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I have started a category:reference page
such as to be able to point to it for reference, e.g. from Kontsevich 15 etc.
brief category:people-entry for hyperlinking references at computational topology
brief category:people-entry for hyperlinking references at tensor network and elsewhere
added to locale a section relation to toposes stating localic reflection
I have started an entry on computational topology partially to record some ideas from some books on that area that I am reading at the moment. There are also new entries on topological data analysis and sources in computational topology.
The term “tensor network”, while essentially just a synonym for “string diagram”, has in recent years become widely used and now fully established in quantum physics, especially in its use for discussion of holographic entanglement entropy. It needs a page of its own, if only to point to string diagram while also listing the relevant physics references
added pointer to this discussion of possible realization of the SYK-model in condensed matter physics:
brief category:people-entry for hyperlinking references at p-adic string theory
Preprint today by Yau et al., relating -adic strings to the Riemann zeta function:
brief category:people-entry for hyperlinking references at tensor network state and holographic entanglement entropy
added these pointers on classification of topological phases of matter via tensor network states:
C. Wille, O. Buerschaper, Jens Eisert, Fermionic topological quantum states as tensor networks, Phys. Rev. B 95, 245127 (2017) (arXiv:1609.02574)
Andreas Bauer, Jens Eisert, Carolin Wille, Towards a mathematical formalism for classifying phases of matter (arXiv:1903.05413)
This is maybe mainly for entertainment. But don’t forget that for newcomers there is a real issue here which may well be worth explaining:
In mathematics it happens at times that one and the same concept is given two different names to indicate a specific perspective, a certain attitude as to what to do whith such objects.
Here are examples:
A quiver is just a directed graph (pseudograph, to be explicit). But one says quiver instead of directed graph when one is interested in studying quiver representations: functors from the free category on that graph to the category of finite-dimensional vector spaces.
A presheaf is just a contravariant functor. But one says presheaf instead of contravariant functor when one is interested in studying its sheafification, or even if one is just intersted in regarding the category of functors with its structure of a topos: the presheaf topos.
(…)
brief category:people-entry for hyperlinking references at tensor network and at holographic entanglement entropy
created a stub for holographic entanglement entropy in reaction to this MO question.
brief category:people-entry for hyperlinking references at tensor network
brief category:people-entry for hyperlinking references at computational topology
a stub for the moment just so as to give a home to
and to cross-link with p-adic AdS/CFT correspondence and tensor network states.
I edited lambda-ring, added a definition from the thesis of John R. Hopkins. Later on I will add the definitions of Hazewinkel, too. This entry has a long (and very instructive) idea-section. Maybe I find time to fill in some more details to these ideas.
stub for cosmic inflation (for the moment just to record some references)
added pointer to today’s