手册

数学

物理

Discovery

Andrius Kulikauskas

  • ms@ms.lt
  • +370 607 27 665
  • My work is in the Public Domain for all to share freely.

Lietuvių kalba

Introduction E9F5FC

Understandable FFFFFF

Questions FFFFC0

Notes EEEEEE

Software

Math, Math research, Math exercises, Math questions

数学笔记本

I'm starting to write up the results that I'm getting as I investigate the root of mathematics.

Current research program

  • Relate the four classical Lie families to the four levels (metalogics, geometries) in the ways of figuring things out.
    • Understand the four classical Lie families (the choice frameworks, root systems, geometries).
      • Understand the most fundamental Lie groups {$A_2$}, then {$A_n$}, and then the other classical families.
  • Understand the four levels (metalogics, geometries) in the ways of figuring things out.
    • Understand the ways of figuring things out in physics.
      • Understand the role of measurement in physics, both relative and absolute.
        • Understand tensor products.
  • Understand the significance of the foursome in mathematics and how it relates to the four levels.
    • Relate the foursome and the Yoneda lemma.
      • Understand Yates index theorem as a statement about the foursome, and relate it to the Yoneda lemma.
  • Consider whether and how {$F_1$} models four stages of God's going beyond himself.
    • Understand groups as analogues of Hopf algebras.
    • Understand finite fields and what {$F_{1^n}$} could mean.
    • Consider these four stages as four interpretations of the variable q in Gaussian binomial coefficients. Relate that to my theory of variables.
  • Relate Bott periodicity and the eight-cycle of divisions of everything.
  • Understand the Snake lemma as the eightfold way.

Math Big Picture

Math foundations?

Geometry

Binomial theorem

Physics

Lie theory

Linear algebra

Complex analysis

  • Using complex numbers, interpret {$d/dz \: e^z$}
  • Study the Catalan numbers and the Mandelbrot set
    • Check what happens if I plug in different values into the Catalan power series.
    • What is a combinatorial interpretation of P - P(n), the generators of the Mandelbrot set, in terms of the Catalan numbers? Get help to generate the difference. What is the best software for that?

Analysis?

Category theory

Logic

Computability theory?


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Puslapis paskutinį kartą pakeistas 2020 sausio 14 d., 13:52
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