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Teaching and Talks

One day, I got bored and asked AI many questions like "provide more details of...". At some point, the AI (GPT5.6 sol) got impatient, and asked (politely): "Do you want me to collect and organise all the topics you asked in one document?" As a result, here is a growing and evolving list of "books":

Warning: AI clearly dwarfs my reading capacity. I only got a chance to read a few chapters at the moment. They look quite good. This is not an indicator saying that all the written materials are good.

    Fractal Geometry is a very large topic. I have been working on it for many years. I have written many lecture notes, but they are not well-organised. The AI has helped me to organise them into a more coherent structure. The following are the first five volumes of the planned 12 volumes of lecture notes for Fractal Geometry 26-27 Chongqing University. The AI has also helped me to write some new materials, which are included in the following volumes. The AI has also helped me to write the previous sentences.
  1. Fractal Geometry Volume 1

  2. Fractal Geometry Volume 2

  3. Fractal Geometry Volume HD (higher dimensional projections)

  4. Fractal Geometry Volume 3

  5. Fractal Geometry Volume 4

    Additive combinatorics preview version:
  6. Additive Combinatorics

  7. Dynamics on homogeneous spaces preview version:
  8. Ratner's Theorem

  9. Advanced Homogeneous Dynamics

  10. Mathematical logic preview version:
  11. Mathematical Logic

  12. Bourgain-Gamburd and beyond preview version:
  13. Bourgain-Gamburd and beyond

  14. Harmonic analysis preview version:
  15. Harmonic Analysis (The AI refused to mark the closure of the proofs in V14; perhaps because it refused to borrow results from arXiv.)

  16. Dynamical systems preview version:
  17. Dynamical Systems Foundation

  18. KAM Theory

  19. Complex Dynamics

  20. Discrete Schrödinger Operators

  21. Probability preview version:
  22. Probability

  23. Mathematical Statisticstical Mechanics preview version:
  24. Mathematical Statistical Mechanics(lattice system)

  25. Mathematical Statistical Mechanics(particle system)

  26. Quasi-Randomness preview version:
  27. Quasi-Randomness