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One phenomenon which I want to emphasise is that Koszul duality in char 0 and infinite dimensions gives two things – one is that the dual gets as input into Sullivan’s machinery to get the integrating object and another is the natural explanation of the story about Weil algebras and Chern-Weil.
Sounds interesting. Could you say in slightly more detail what you mean by this?
New entry Mohammed Abouzaid and several updates to references at mirror symmetry. I have reported elsewhere recent changes at quantum mechanics (including reordering the sections and writing a hopefully useful idea section with separate idea’s subsection on nPOV), and reported elsewhere few days ago of changes entries bialgebra cocycle, then new Gerstenhaber-Schack cohomology, Gel’fand-Fuks cohomology. New stub Mahmoud Zeinalian wanted at Hochschild cohomology.
I added references to scheme and removed now obsolete query box
Zoran: this gives wrong impression that Grothendieck school was working with ringed spaces and not functor of points. This is true for EGA but not for most of works of Grothendieck school. The things about generalization called locally affine space should go under locally affine space and under [[functor of points] and not here. There is also redundancy in new text.
New entries residue field, unramified morphism (of schemes) and Joachim Cuntz, expansion of Daniel Quillen. All this motivated with Urs’s interest in Rosenberg-Kontsevich work on formal smoothness etc. As MPI has changed their web site many of links to preprints should change from format
http://www.mpim-bonn.mpg.de/preprints/send?bid=3589
(replace 3589 by whatever number from their list) to the format like
http://www.mpim-bonn.mpg.de/preblob/3589
In this way I changed most of the links at Alexander Rosenberg.
New material at separable functor. New entry Gabriel localization and new stubs extension of scalars, S-category, Maschke’s theorem, separable coring. McCurdy/Street reference at Frobenius monoidal functor.
New entry characteristic zero. It required a separate treatment from the general notion of characteristic, partly because of the important Lefschetz principle. Also the new entry Hodge to de Rham spectral sequence degeneration or badly named degeneration conjecture. Yesterday new entry adjoint monad, reported elsewhere.
New: additions at thick subcategory. I noted that the original reference of Pierre Gabriel has also used the notion in the strong sense (that is not only closed under extensions, but also under subquotients). Today, improvements at spectrum of an abelian category.
I reported elsewhere recently some new entries related to the business of geometry related to topologizing subcategories, e.g. defining ideal of a topologizing subcategory, the appropriate section at conormal bundle, new entries neighborhood of a topologizing subcategory, differential monad, D-affinity, changes at local abelian category. Unrelated LNM 80, Paolo Aschieri, Nori motive, disambiguation page immersion, new reference at period etc.
New entry algebraic triangulated category and a new reference (Schwede’s book in progress) under symmetric monoidal smash product of spectra.
New entry Poisson pencil. It is a refelction of my recent revival of interest in quantization and quantum groups, like witnessed in recent entries dynamical quantum group, dynamical extension of monoidal category, additions to Hopf algebroid and so on. Unfortunately, while working on the side on these issues, I have little time to enter it in Lab, due other duties these days in Zagreb.
New entry Michel Van den Bergh in the course of writing on an extension of the entry noncommutative algebraic geometry and related new entries spectral cookbook, noncommutative sheaf, sheaf on a noncommutative space. Should I better say sheaf over a noncommutative space ?
I changed the title of degeneration conjecture (which is still in the redirect) to degeneration of Hodge to de Rham spectral sequence, but need to elaborate (I am not sure if we need to have a separate entry on commutative classical fact and on noncommutative partly conjectural version). Small additions to spectral theory. Elsewhere reported changes at Grothendieck pretopology, Grothendieck pretopology and splitting of part of it historical note on Grothendieck topology.
New entry semi-transitive coring related to today’s activity in preparation for a more detailed treatment of Tannaka duality (new stub Tannaka-Krein theorem, few changes in Tadao Tannaka and many at Tannaka duality) and some functional/harmonic analysis entries which should be useful there, including locally compact topological group, Gelfand-Raikov theorem, system of imprimitivity, operator topology, Radon measure, changes at projection measure and spectral measure etc.).
New references at cluster algebra and link to the Lustig’s 1990 ICM paper at intersection cohomology. Notice a conference this month (June) in Oregon on cluster algebras and canonical bases (cf. cluster algebra for a link).
Apart from discussion and few changes to entries related to classical mechanics and alike in last few days, I created few new stubs: monad in nonstandard analysis, Fokker-Planck equation, normed algebra, coexponential map, Alexander-Čech duality, radical, dynamical system, hyper-envelope of a Lie algebra. Renamed Verinde formula as Verlinde formula, extended kernel functor. New references in some other entries.
Many more references at Borel-Weil theorem. Notice that the original writeup by Serre is now at numdam. New group theory entries Borel subgroup, parabolic subgroup, nilpotent group, lower central series, linear algebraic group, derived series. Added Banaschewski-Mulvey constructive proof reference to Stone-Weierstrass theorem.
New entries quantum logic, Hilbert lattice, Boris Zilber, Zariski geometry yesterday, and minor, principal minor today.
Recent additions: new person entries Robin Hartshorne, Cosma Shalizi. new entries absolute de Rham cohomology, Bernoulli number, Hausdorff series, L-function, rigid cohomology, Monsky-Washnitzer cohomology, more references at de Rham cohomology, de Rham theorem, ringed topos, crystalline cohomology etc.
I am a bit unhappy with probability theory page as it is mainly about little used Giry monad which and few related papers in similar approach, which rather deserves its own entry, but I have no picture on what content should be in probability theory so I leave the reform of the page to later.
At my personal page a new page with some original material: Fock module and smash product (zoranskoda).
More references at Gabriel-Ulmer duality and one at nonstandard analysis. Recent new entries Gauss-Manin connection, Dmytro Shklyarov, Orlov spectrum.
Some additions to normal bundle, Pontrjagin-Thom collapse map (aka Thom/Potrjagin construction) and some related entries. Several new entries reported elsewhere, including unital category. Several new entries in number theory including algebraic number theory, class field theory, Weil reciprocity law, monic polynomial, algebraic number, discrete valuation, and updates to old ones.
Of course, the purpose is to write enough background for the geometric picture of class field theory where the reciprocity laws of number theory are somewhat analogous to the geometric idea of Grothendieck Galois theory at the level of fundamental groups in algebraic context and taking the maximal abelian quotients to simplify things (including the independence from the base point). This is absolutely beautiful subject which went from Kronecker’s Jugendstraum, through all the classical development of class field theory, toward Grothendieck’s and Beilinson’s ideas of motives and beyond on one side and with other ramifications related to Langlands program, to Milnor’s K-theory and so on.
Added more number theoretic stubs integral closure, quadratic reciprocity law, fractional ideal, Dedekind ring, Artin reciprocity law…
do you have a list of all number theoretic entries somewhere? I think we should create such a list, at least at number theory or better yet in a “floating toc”. Otherwise it is hard to see which material is available.
Right, I was thinking about it, to add soon or now a list of entries into algebraic number theory. This will be created soon, though I am more interested in content creation now. For the floating toc I would however still wait much until the shape of the cluster becomes more definite so that some seemingly important ones do not get there, while the space for more important ones to be created in future will be practically occupied. Everybody can go to algebraic number theory to see the list, once we create it, so at least each of these should have this link. It is still very early phase. I do not enjoy navigating through an entry with lots of irregular balast and lots of scrolling, so for small clusters I prefer not to start toc yet.
But we had also the entries like algebra, ring etc. where many of these entries should also be listed (e.g. Dedekind ring). I personally prefer to say arithmetic than number theory, like I prefer to say topology than the “theory of topological spaces”, as word “theory” makes it sound human-dependent, while I believe in the internal existence of the subject. I do not have much inclination to do almost any entries on analytic number theory at this point; my interest is much more with algebraic number theory.
OK, a very rudimentary starting list is now at algebraic number theory.
Thanks, looks good!
I have added some more hyperlinks to the intro text.
I started today entries p-adic number, valuation, abelian variety, Kronecker-Weber theorem, conductor, superspace, commutative localization.
I add some material to and split of a part from valuation ring into new entries Riemann surface via valuations (which needs much of extension to other fields, from the work of Dedekind and Weber) and Hahn series. There is some more organization needed between valuation, discrete valuation and valuation ring. I think that I made valued field redirect to valuation. Is the definition at local field that it is a locally compact Hausdorff (non-discrete) topological field fully equivalent to the definition (Serre’s lectures in Cassels-Froehlich Brighton Conf, volume) that it is a field complete with respect to the topology defined by a discrete valuation and such that its residue field is finite ? The second definition seem to exclude the archimedean case listed currently at local field, so the answer is probably no.
The definition in Weil’s Basic Number Theory is that a local field is a non-discrete locally compact Hausdorff field, and that’s what I was going by when I was editing local field. It seems to me this is a sensible definition. But I think if you simply add the hypothesis that there is a compact subring, those local fields will match Serre’s definition.
New entry coproduct from exponentials (zoranskoda). The formula at the bottom was used in the article Meljanac, Svrtan, Škoda, but unfortunately I did not do the derivation there (it is elsewhere in Meljanac opus in some form) what would be nice for completeness (I will add it if the referee asks for more details, it is under review).
New disambiguation page stability, stab for Bridgeland stability conditions, changed the name pullback stability to (used repetedly in the text of the entry) stability under pullback (leaving the old redirect); added a link at Nikolai Durov of his thesis (can’t believe his main work was not linked there); new entry standard conjectures (I think it makes sense only as a plural as it is a single body of conjectures); changes at nonstandard analysis, new stubs Loeb measure, function field, Reidemeister-Schreier theorem, geometry of 19th century, person entry von Staudt, Fodor Bogomolov and changes at history of mathematics.
Updated some former AMS links at math resources, math institutions, math archives and alike, as some of them changed to the site “Math on The Web” (related discussion), which seem to be run by a private business now. (By the way, “math” is here just a short mnemonic, it is not meant to exclude other areas of interest of nLab like history of math, relevant philophy sites or mathematical physics. But it is not good to be called long and wrongly emphasised “Math Physics and Philosophy links” as long as the emphasis of what we consider reliable sites are mainly mathematical in wider sense.) New page under construction moment map. Updates at the cycle of enetries thermodynamics, tropical geometry, field with one element, matroid, rig notice the very interesting recent papers of Kapranov, Marcolli and of Itenberg-Mikhalkin ! Maybe not very deep analogies but interesting new intuition and relations between formalisms ! New references at rigid analytic geometry, cyclic cohomology, chiral algebra, Drinfel’d double, topological quantum field theory, Nikolai Durov and elsewhere. New entries inertia groupoid, KMS state, George Lusztig, Gersten resolution, topological cyclic cohomology, Dijkgraaf-Witten theory, principal connection, simplicial connection, frame bundle. New redirects at many places, particularly some person names. Minor updates at affine connection, Élie Cartan, connection, Cartan geometry, Felix Klein, history of mathematics, Grothendieck Galois theory. A| week earlier, I had forgotten to report geometric stability theory.
New stubs, only numerous references and links: spin foam, Etera Livine, Hirosi Ooguri, Boulatov model, Florian Girelli, Lie triple system, new references at BF-theory and Snyder space. I hope John enters some content at spin foam. in my personal lab new stub ncFourier (zoranskoda) which is not about general notions of noncommutative Fourier transforms (that is why the title twisted), but a specific one coming in Majid’s work and then rediscovered in the context of spin foam models. Here there is a relation between “group field theory” and field theory on a noncommutative space; at the level of functions, the noncommutative Fourier transform does the passage.
New: quantum group Fourier transform, S. L. Woronowicz, dual bialgebra, coregular action, star exponential.
Edited: KMS state, Fourier transform, affiliated operator, quamtum anomaly, punny title(mainly references).
New: chiral de Rham complex, Grothendieck duality, universality, generating function in mechanics, symplectic field theory, Hofer geometry, harmonic analysis, Steiner system, block design
Edited: chiral differential operator, tropical geometry, convex space, duality, distribution, quantum logic, Kochen-Specker theorem, Bohr topos, universality class, universal colimit, polyfold, symplectic topology, Floer homology, rigid body dynamics, integrable system
New: Calogero model, contraction, decomposable tensor
Edits: moment map (extensive)
Hi Zoran,
thanks for moment map.
I have created a stub for tensor just so that something more general than just contraction will link to it. Otherwise the entry may be really hard to find. Or to know that it exists. Even for Google.
We should probably complement the page eventually with another notion of tensors in enriched category theory which is under copower but some sort of redirect should be included (I do not know how to competently phrase the disambiguation here). Edit: I did write some temporary version, though.
New: Ore extension (with redirect skew-polynomial ring), differential geometry (zoranskoda), topological quantum computation, Vladimir Retakh, topos approach to quantum mechanics (with redirect quantum topos theory), connection in noncommutative geometry
Edited: Riemann surface, differential geometry, Pavel Aleksandrov, Khovanov homology, symmetric space, alternative algebra, frame bundle, connection for a differential graded algebra, noncommutative principal bundle, connection, Hall algebra, symplectic field theory
Hey Zoran,
thanks for all these entries. Since you are investing so much energy into it, I’ll dare repeat an observation which in some form I have made before.
Here goes:
I notice that the entry topological quantum computation , for instance, points to no other entry and is pointed to by no other entry. And you don’t announce its creation in an nForum thread with “topological quantum computation” in the title, but hide it here within a huge number of random links.
I don’t understand why you do this. This is almost asking for the entry to be forgotten. The next person (maybe in a month, in a year) who sets out to write something about quantum computation is very unlikely to see that there is already something about it on the nLab. Because neither Google will know it (or at least not give it high page rank) nor searching the thread titles here will show it – nor will probably many readers of the forum here remember that you had this term listed here within a whole bunch of other, unrelated, terms.
Do you see what I mean? It seems to me that for the effort of creating an entry to be well-invested, a minimum of cross-linking is required.
It would take me several times (one order of magnitude) more time to think of suitable linking for a so-far not so related topic of topological quantum computation than it took me to create it (it was several seconds). I tried, by looking for quantum information, but found that that entry was in unsatisfactory state and hence that I do not see the proper place and plan there to link it. I remember and review my pages and they eventually fit into the scheme. Recall how many unlinked entreis in algebraic geometry I created so far and then suddenly recently they started becoming a network. I spend time on content and won’t spend time on other things when the time and the environoment is not ready for it. When it is, then I will connect it.
This is almost asking for the entry to be forgotten.
Why not ? I invested 10 seconds in creating it as I cut the references from the nForum where I spent much more time for it. The linking it PROPERLY would take about several minutes. So spending several minutes to insure 10 second work is not rational.
To me opening a separate discussion for each entry is a bigger problem, because then so many small entries in nForum appear that it is hard to recall in which entry some disucssion was and I have a big problem with this. So often I spend hours searching for old discussions when I find a new argument or issue to add to them.
ON THE OTHER HAND, I was suggesting many times that we make a new search option to backlink each entry to all nForum entries which mention it and saw almost no interest from nForum people even to discuss the suggestion.
Sure, it takes another 20 seconds. I am just thinking that this makes the first 10 seconds more worthwhile. I have now added an Idea-sentence at topological quantum computation and cross-linked it with topological quantum field theory.
To me opening a separate discussion for each entry is a bigger problem, because then so many small entries in nForum appear that it is hard to recall in which entry some disucssion
Hm, okay, but this was the very idea in the beginning of the nForum. To have a place where we can open precisely one thread for precisely every nLab entry. I always find it sad that you work against this idea, it would otherwise be much more systematic. Also it would solve the backlink problem: if it is clear that for every Lab entry there is an Forum entry of the same title.
And thats also what the Forum “categories” are meant for: the entries that are not meant for general discussion but just about a fixed entry go by “latest changes”, others go elsewhere.
Sure, it takes another 20 seconds.
Come on, I spent a minute looking for quantum information and alike and was NOT satisfied. For careless one might be 20 seconds, but I spent much more and did NOT succeed to link (this was before your complaint, at the time of creation). I do not want to link on the basis of superficial resemblence. Recall your insistance on having comments in synthetic geometry that it is an approach to nonstandard analysis, what was wrong, and finally rectified. It took us much more time to discuss this with you and clear up the issue. You see how much time also we spent because I superficially linked Alexandrov and Alexandroff spaces. Being careful takes much more time, but saves time eventually.
And thats also what the nForum “categories” are meant for: the entries that are not meant for general discussion but just about a fixed entry go by “latest changes”, others go elsewhere.
Yes, but many interesting discussion happens spontaneously within comments on latest changes and I had spent many hours looking for those. People do not use tags, and sometimes repeat the similar title for more than one discussion/thread related to the same entry. Linking carefully to other entries takes much thought and time (hence it is easier to do at a mature time when the authors feels competent or readty to do it and not at the time when you find it suitable for criticizing – why do you impose your time-sharing feeling to other contributors ? I find it unnatural and oppresive that somebody tells me at which moment I should dedicate time for linking), while putting a tag literally takes several seconds when creating the first item and title in the thread.
I always find it sad that you work against this idea,
But who rejected the tags ?
To have a place where we can open precisely one thread for precisely every nLab entry.
I do not think that this was ever said and you yourself do not follow this (I recall many times that you returned to an old entry and created a new thread for the old entry). Second many items are created in batches and groups, and should be discussed so. I have created for example once a thread on D-geometry regarding many related entries I did there.
Also it would solve the backlink problem: if it is clear that for every nLab entry there is an nForum entry of the same title
This would FAR not suffice. Backlink should be to ANY entry where the entry was mentioned. Not only at latest changes but in ALL sections of nForum. We often compare various notions, and entries. For example we discuss there is a repetition about it. We also argument by citing various other entries. And you would reduce all the richness of discussion in forum to reference in a single thread per entry ? For example for TOPOS which appears in many entries (only 16 are tagged at the moment for word topos, I have no easy way to tell how many of those are referring to the actual entry topos, and how many among non-tagged are) ? I want a backlink to any entry which mentions in brackets the entry or its aliases.
There is a difference between google search for all words and search which searches only for page names and finds all aliases.
Edit: in fact I do not think that the latest changes discussions are that often useful to search for, unless one previously participated in them and recalls some intersting issue. When all Forum is in question than the balance changes. Latest changes are most useful when the edit is recent and not yet seen by active members, it tells me where the CURRENT interests are, so the last active edits in latest changes grouped or not, are most useful to me. So that I know whom I can help in his effort or where I can find something new and interesting to connect to, or where somebody has revised the entry I cared about before.
I am just thinking that this makes the first 10 seconds more worthwhile.
De gustibus non disputandum est :)
Hi Zoran,
okay, that’s the reaction I should have expected. I saw before that you don’t like me to express these opinions and make suggestions. Since we are working on this project called “nLab” together it’s a bit unfortunate that we are not able to find compromises in how to go about it. But if it just doesn’t work, I’ll stop insisting.
I should also say that when I have things grouped then when I return to the topic I will remember which entries I worked in an effort batch and will know how to continue. Like this summer I had started few entries in arithmetic and once I want to continue that circle I want to clearly see the list of those entries I worked on that week, and not all entries in arithmetic (or other authors) nor partail list which I could remember.
bit unfortunate that we are not able to find compromises in how to go about it
I think you exaggerate by asking to do something in the very moment when the entry is created. Did you hear of under construction status ? Did you take compromises yourself ? You dismissed the tag idea after first mention. One thing is to ask for compromise and another is to accuse somebody of “work against this idea” without first seeing the context.
You see, you have your model of work. Some things are easy for you and hard for others. Some things you do lightly which somebody does carefully, some things you do carefully which others do carelessly. Some things are easy in your browser, your googling habits or suited to your needs or bandwidth, some are easy in mine.
Okay, sure.
New entries: geometric measure theory, ergodic theory, rectifiable set (redirecting also rectifiability), Langlands program, orbit method, collective field theory, large N limit, Schur function
Book entry Combinatorial species and tree-like structures
Edits: measure theory, geometric Langlands program, symmetric space, universal enveloping algebra, AKSZ model (Bouwknegt-Jurčo reference), hyper-envelope of a Lie algebra, Yang-Mills instanton (references), instanton, semiclassical approximation, twisting cochain, species, quandle, Dominic Joyce, Gian-Carlo Rota, coinduction (Escardo-Pavlović reference), Maurer-Cartan equation.
Spelling pseudoabelian category added to redirects of Karoubian category; renamed category of descent data (from cryptic shorthand descent category which is left as redirect).
As usually, the most important among above are reported elsewhere in Forum.
Some of the recent activity (some of it was or will be reported elsewhere) includes
New entries: special function, elementary function, elliptic Selberg integral, complex analysis, gamma function, distribution of subspaces, directional derivative, Knizhnik-Zamolodchikov equation, Macdonald polynomial, random matrix, combinatorial representation theory, Jack polynomial, quasi-Hopf algebra, Wronskian, Vandermonde determinant, Euler beta function, beta function
New person entries: Vladimir Guletskii, Bernard Leclerc, Arun Ram, Claudio Procesi, Alexander Varchenko,
Recent edits: Nora Ganter, WZNW model, hypergeometric function, Giovanni Felder, Selberg integral, analysis, Fréchet space, linear algebra, hyperfunction, Cartan connection, spectral theory, Drinfeld-Kohno theorem, double Hecke algebra, noncommutative motive, arrangement of hyperplanes, Calogero model, Vladimir Hinich, crystal basis, braid group, bialgebroid, Drinfel’d double, Poisson-Lie algebroid, Hopf algebroid, symplectic groupoid, Andrei Zelevinsky, matroid, quantum group, quantum flag manifold, Schur function configuration space, Fadell’s configuration space, Leonhard Euler, ergodic theory, books in algebraic geometry
I am having lots of problems in last couple of years, and I now more and more often edit in a hurry and often do not report at Forum. I did report in some periods, like in a spree of working on model theory entries. Some of the entries I created in recent months (some could have been reported elsewhere) include elementary class of structures, descent algebra, Nori motive, Laurent phenomenon, Laurent polynomial, scissors congruence, Raphaël Rouquier, Georgia Benkart, down-up algebra, Donald Knuth, complex connection, ICM, Rémi Léandre, connection in noncommutative geometry, morphism of finite presentation, regular local ring, infinitesimal neighborhood,, Jounolou cover, semiseparated scheme, blueprint, examples in topology, universal bundle, Milnor construction, Ziegler spectrum, Serre functor, non-archimedean analytic geometry, adic space, structuralism, n-angulated category, spectral category (recycled), Gribov anomaly, first-order theory, categoricity, stability theory, age, amalgamation theory, amalgamation property, spectral network, Nekrasov function, AGT conjecture (merged later with Urs’s addition AGT correspondence), flux compactification, Frederic Denef, continuous logic, simple theory, forking, Galois type, Rami Grossberg, infinitary logic, Mike Prest, Mitsuhiro Takeuchi, Takeuchi product, Giovanni Sambin, hafnian, Benjamin-Ono equation, Jacobian variety, Makkai duality, Martindale localization, Yang-Baxter equation, classical r-matrix, associated graded ring, filtered ring, PBW theorem, quantum Yang-Baxter matrix, star product, Duflo isomorphism, Schubert calculus, enumerative geometry, intersection theory, formal geometry
and some unreported recent changes/additions in Hopf algebroid, reconstruction theorem, imaginary element, affine connection, valuation, valuation ring, dilogarithm, bialgebra cocycle, Gerstenhaber-Schack cohomology, Calogero model, integrable model, rewriting, Catharina Stroppel, smooth scheme, conormal sheaf, algebraic approaches to differential calculus, Grothendieck connection, descent morphism, microlocal analysis, plus construction on presheaves, Joel Robbin, pointless topology, quasi-separated morphism, separated morphism, separated geometric morphism, math institutions, cartesian space, Boris Zilber, Euler class, Barratt-Eccles operad, bialgebra, Gian-Carlo Rota, umbral calculus, analysis, Euler integration, Calkin algebra, Euler characteristic, separable algebra, Milnor fiber, A-infinity-category, Vladimir Berkovich, analytic spectrum, analytic affine line, Tomasz Brzezinski, geometric measure theory, Gabriel-Ulmer duality, coring, algebraic structure, Quillen exact category, dynamical system, o-minimal structure, gauge fixing, Curci-Ferrari model, renormalization, motivic integration, Michael Makkai, ultraproduct, ultracategory, Macdonald polynomial, energy, elliptic cohomology, tropical geometry, strict omega category, flux, quasinormal mode, moment map, math resources, books and reviews in mathematical physics, canonical extension, topos of types, Saharon Shelah, spectrum of abelian category, metaplectic representation, Shinichi Mochizuki, Nikolai Durov, EGA, Maxwell equations, electromagnetism, Moss Sweedler, theory, model theory, character, bialgebroid, additive functor, Pfaffian, ordinary differential equation, Liouville integrable system, Lax equation, Jacobian, Nils Abel, field of fractions, localization of a ring, localization of a module, universal localization, Andrew Ranicki, Bousfield localization, conformal block, associated graded object, Michael Spivak, Vladimir Drinfel’d, quantum group, geometric representation theory, EPR paradox, deformation theory, von Neumann algebra factor, Jones polynomial, history of mathematics, eta invariant, Hausdorff series, moduli space, curve, algebraic curve, birational map, moduli space of curves, compactification, David Hilbert, adjoint triple, Kapranov’s noncommutative geometry, Dolbeault complex, differentiable manifold, category of fibrant objects, Toda bracket
Today new: cohomological induction, induced comodule, corepresentation, Sigurdur Helgason, Verma module, tangent Lie algebra, Chevalley group,
Major changes: Lie theory, Gregg Zuckerman, invariant differential form,
Minor changes: induction, induced representation (including new redirect: induced module), gebra theory, Lie’s third theorem, homogeneous space, quantum group