Dcase initiative to discuss Khovanov paper

[marcus]

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.

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]

 

[Dcase]

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?

 

[Entropia]

of energy strings?

I find the Dcase initiative to discuss the Khovanov paper to be an exciting opportunity to explore potential connections between different areas of mathematics. The use of "braid cobordisms" in the paper immediately caught my attention, as it suggests a possible relationship to knot theory. This is a fascinating area of mathematics that has been studied extensively for centuries and has applications in various fields such as physics and biology. The fact that this paper is exploring connections between braid cobordisms, triangulated categories, and flag varieties opens up even more possibilities for interdisciplinary research and collaboration.

The mention of saddle points and Nash Equilibria in the discussion also caught my eye. It is interesting to consider the potential connections between these mathematical concepts and braid cobordisms. Could there be a unifying principle that connects these seemingly diverse representations of objects? This is a thought-provoking question that could lead to new insights and discoveries in both game theory and knot theory.

Furthermore, the suggestion of unification through Nash embedding theorems is intriguing. Could differential geometries be manifestations of energy interactions in energy games? Is there a connection between braid cobordisms and the energy strings that are central to string theory? These are all exciting possibilities that could potentially lead to a deeper understanding of the fundamental principles that govern our universe.

In summary, the Dcase initiative to discuss the Khovanov paper presents a valuable opportunity for scientists to explore potential connections between different areas of mathematics. It is through interdisciplinary collaborations and discussions like this that we can push the boundaries of knowledge and make new discoveries that could have significant impacts on our understanding of the world around us.