Please Clarify

Princeton Mathematics Department is ranked number one in the world, and other universities should have little to say about that.

Princeton's Physics Department is very strong, ranking among the top seven in the world.

The Physics Departments of Harvard, Stanford University, Princeton, MIT, Cambridge University, Oxford, and Caltech each have their own strengths and flagship programs. Their scores on the physics ranking list are quite close, and if any of them wants to be the Boss in the Physics Community, there will always be someone from the other six who disagrees.

Princeton's Physics Department focuses its resources on Condensed Matter Physics, cosmology, and High Energy Physics. Hackman, who came to visit, is a professor in Condensed Matter Physics at Princeton University's Physics Department.

Hackman's appearance suggests he might be here to cause trouble... Shen Qi remained calm and composed, responding to any situation with equanimity.

To everyone's surprise, Hackman immediately said, "Shen, our Physics Department needs you."

"Hmm?" Shen Qi smiled faintly. Friendly forces?

Hackman: "Your paper published in PRL, which redefines defects in continuous media and crystals based on the topological treatment of Homotopy Group, is of great reference value to us."

"Hmm." Shen Qi suddenly understood; they were indeed allies.

"I don't care about purely mathematical problems, but Shen, you also have in-depth research in physics, and your existence is very valuable to us," Hackman said.

Hackman's words pleased Shen Qi, and he adopted a friendly attitude. "Go ahead, Professor Hackman, what do you need me to do?"

Hackman noticed a recent copy of PRL on Shen Qi's desk. He flipped to the section on "Research on Defect Topology Based on Stable Homotopy Group of Spherical Surfaces" and asked, "How was this homology group on the Adams Spectrum calculated?"

"Didn't I write that in the paper?" Shen Qi countered.

"The calculation results are very impressive, but your calculation process... well, it's rather complicated. Here's the thing, I happen to have a project that requires citing the theoretical basis from your paper, mainly the mathematical processing, so I think it's best to clarify things," Hackman said.

Shen Qi finally understood Hackman's purpose. This guy came to ask for help when he didn't understand something, and this pragmatic academic attitude was commendable. It should be noted that not every physicist with numerous honors and titles is as proficient in mathematics as Edward Witten.

"Professor Hackman, it's like this, let me explain. In the study of the structure of matter in Condensed Matter Physics, I use this mathematical processing method to derive short exact sequences of short cohomology group on Zp..." Shen Qi patiently explained his calculation method.

"OK, very good." Hackman understood. He shook hands with Shen Qi: "Thank you. Come to my office in the Physics Department for coffee sometime. Also, I'd like to make a suggestion: in the future, when you write physics papers, could you appropriately include some experimental data or Computer Science simulation data? This would make it easier for more physicists to understand your theories. If everyone came to your office to ask questions like I do, and you were so enthusiastic, you would be as busy as our president."

Shen Qi nodded. "I accept your suggestion, Professor Hackman. By the way, you said you would cite my paper in your research project, so would you mind revealing what your project mainly researches?"

"Of course, you have the right to know. Inspired by Graphene, my project mainly studies the electronic structure and optical properties of Graphitic Carbon Nitride Quantum Dots. Analyzing various microstructures in materials using traditional Condensed Matter Physics methods has become quite challenging. Your proposed defect topology treatment method based on spherical stable Homotopy Group has been extremely helpful to me. Thank you again, Professor Shen." Hackman expressed his gratitude to Shen Qi and left with a sense of accomplishment.

Professor Hackman's suggestion makes some sense. My paper is too mathematically oriented. In most people's minds, I am still a mathematician... Shen Qi opened the ADF software on his computer to enhance his physics and chemistry skills.

ADF is a Computer Science simulation analysis software that Shen Qi has had installed for several months. He plays with it occasionally, but most of his work relies on his imagination.

The research findings were purely speculative, and Professor Hackman came to complain because he couldn't understand them.

Therefore, Shen Qi needs to change some of his working methods when operating the ADF, at least for the current stage of physics research.

ADF is widely used in Materials Chemistry, Solid State Physics, catalysis, batteries, spectroscopy and other fields. It can simulate chemical reactions, construct microstructures, and calculate various data, making it quite versatile.

ADF can simulate most real-world operations performed in the laboratory, thus saving significant experimental costs.

"Graphitic Carbon Nitride, g-C3N4, is a new type of synthetic material that is in powder form at room temperature and pressure and is non-toxic."

Shen Qi did some research and gained a general understanding of Graphitic Carbon Nitride. He had never seen the actual product, but he was already making changes; at least he was trying to understand the real thing.

With pollution becoming increasingly severe, energy and the environment are two major challenges facing all countries, and Solar Energy, as a clean energy source, has received widespread attention from various nations.

Photocatalysis is considered a promising technology for converting low-density Solar Energy into high-density chemical energy. However, traditional semiconductor photocatalysts, such as TiO2, have low light absorption efficiency due to their large internal structural defects.

Therefore, it is imperative to find a new type of photocatalyst that has strong activity under visible light, and thus, Graphitic Carbon Nitride g-C3N4 was synthesized by scientists.

g-C3N4 is of higher quality than TiO2, but this new synthetic material also has its own defects and still cannot satisfy the scientists' ambitions.

Scientists were not about to give up. They forcibly altered the microstructure and physical properties of g-C3N4, including its optical and electrical properties, by doping it with metal or non-metal atoms, in order to achieve the goal of efficiently converting Solar Energy, ultimately solving pollution and benefiting mankind.

Professor Hackman's team in the Physics Department next door is engaged in this great cause that benefits humanity and saves Mother Earth.

Professor Hackman's dilemma is: which element, in what manner, and at which part of g-C3N4, should be incorporated to achieve the best results?

This brings us back to the fundamental theoretical research in Condensed Matter Physics: can the theory of microstructure analysis and defect definition in condensed matter be optimized?

In his paper "Research on Defect Topology Based on Stable Homotopy Group of Spherical Surfaces" Shen Qi proposed a theoretically feasible optimization scheme, which gave Professor Hackman hope.

When Shen Qi drafted this paper, he didn't pay attention to new materials like Graphitic Carbon Nitride. He focused on macroscopic theoretical research and didn't care much about specific material applications.

Now Shen Qi is curious about concrete matter, and mathematics, physics, and chemistry are deeply integrated and intertwined in his mind.