# John Baez

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## Registered User

 Name John Baez Member for 3 years Seen yesterday Website Location Riverside Age 52
I'm a mathematical physicist. I used to work on n-categories and fundamental physics, but now I'm thinking about network theory and environmental problems. If you want to help me with that, please check out the Azimuth Project and write some articles there, and/or send me an email.
 2d awarded ● Popular Question 2d awarded ● Good Question 2d revised Quasicrystals and the Riemann Hypothesisfixed equation Jun14 comment Quasicrystals and the Riemann HypothesisThanks, that's very helpful. Jun13 revised Quasicrystals and the Riemann Hypothesisadded link Jun13 awarded ● Nice Question Jun13 comment Quasicrystals and the Riemann HypothesisBy the way, I don't see how to derive the equation I wrote down from the one in Lemma 1. I haven't tried very hard, but I'd like to be assured it's possible. I'd need to see what happens with the term involving the logarithmic derivative of the gamma function. Jun13 revised Quasicrystals and the Riemann Hypothesisf is a tempered distribution Jun13 comment Quasicrystals and the Riemann HypothesisI think that helps a lot. If the Riemann Hypothesis holds, all the $k_j$ are real, so the Fourier transform of the right-hand side will be a linear combination of the Dirac deltas. If the Riemann Hypothesis is false, some of the $k_j$ will be complex, so I see no reason to expect the Fourier transform of the right-hand side to be a linear combination of Dirac deltas. However, it would take me some work to prove it's not. Has someone done that? Jun13 revised Quasicrystals and the Riemann Hypothesisadded figure Jun13 asked Quasicrystals and the Riemann Hypothesis May24 awarded ● Nice Question May20 comment What are the main structure theorems on finitely generated commutative monoids?In case anyone reads this in the distant future, my question is now my last sentence, though it wasn't when Andres Caicedo asked. May20 answered Finitely generated monoids are finitely presented? May20 revised What are the main structure theorems on finitely generated commutative monoids?added information about numerical monoids May20 comment What are the main structure theorems on finitely generated commutative monoids?Benjamin wrote: "A finite commutative semigroup has a grading by a semilattice such that the homogeneous components are nilpotent extensions of abelian groups." Great! That sounds like the kind of thing I want to know about. May20 comment What are the main structure theorems on finitely generated commutative monoids?Benjamin wrote: "Another big result is that the first order theory is decidable. I can't recall the reference but Mark Sapir knows it." Two references to this - papers by M. A. Taiclin - are in the link I provided in my second item. This link is a long review article by Mark Sapir and a coauthor. The references are numbers 386 and 387. I added some words to clarify that indeed the whole elementary theory is decidable. May20 revised What are the main structure theorems on finitely generated commutative monoids?clarified the question May20 revised What are the main structure theorems on finitely generated commutative monoids?added 86 characters in body May19 comment What are the main structure theorems on finitely generated commutative monoids?Andres wrote: "is your question the last sentence?" No, it's the title: what are the main structure theorems on finitely generated commutative monoids? May19 comment What are the main structure theorems on finitely generated commutative monoids?Qiaochu wrote: "This sounds quite hard." I'm not expecting a full classification, just theorems that help us classify certain restricted classes of finitely generated commutative monoids, or at least describe their structure. For example, knowing that every cancellative one embeds in $\mathbb{Z}^n$ is worth something. Locally compact Hausdorff topological abelian groups is another category where we'll never get a full classification, but there are beautiful partial results. May19 comment Why are affine Lie algebras called affine?That's what I thought too. I wouldn't be surprised if 'affine Coxeter diagrams' or 'affine Dynkin diagrams' were well-known long before people seriously started studying the corresponding Lie algebras. May19 asked What are the main structure theorems on finitely generated commutative monoids? May8 awarded ● Necromancer May6 comment What do coherent topoi have to do with completeness?I believe Torsten meant it doesn't have a model in the category of sets. I believe any consistent theory in geometric logic has a model in some topos. For example, we can take the theory, build its 'syntactic site', and find a model in the topos of sheaves on its syntactic site. For details see section 4.1 of the exposition by Benjamin Frot mentioned below. May6 answered What do coherent topoi have to do with completeness? Apr29 awarded ● Popular Question Apr18 comment Simple proof of the existence of Nash equilibria for 2-person games?Thanks! You might like to see my own proof here: johncarlosbaez.wordpress.com/2013/02/27/… johncarlosbaez.wordpress.com/2013/03/05/… johncarlosbaez.wordpress.com/2013/03/07/… johncarlosbaez.wordpress.com/2013/03/11/… It's not very efficient but it proves a few related results in the process and only uses some basic facts, like what you said about compact sets. Mar8 comment Simple proof of the existence of Nash equilibria for 2-person games?Thanks, Rabee Tourky! Unfortunately I don't know linear programming, but it's probably at work behind this elementary proof that Nash equilibria exist for finite 2-player zero-sum games: johncarlosbaez.wordpress.com/2013/03/07/… This is based on Andrew Colman's 1982 book Game Theory and its Applications in the Social and Biological Sciences. Mar8 comment Simple proof of the existence of Nash equilibria for 2-person games?Thanks, Michael Greinecker! Since Milnor gave 3-page proof of the Brouwer fixed-point theorem using just multivariable calculus and a wee bit of analysis (people.ucsc.edu/~lewis/Math208/hairyball.pdf), I'm not convinced proving it from the existence of Nash equilibria by taking a limit as a finite game converges to an infinite one implies that the existence of Nash equilibria for finite 2-person games is 'just as hard' as the Brouwer fixed-point theorem. There still could be an easy proof for finite games. But still, all this is very interesting! Feb14 awarded ● Nice Question Feb12 comment Simple proof of the existence of Nash equilibria for 2-person games?Thanks! There's a lot of nice history in this paper. And I guess you wouldn't say any proof of the existence of a Nash equilibrium for two person finite zero sum games is a proof of Kakutani's fixed point theorem? The trick in this paper seems to involve taking $A$ arbitrary, $B = I$. Feb12 revised Simple proof of the existence of Nash equilibria for 2-person games?edited body Feb12 asked Simple proof of the existence of Nash equilibria for 2-person games? Jan12 awarded ● Enlightened Jan11 awarded ● Nice Answer Jan11 accepted Reconstructing the argument that yields Graham’s number Jan11 answered Reconstructing the argument that yields Graham’s number Jan9 awarded ● Nice Answer Jan8 accepted Meaning of a phrase from “The algebra of grand unified theories”. Jan8 revised Meaning of a phrase from “The algebra of grand unified theories”.deleted 1 characters in body; deleted 1 characters in body Jan8 answered Meaning of a phrase from “The algebra of grand unified theories”. Jan7 answered Characterising categories of vector spaces