En Passant VI

Posted on October 29, 2019 by Persiflage

I just learnt (from a comment on this blog) that Pierre Colmez hosts a wonderful page on Fontaine and Wintenberger here. I particularly recommend reading both the personal recollections of their friends and collaborators (sample quote from Mark: These \(p\)-adic Hodge theorists seemed to me like an order of monks, who were able to reveal the hidden design of a tapestry by examining it one thread at a time), as well as this article by Colmez which gives a beautiful introduction to Fontaine’s work (rather than my own somewhat superficial summary).

One can’t mention the early work of Fontaine in \(p\)-adic Hodge theory without also mentioning the recent passing of John Tate (my mathematical grandfather). Tate’s enormous contributions to mathematics are very well-known by readers of this blog, many of whom certainly knew him personally much better than me. I first met him at the 2000 Arizona Winter School, where there was an impromptu celebration for his 75th birthday. We crossed paths a few times since then, chatting about a number of things from \(p\)-adic modular forms to smoked trout (his wife made a particularly tasty version of the latter for some Harvard holiday party). I last saw him at the banquet for Barry’s 80th birthday when he called out my name in a friendly way to say hello, and I felt the flutter of satisfaction that comes when one of your idols remembers who you are. Instead of trying to write a summary of his work, however, let me instead recommend (again) that you purchase for yourself a copy of the Serre-Tate correspondence, also discussed previously on this blog.

Posted in Mathematics | Tagged , , , , , , | Leave a comment

Appropriate Citations

Posted on October 27, 2019 by Persiflage

Once I wrote a paper (two, in fact) on even Galois representations. The second paper in particular proved what I thought was a fairly definitive result ruling out the existence of a wide class of even de Rham representations with distinct Hodge-Tate weights. It turns out that almost nobody seems to cite these results, probably because they aren’t particularly useful — at least in any obvious sense. On the other hand, almost everyone who does cite the paper seems to cite it for a specific proposition (3.2) which is an easy consequence of the results of Moret-Bailly. The proposition, more or less, is a potential inverse Galois problem with (any finite collection) of local conditions. The main application of such a proposition (both in my paper and in papers which cite it) is that, given a local mod-\(p\) representation which looks like it could come (say) from the localization of a global representation associated to an automorphic form, the proposition often allows one to produce such a form at the cost of making a finite totally real extension in which \(p\) splits completely. This suffices for many purposes.

It turns out, however, that the lemma (pretty much in an equivalent form by an equivalent argument) was already proved by Moret-Bailly himself in this paper. This means that if you cite my paper for this particular lemma, you should definitely cite the paper of Moret-Bailly. Of course, if you are also applying it in a context similar to my paper (say in order to construct automorphic forms with certain local properties), you should certainly feel free to continue to cite my paper as well.

Posted in Mathematics | Tagged , , | Leave a comment

A homework exercise for Oaxaca

Posted on October 12, 2019 by Persiflage

Here’s a homework problem for those coming to Oaxaca who have a facility for working with Breuil-Kisin modules and finite flat group schemes. Let \(\mathbf{F}\) be a finite field of characteristic \(p\), and consider a Galois representation:

\(\rho: G_{\mathbf{Q}_p} \rightarrow \mathbf{GL}_2(\mathbf{F}).\)

which (one should imagine) is the local restriction of a global representation coming from a modular form. By a standard global argument, one can find a congruent form in weight \(2\), and thus a lift to a representation which is de Rham with Hodge-Tate weights \([0,1]\). For almost all such representations one can ensure that lift is potentially crystalline and hence comes from a representation which is potentially Barsotti-Tate. An immediate consequence is that the representation \(\rho\) itself is — after restriction to some finite extension \(K\) — the generic fibre of a finite flat group scheme. Without any other conditions this is obvious, since one can take \(K\) to be the splitting field of \(\rho\). However, the global argument gives a further restriction that one can take \(K/\mathbf{Q}_p\) Galois with the property that, for some \(2\)-dimensional representation \(V_K\) lifting the restriction of \(\rho\) to \(G_K\), there is a representation:

\( \varrho: \Gamma:=\mathrm{Gal}(K/\mathbf{Q}_p) \rightarrow \mathrm{GL}(D_{\mathrm{cris}}(V_K)) \rightarrow \mathrm{GL}_2(\overline{\mathbf{Q}}_p) \)

which is faithful on the inertia subgroup. In particular, this forces \(\Gamma\) and \(K\) to be “small” in some sense. One can prove this result directly without recourse to any global arguments. For example, consider the case when \(\rho\) is reducible, and, if the ratio of characters is cyclotomic, then additionally assume the extension is not très ramifée. In this case, I claim that one can take \(K\) to be the (unramified extension) of \(\mathbf{Q}_p(\zeta_p)\) which contains the fixed field of the characters on the diagonal. The restriction of \(\rho\) to \(K\) is then the extension of the generic fibre of the trivial group scheme by the multiplicative group scheme. But our assumptions imply that the Kummer extension that arises will come from the pth power of a unit and hence come from a finite flat group scheme over \(K\). The (abelian) group \(\mathrm{Gal}(K/\mathbf{Q}_p)\) has no problem admitting a representation of small dimension which is faithful on inertia.

When \(n = 3\), the automorphic picture would suggest that one can find de Rham lifts with Hodge-Tate weights \([0,1,2]\), and this is the type of thing that I guess one knows now in full generality by Emerton-Gee (but probably earlier in this case). But suppose we are still interested in whether there exist lifts of \(\rho\) which are potentially Barsotti-Tate. We can ask the weaker question: does \(\rho\) come (after restriction to \(K\)) from the generic fibre of a finite flat group scheme for a Galois extension \(K/\mathbf{Q}_p\) which admits a representation:

\( \varrho: \Gamma:=\mathrm{Gal}(K/\mathbf{Q}_p) \rightarrow \mathrm{GL}_3(\overline{\mathbf{Q}}_p) \)

which is faithful on inertia? This seems like a question which one should be able to answer. In particular, suppose that \(\rho\) is some representation with upper-triangular image. It seems possible that if \(K/\mathbf{Q}_p\) is any extension such that \(\rho\) is the generic fibre of a finite flat group scheme over \(K\) then \(K\) might be “too big” to admit such a \(\varrho\). If that were true, this would give a direct proof that \(\rho\) does not admit lift which are potentially crystalline with Hodge-Tate weights \([0,0,1]\), which would (essentially) answer the final question in this post. (I say “essentially” because one should also consider potentially semistable lifts as well. Certainly one should be able to address this by similar methods, but for now, perhaps just assume that the ratio of any two consecutive characters occurring in \(\rho\) is not cyclotomic.)

This seems to be an eminently answerable question to someone who knows what they are doing, and there are certainly some experts in this sort of computation who will be in Oaxaca in a few weeks time. So maybe one of you can work out the answer (calling the Hawk!).

Posted in Mathematics | Tagged , , , , , , | 3 Comments

Read my NSF proposal

Posted on October 9, 2019 by Persiflage

Since this is NSF season, I took the opportunity to go back and look at some of my old proposals. I am definitely too shy to put my *most recent* proposal online, but I thought it might be interesting to share the very first proposal I ever submitted back in 2006. You can find it here. Honestly, it’s not as bad as I might have imagined. Here are some first impressions:

  • The first thing that strikes me is that there is no “results from prior support section.” In particular, there is a pretty limited discussion of my previous work. It looks like I don’t even try to name drop my paper with Matt in Inventiones which I had been recently accepted before writing this grant; how virtuous.
  • I attribute a theorem to “Taylor” which is really a theorem of Taylor and Harris-Soudry-Tayor. Sorry Michael! (I do reference [HST] later on in the proposal.)
  • What is claimed in Theorem 3 is not entirely accurate — this was later fixed by my student Vlad Serban in this paper.
  • It’s less than the full 15 pages — Possibly this is an incomplete draft?
  • Already in 2006, I had started thinking about the modularity of elliptic curves over imaginary quadratic fields. Many ideas are missing. There is at least one reasonable idea here, however, namely, that if one can prove that the “half” Hida families (taking limits for one prime above \(p = \pi \pi’\) but not the other) are flat over \(\mathbf{Z}_p)\), then one is effectively in an \(\ell_0 = 0\) situation. Of course, even today, nobody has any idea how to prove this flatness. The problem is that one can sometimes show that it is pure of co-dimension one over the Iwasawa ring, but then one has to deal with a \(\mu\)-invariant type question proving that the support over \(\Lambda\) does not contain \((p)\). GB and I occasionally discussed whether it was reasonable even to conjecture this. I think I am more bullish that it should always be flat, but the question remains open.
  • Using poles of (as yet unconstructed) \(p\)-adic L-functions to prove lifting criteria from smaller groups is a great idea! I’m sure I discussed this with Matt. If you don’t want to find it in the PDF, here is the basic idea. Given an autormophic form \(\pi\), Langlands explains how (morally) to determine whether it arises via functoriality from a smaller group by considering \(L(\pi,\rho,s)\) for every representation \(\rho\) and determining the order of vanishing (or the order of poles) of this L-function at \(s=1\). This is the automorphic analog of the group theoretic fact that one can determine a representation \(V\) of a group \(G\) by knowing not only the dimension of the invariant subspace of \(V\) but also of \(S(V)\) for every Schur functor applied to \(V\). Actually, it’s more than just an analogy, since both are just consequences of the Tannakian formalism (which only conjecturally applies to automorphic forms). For example, a completely concrete example of this is that a cuspidal \(\pi\) for \(\mathrm{GSp}(4)\) should arise as an induction from \(\mathrm{GL}(2)/F\) for a quadratic extension \(F\) if and only if \(L(\pi \otimes \chi,\rho,s)\) has a pole at \(s=1\) where \(\rho\) is the standard 5-dimensional representation and \(\chi\) is the quadratic character of \(F\). I believe this is even a theorem in this case. The point made in the proposal is that this formalism should apply equally to ordinary Siegel modular forms of non-classical weight, where the consequence of course is the weaker claim that \(\pi\) comes via induction from a non-classical ordinary form \(\varpi\) for \(\mathrm{GL}(2)\). Here is a nice example which suggests that this picture is consistent. Start with a classical ordinary \(\varpi\) for \(\mathrm{GL}(2)\) over an imaginary quadratic field (with some Galois invariance condition on the central character). After inducing, we obtain an ordinary Siegel modular form \(\pi\) such that \(L(\pi \otimes \chi,\rho,s)\) has a pole. This should also be true more or less for the \(p\)-adic L-function, defined correctly. But now as we vary \(\pi\) over the ordinary family, the locus where the \(p\)-adic L-function has a pole should have codimension one. Thus the philosophy predicts a one-dimensional family of ordinary deformations of \(\varpi\). And this is indeed something that Hida proved. But everything we know strongly suggests that this will be a non-classical family in general, so this lifting criterion is something that is really completely different from the classical analog. It also suggests and even partially implies corresponding results for lifting torsion classes as well. I think that this project is definitely something worth pursuing, but I’ve never learnt enough about \(p\)-adic L-functions to do so. Whenever I have talked to someone who has constructed such functions, they are always working in some context where normalizations have been made to ensure that the L-functions are Iwasawa functions and certainly don’t have poles. Anyway, I think this remains the most attractive open problem in this proposal.
  • Question 2 has been answered (and much more) by Ian Agol. Agol (et. al.) pretty much put an end to the cottage industry of using number theory to answer various special cases of these Thurston conjectures. Interesting problems still remain, of course.
  • I haven’t had anything really interesting to say about the geometry of the Eigencurve since writing this proposal. But Hansheng Diao and Ruochuan Liu did end up proving that the Eigencurve is indeed proper in this paper.
  • I redacted some stuff! There’s an idea in this proposal that I might want to give to a graduate student — so I blacked it out (no peeking using secret technologies)
  • The broader impact section suffers from the fact that this was my first year as a tenure track assistant professor. But the panel understands that there is only so much you can do at this point. The more senior you are, the more you should be doing.

In the end, I think this was not a bad proposal from a young researcher. There are some good ideas and some good problems. Probably the part on the geometry of the eigencurve is the weakest bit, and that is not unrelated to the fact that I stopped thinking about these types of questions. I think I accomplished less of what I set out to do than for some of my more recent proposals. This is not entirely surprising from looking at the proposal — a (forgivable) weakness is that it’s somewhat speculative and optimistic. What did I end up doing instead? Probably my most interesting result in the next cycle was my result with Matt on bounds for spaces of tempered automorphic forms using completed cohomology. This proposal was (in the end) funded — I think I certainly must have benefited from the fact that panels look generously on proposals from people within 5 years (or is it six?) from their PhD (“early career researchers”).

Posted in Mathematics | Tagged , , , , , , , , , , , , , , | 3 Comments

I asked… and you responded!

Posted on September 30, 2019 by Persiflage

I often ask mathematical questions on this blog that I don’t know how to answer. Sometimes my smart readers are able to answer the questions I ask. Surely they deserve some recognition for this? Here are two such occasions which come to mind (one very recent):

In this post, I asked whether there are infinitely many integers \(n\) such that all the odd divisors of \((n^2 + 1)\) *not* of the form \(1 \bmod 2^m\) for large enough fixed \(m\), and asked whether that was an open problem. The answer: it was then, but no longer! It has now been answered by Soundararajan and Brüdern in Theorem 4 of this preprint. Problem solved!

In this post, I was looking at tables of George Schaeffer at non-liftable weight 1 modular forms of level \(\Gamma_1(N)\) for various quadratic characters, and noting that often there were forms with large prime factors. I said:

I said “However, something peculiar happens in the range of the tables, namely, there is not a single example with \(N\) prime. This leads to the (incredibly) vague question: can this be predicted in advance?”

But later GB pointed out to me that when \(N\) is not prime, and the corresponding quadratic character (in the tables) is not divisible by a prime \(q\), then the Galois representation at the auxiliary prime \(q\) need not be unramified (it can be of Steinberg type) and the corresponding Galois representations can have have significantly larger root discriminant — the ramification index at those primes is \(e_q = \ell\) for the residue characteristic \(\ell\) rather than \(e_q = 2\). And indeed, looking more closely at the tables, most of the big primes \(\ell\) for which there exist non-liftable forms of level \((N,\chi)\) occur when the conductor of \(\chi\) strictly smaller than \(N\).

Posted in Mathematics | Tagged , , , , | Leave a comment

Hausdorff Trimester Summer School, May 11-15, 2020

Posted on September 26, 2019 by Persiflage

This post is to encourage both PhD students and any junior researchers who are interested to consider applying to a summer school on the arithmetic of the Langlands Program. (Some financial support will be available.) This is the first event of the Haussdorff Trimester mentioned previously on this blog. A great lineup of speakers has agreed to give courses, namely:

  • Arthur-Cesar le Bras and Gabriel Dospinescu on p-adic geometry,
  • George Boxer and Vincent Pilloni on Higher Hida theory,
  • Patrick Allen and James Newton on Automorphy lifting,
  • Eva Viehmann and Cong Xue on Shtukas,
  • Sophie Morel and Timo Richarz on Geometric Satake.

It’s worth noting that little to no expositional material exists for many of these of these topics, so this is a rare opportunity to learn about recent developments from a group of exceptional speakers. The online application is here. The default academic status on that link appears to be that you are a full professor who obtained their PhD in 1965, but I assure you that is not the target audience!

Posted in Mathematics | Tagged , , , , , , , , , , , , , , | 9 Comments

NSF Application Tips: LaTeX edition

Posted on September 6, 2019 by Persiflage

I’ve previously written about applying for an NSF grant here. But for those applying this year, I have a few further technical tips concerning the technical specifications of your LaTeX document. If you are the type of person who uploads all their files at the last moment (not me), then you could be in for a rude shock if you haven’t written your proposal up to code — rules are being checked by computer and are much more stringent this year.

The first requirement is that the various subject headings “Intellectual Merit,” “Broader Impacts,” etc. need to be on separate lines and without any further characters. If you make some error (say write “Broader Impact”) your file will not be accepted and you won’t be able to submit it. (You will get an error message.) Of course, these things are easy to fix. There were, however, a few other problems which stumped me for a while.

The margins cannot exceed the allowed specifications. In particular, if your document has page numbers, the machine will interpret your file as extending too far in the lower margin. Hence you need to manually remove the pagination. This can be done, for example, by including \pagenumbering{gobble} in the preamble.

As for the left and right margins, at least 1 inch margins are required. You might think this is easy to enough to ensure by including (for example) the command

\usepackage[margin=1in]{geometry}

However, that didn’t work for me. I *could* fix it temporarily by extending the margins slightly further, but that had the problem of making the proposal too long. For me, fitting my proposal into the 15 allowable pages is pretty much like trying to write a tweet: make a draft, then find it is way too long, and then painfully eliminate unnecessary sentences until it *just* fits. The difference, of course, is that it’s worse than a tweet — at least a tweet is very transparent as to the allowable number of characters; LaTeX is completely mysterious (to me) in its algorithm for spacing and paging, so I end up do a lot of back and forth editing paragraphs by making minor word changes so that they end precisely at the right margins (instead of wasting almost an entire line by dribbling a few words onto the next line). Then, of course, there are those times when your document is three lines too long and so you savagely cut three lines from your beautiful introduction only to find that it is still exactly three lines too long. All of this is to say that extending the margin to 1.1 inches was not an acceptable option for me. So the algorithm was to do a binary search (try uploading the first half of the proposal, then the second quarter, etc.) until I found the offending section of the file. The left margin issue was ultimately caused by an enumerate environment where I had used the following construction:

\item[{\bf Coherent]}

LaTeX had automatically adjusted the location of the word Coherent slightly into the left margin space, which was making the NSF system decide that my entire proposal was unacceptable. This was fixable by adjusting the enumerate environment thus:

\begin{enumerate} [leftmargin=2cm]

The right errors could ultimately be resolved by addressing all the “badness” in the output file. (For example, I had used a few \mbox commands to squeeze things onto a line and that came back to bite me.)

At this point, the file could be uploaded, but I it was still generating severe warnings about fonts, namely:

• Your file contains font type(s) that are not supported. For details about font types currently supported in the system, please refer to the Proposal Preparation Document Upload FAQs. NSF may return a proposal without review if it includes font types other than those specified in the Proposal Preparation Site Document Upload FAQs.
• Your file contains font size(s) that are not supported. For details about font sizes currently supported in the system, please refer to the Proposal Preparation Document Upload FAQs. NSF may return a proposal without review if it includes font sizes other than those specified in the Proposal Preparation Site Document Upload FAQs.

Returning again to the binary divide and conquer method, the first problem was isolated to the use of the LaTeX symbol \boxtimes. The second I never completely work out but at least determined that

\sum_{n=0}^{\infty} \frac{q^{n^2}}{(q)_n}

(which comes out to)

$$\displaystyle{\sum_{n=0}^{\infty} \frac{q^{n^2}}{(q)_n}}$$

caused an error (the thought is that the subscripts are being identified as too small a font). Now these were only warnings and did not necessarily mean there was going to be any actual issues with submission, but just in case, I emailed NSF technical support, who after five days eventually got back to me with the following:

Thank you for contacting the Fastlane Helpdesk. Regular document text needs to follow the font and font size requirements specified on https://www.nsf.gov/pubs/policydocs/pappg19_1/pappg_2.jsp#IIB2. The formulas aren’t restricted by these requirements (including inline formulas). Formulas that trigger the warning messages can be ignored as only some latex formats are currently supported.

This response is honestly not that useful given that the error message doesn’t indicate where in the file the problem is — perhaps the use of \boxtimes earlier on is acceptable whereas the fact that the entire Broader Impacts section is written in Zapf Dingbats is not?

Posted in Mathematics, Uncategorized | Tagged , , , | 12 Comments

Administrative Note

Posted on September 5, 2019 by Persiflage

Ideally nobody will really notice, but this blog has moved from www.galoisrepresentations.wordpress.com to www.galoisrepresentations.com. This blog still runs on the (open source) wordpress system, the only difference is that it is longer hosted by wordpress. The reason for hosting this blog elsewhere is that I now have access to plugins without having to buy a very expensive business plan from wordpress. And the particular plugin that I have been wanting to use is \(\LaTeX\). There was LaTeX functionality previously built in, but it was pretty poorly integrated and looked pretty bad.

The old blog automatically links to here, and should do so for quite some time, but if you are fastidious about this matters you might want to update your links (if you have any). This new blog should have all the old posts and the LaTeX rendering should be improved on those old posts as well. I *think* that followers of this blog will automatically be subscribed to the new location, but I guess we (or you) will find out.

There may be one or two teething problems, so please leave a comment here if something doesn’t seem to be working or you notice something is broken.

Posted in Uncategorized | Tagged , , | 8 Comments

Arbeitsgemeinschaft 2020

Posted on August 17, 2019 by Persiflage

The April 2020 Oberwolfach Arbeitsgemeinschaft will be on derived Galois deformation rings and the cohomology of arithmetic groups!

For those who don’t know, the Arbeitsgemeinschaft (“study group”) is different from usual Oberwolfach workshops (or workshops more generally) — the idea is that the participants learn the material and then teach it to each other. I have never actually been to one (please leave a comment on your experience if you have), so I’m not sure that I can describe it better than reproducing the official blurb here:

The Arbeitsgemeinschaften mainly address to non-specialists who want to broaden their outlook on mathematics and to junior researchers who wish to enter a field for future research. Experts are also welcome. The idea is “learning by doing” – similar to the Seminaire Bourbaki. Participants have to volunteer for one of the lectures described in the program of the Arbeitsgemeinschaft. After the deadline for application the organizers choose the actual speakers to give them enough time to understand the subject and to prepare for their lectures.

If you are interested in learning this material, please consider applying! There is currently an ambitious mix of material from the cohomology of arithmetic groups to the Taylor-Wiles method to to derived deformation rings. The expectation is certainly that you are not an expert on all of these topics. (The precise emphasis of the workshop will naturally depend on the exact mix of participants.) Click here to see an outline of how we have conceived what the lectures might be. When you apply, you can choose which lecture you (might be) prepared to give, assuming you are given enough advanced warning! All the links you might need (for applying and other information) can be found here:

2020 Arbeitsgemeinschaft: Derived Galois Deformation Rings and Cohomology of Arithmetic Groups

Note that the timing of this workshop is planned to immediately precede the
Hausdorff Trimester in Bonn of which I have mentioned previously and will give more information about in an upcoming post. Consider going to both!

update: It was pointed out to me that April 4 does not immediately precede May 4 in any reasonable sense of the word.

Posted in Mathematics | Tagged , , , , , , | 1 Comment

Mathematische Zeitschrift (Part II: for authors)

Posted on August 5, 2019 by Persiflage

In this post, I give some tips for authors considering submitting to Math Zeitschrift, especially a paper in algebraic number theory. The first suggestion is to read Part I. This should give you a good sense of the standards required. (Of course, it’s always hard to judge your own work without bias.) I do, however, have a few more specific tips for authors:

Submit the paper to the journal rather than email me directly: It’s certainly not a faux pas to send it to me directly, it’s just that it’s easier for me for various administrative reasons if you send the paper through the official channels. (I have a remark to that effect here but perhaps people find my email address directly though the editorial board listings.) There are two associate editors besides myself who deal with number theory papers at Math Zeit: Philippe Michel and Dipendra Prasad. Most of the time it will be clear which editor should be assigned what paper, but I believe you can also make a suggestion for which editor is appropriate when submitting. We can and do swap papers around if we believe another editor is more qualified to handle the paper.

Please don’t ask me before submitting if you think a paper is “of the right level” to submit to Math Zeit: Again this is not an unreasonable question, it’s just that it puts me in an awkward situation — if I say “yes,” then I will feel guilty if the paper is ultimately rejected, so I will usually just explain that as a matter of policy I refrain from giving any such opinions. If there is any situation in which I feel some conflict of interest with regard to a paper, I will usually ask Dipendra to take over (I think I have only done that once).

Don’t suggest a “suitable referee” unless you are doing so as a bluff and don’t want me to choose that person … except maybe I will call your bluff … unless maybe it is a double bluff!

Please don’t complain if your paper is rejected. It really isn’t doing you any favors. There is some cause for complaint if your paper gets rejected after six months without any indication that it’s been read, but that doesn’t happen with the papers I reject.

How long should I wait before asking about the “status” of my article? If you ask me what the status of your article is, the answer is always going to be the same: “the paper is under review.” What other possible answer were you expecting? Perhaps: “the paper has just received a glorious review which is currently sitting on my desk; since your email has just arrived that gives me a convenient reason to write back straight away and accept the paper without further revision.” Of course the real question you want to ask is something like “have you forgotten about the paper” or “can you ask the referee to hurry up.” The reality is that with some journals and editors such reminders are actually necessary. But not with me — I am organized and on top of my editorial duties, and I schedule automatic reminders to reviewers noting them of their previous commitments to review by a certain date. In particular, such emails will make absolutely no difference to how quickly your paper is being refereed, and in the future when I receive such emails I will just send a link to this post. At least when you read this, you will (by looking at the previous post as well) be informed of the rough time scale at which the journal is operating. Even though I find this question mildly annoying, I cannot fault the authors at all for asking such a question, so you certainly shouldn’t feel any need to apologize. After all, how are you to know how responsible I really am? I do think, however, that many of these emails stem from the naivety of youth — when you are a grizzled veteran you will have more experience with how long a referee process usually ends up taking. Even for other journals, I generally don’t recommend sending such an email before a year. After all, if after your email the editor finds that your paper has been under the couch cushions for 11 months, I think that actually increases your chances of an acceptance, because the editor’s resulting guilt may induce them to be somewhat more favorably inclined towards your paper.

I have to admit (surprising though I’m sure this will be to regular readers) that I myself are not immune to mild frustration with journals, especially those for whom the evidence is considerable that the delinquencies in handling my paper may be due to editorial mismanagement. I very nearly wrote a blog post entitled “DUKE HOSTAGE CRISIS DAY NINE HUNDRED” documenting one of my recent experiences, but Richard Hain was apparently brought on board to tidy ship at the last moment and the situation was resolved a cool 54 days short of the intended posting date.

All that said, there is one context in which such an email may make a difference. If one of the authors is just about to go on the job market, then I do feel inclined (if possible) to make what ever efforts I can to expedite the process whenever that is reasonable. Actually I make such efforts unilaterally with younger people I have reason to believe may be applying for jobs (it doesn’t always work, of course).

When you get a referee report, please don’t rush to revise it as quickly as possible. It is exciting to get a report which indicates that your paper has a good chance of being published. There’s a temptation to rush through the referee report as quickly as possible addressing to the minimal extent the complains and sending it back immediately. You will do yourself (and everyone else) a favor by reflecting a little bit more both on what the referee says and on the paper itself. You probably spent a long time writing the paper; but it most likely has been a while since you looked at it and so the time when you get a referee report back is an excellent opportunity to return to the paper with fresh eyes and see how it can be improved. It’s true that referees often request pretty annoying things, but definitely sometimes those suggestions are good ones and should be taken seriously. Note that it is always a good idea to include in your resubmission a file indicating exactly how you responded to the referees comments.

Why should I submit to Math. Zeit. rather than other “similar” journals? How does one go about choosing a journal? It’s always been a tough question. I think that one reason to submit to a journal is that you come across interesting papers which are published in said journal. So take a look at the number theory papers published there recently and then think about submitting. I think that Math Zeit has some great papers and I’m happy with the papers that I get to accept. For example, during my tenure, I think there have been quite a few quality papers on Shimura varieties. I suspect that accepting one quality paper in subfield X often begets another submission by people in the same field. (In order to leverage that as an editor, of course, one then has to increase the standards of the journal in that particular subdiscipline.)

Have you made any blunders as an editor? There have definitely been one or two papers which were rejected but which I later came to think should have been accepted. At least the one paper in particular I am thinking of ended up in a nice home, so all’s well that ends well.

Posted in Mathematics | Tagged , , , , , , , | 4 Comments