Dcase initiative to discuss Khovanov paper

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The discussion centers on the Dcase initiative's exploration of Mikhail Khovanov and Richard Thomas's paper titled "Braid cobordisms, triangulated categories, and flag varieties." The paper, which spans 89 pages and includes 21 figures, suggests a potential relationship between braid cobordisms and knot theory. Participants also discuss the implications of saddle points in helicoids as they relate to Nash Equilibria in game theory, and the possibility of unifying diverse mathematical representations through concepts like the Nash embedding theorems. The conversation highlights the intersection of differential geometry and game theory, particularly in the context of energy interactions.

PREREQUISITES
  • Understanding of braid cobordisms and their relation to knot theory
  • Familiarity with Nash Equilibria and game theory concepts
  • Knowledge of differential geometry principles
  • Basic comprehension of biophysiology, particularly the Krebs cycle
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  • Research "Braid cobordisms, triangulated categories, and flag varieties" by Mikhail Khovanov
  • Study the implications of saddle points in game theory and their relation to Nash Equilibria
  • Explore the unification of mathematical representations in differential geometry and game theory
  • Investigate the application of Einstein's equation in chaotic games and its implications for nuclear physics
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Mathematicians, theoretical physicists, and researchers in biophysiology interested in the intersections of knot theory, game theory, and differential geometry.

marcus
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Dcase you accidentally put this in the bibliography thread, where we don't have extra room for discussion.
Biblio is primarily for links to preprints and abstracts of selected new research---non-string QG.
Please make a separate thread to initiate discussion of any of the papers in the bibliography thread.

Dcase said:
1 - The language of "braid cobordisms" suggests a possible relationship to knot theory, from my perspective.

'Braid cobordisms, triangulated categories, and flag varieties'
Mikhail Khovanov, Richard Thomas
89 pages, 21 figures

http://arxiv.org/abs/math.QA/0609335

2 - In 3D braids appear to be helices. Some game theorists think that saddle points [found in helicoids] are equivalent to Nash Equilibria from Mathematical Game Theory.

http://ggierz.ucr.edu/Math121/Winter06/LectureNotes/09SaddlePointsNashEqui.pdf#search=%22saddle%20points%20Nash%20Equilibrium%22

3 - Is it possible that two such diverse mathematical representations of objects might somehow be unifiable? [through Nash Equilibrium and Nash embedding theorems]

Are differential geometries essentially manifestations of energy interactions of energy games [attractor v Disipator / braid v unbraid]
 
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Hi Marcus:

Thanks for starting the thread. Sorry for posting to a bibliography for discussion.

I wonder if the 'beautiful mind' of John Nash somehow realized that both differential geometry and game theory represented mathematical objects?

In biophysiology, the simple loop diagram [although a helix diagram is more likely since the same H is unlikely to always be the same donor-acceptor] of the Krebs cycle demonstrates that nucleic acid life is all about energy exchanges eventually leading to various phenotypic expressions, often with great symmetry.

Perhaps if Einstein's most famous equation were modified as a chaotic game,
v^2 * E-attracting = E-dissipating
lim v -> c
where E-attracting is m and E-dissipating is E,
it might represent the transformation of a star into a supernova as welll as have application to nuclear physics with gauge as the only difference?