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数学

Discovery

Andrius Kulikauskas

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

Lietuvių kalba

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Software

See: Classical Lie Groups

I'm applying for the Summer School on the Foundations of Geometry in Historical Perspective.

Research goals

  • I am seeking the cognitive foundations of everything, including all of mathematics, but especially geometry.
  • I am currently investigating why, intuitively, there are four classical infinite families of Lie groups and algebras, and how they ground different geometries, which I expect are affine, projective, conformal and symplectic.
  • I am looking out for the various kinds of dualities which appear in mathematics.

Summer school goals

  • I wish to gain an intuitive understanding of the nature of affine, projective, conformal and symplectic geometries, as well as other potentially fundamental geometries.
  • I wish to understand how the intuitive characteristics of various geometries are grounded in different structures such as the classical Lie groups and algebras.
  • I would like to acquire a general understanding of the fundamental theorems, structures and concepts of modern geometry.
  • I would like to understand the basics of algebraic geometry, including Grothendieck's constructs, especially topoi.
  • I would like to understand the relationship between geometry and logic.

A historical approach may help me personally understand the bigger picture, or at least, how various ideas have unfolded so far.

FoundationsOfGeometry


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Puslapis paskutinį kartą pakeistas 2018 kovo 25 d., 13:24
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