it ————Gu's first theorem!