Is the field of q-series 'dead'? [closed]












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I had a discussion with my advisor about what am I interested as my future research direction and I said it is special functions and q-series. He laughed and said that the topic is essentially dead and the people who study it are dinosaurs. I'm really confused by this statement and don't know what to think. Is this area really dead and not worth pursuing a research in it?










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$endgroup$




closed as primarily opinion-based by András Bátkai, YCor, LSpice, Igor Pak, Ben McKay May 27 at 13:18


Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.















  • 13




    $begingroup$
    @Ycor The advior said this in public meeting of undergraduate students with the research staff.
    $endgroup$
    – Tyrell
    May 23 at 11:11






  • 6




    $begingroup$
    Anyway it was addressed to a few undergrads and I'm not sure it is very useful to overspread, apart from being offensive to possible people working on it. It's an advisor's responsibility not to send students in active areas, and they do it according to their own knowledge and possibly bias. I remember having been told to avoid some directions before PhD and this turned out, I think, to be good advice, and also heard that some directions are dead, which turned out to be false. It makes sense to ask other people as you do here about research in these directions, without copying all this.
    $endgroup$
    – YCor
    May 23 at 11:31






  • 21




    $begingroup$
    @YCor: There being no -1 for comments, I'm recording one here. Academic conversations are not commonly understood to be Deep Background, at least not where I am. Second opinions are almost always worth getting when considering research subjects to choose. MathOverflow is as good as any other place for getting these second opinions, and may be the most accessible one (the OP isn't necessarily at a major university and even then may be too shy to ask a question like this).
    $endgroup$
    – darij grinberg
    May 23 at 13:14






  • 9




    $begingroup$
    @YCor: I'm not sure I got your "as" right, but the tenor of your comment still seems to be that you are admonishing the OP for going public. And I just don't agree with that.
    $endgroup$
    – darij grinberg
    May 23 at 13:21






  • 3




    $begingroup$
    @darijgrinberg we indeed disagree on this. This was not considered as offensive towards the OP (and the OP doesn't claim this). Also I don't blame public accusation of the advisor, since it's anonymous. All the benefit I see from this is an anonymous depreciation of some field, and this can be offensive to people working in this field.
    $endgroup$
    – YCor
    May 23 at 13:29
















25












$begingroup$


I had a discussion with my advisor about what am I interested as my future research direction and I said it is special functions and q-series. He laughed and said that the topic is essentially dead and the people who study it are dinosaurs. I'm really confused by this statement and don't know what to think. Is this area really dead and not worth pursuing a research in it?










share|cite|improve this question









$endgroup$




closed as primarily opinion-based by András Bátkai, YCor, LSpice, Igor Pak, Ben McKay May 27 at 13:18


Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.















  • 13




    $begingroup$
    @Ycor The advior said this in public meeting of undergraduate students with the research staff.
    $endgroup$
    – Tyrell
    May 23 at 11:11






  • 6




    $begingroup$
    Anyway it was addressed to a few undergrads and I'm not sure it is very useful to overspread, apart from being offensive to possible people working on it. It's an advisor's responsibility not to send students in active areas, and they do it according to their own knowledge and possibly bias. I remember having been told to avoid some directions before PhD and this turned out, I think, to be good advice, and also heard that some directions are dead, which turned out to be false. It makes sense to ask other people as you do here about research in these directions, without copying all this.
    $endgroup$
    – YCor
    May 23 at 11:31






  • 21




    $begingroup$
    @YCor: There being no -1 for comments, I'm recording one here. Academic conversations are not commonly understood to be Deep Background, at least not where I am. Second opinions are almost always worth getting when considering research subjects to choose. MathOverflow is as good as any other place for getting these second opinions, and may be the most accessible one (the OP isn't necessarily at a major university and even then may be too shy to ask a question like this).
    $endgroup$
    – darij grinberg
    May 23 at 13:14






  • 9




    $begingroup$
    @YCor: I'm not sure I got your "as" right, but the tenor of your comment still seems to be that you are admonishing the OP for going public. And I just don't agree with that.
    $endgroup$
    – darij grinberg
    May 23 at 13:21






  • 3




    $begingroup$
    @darijgrinberg we indeed disagree on this. This was not considered as offensive towards the OP (and the OP doesn't claim this). Also I don't blame public accusation of the advisor, since it's anonymous. All the benefit I see from this is an anonymous depreciation of some field, and this can be offensive to people working in this field.
    $endgroup$
    – YCor
    May 23 at 13:29














25












25








25


3



$begingroup$


I had a discussion with my advisor about what am I interested as my future research direction and I said it is special functions and q-series. He laughed and said that the topic is essentially dead and the people who study it are dinosaurs. I'm really confused by this statement and don't know what to think. Is this area really dead and not worth pursuing a research in it?










share|cite|improve this question









$endgroup$




I had a discussion with my advisor about what am I interested as my future research direction and I said it is special functions and q-series. He laughed and said that the topic is essentially dead and the people who study it are dinosaurs. I'm really confused by this statement and don't know what to think. Is this area really dead and not worth pursuing a research in it?







soft-question gm.general-mathematics applied-mathematics advice research






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asked May 23 at 10:16









TyrellTyrell

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2673 silver badges5 bronze badges





closed as primarily opinion-based by András Bátkai, YCor, LSpice, Igor Pak, Ben McKay May 27 at 13:18


Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.











closed as primarily opinion-based by András Bátkai, YCor, LSpice, Igor Pak, Ben McKay May 27 at 13:18


Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.









closed as primarily opinion-based by András Bátkai, YCor, LSpice, Igor Pak, Ben McKay May 27 at 13:18


Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.










  • 13




    $begingroup$
    @Ycor The advior said this in public meeting of undergraduate students with the research staff.
    $endgroup$
    – Tyrell
    May 23 at 11:11






  • 6




    $begingroup$
    Anyway it was addressed to a few undergrads and I'm not sure it is very useful to overspread, apart from being offensive to possible people working on it. It's an advisor's responsibility not to send students in active areas, and they do it according to their own knowledge and possibly bias. I remember having been told to avoid some directions before PhD and this turned out, I think, to be good advice, and also heard that some directions are dead, which turned out to be false. It makes sense to ask other people as you do here about research in these directions, without copying all this.
    $endgroup$
    – YCor
    May 23 at 11:31






  • 21




    $begingroup$
    @YCor: There being no -1 for comments, I'm recording one here. Academic conversations are not commonly understood to be Deep Background, at least not where I am. Second opinions are almost always worth getting when considering research subjects to choose. MathOverflow is as good as any other place for getting these second opinions, and may be the most accessible one (the OP isn't necessarily at a major university and even then may be too shy to ask a question like this).
    $endgroup$
    – darij grinberg
    May 23 at 13:14






  • 9




    $begingroup$
    @YCor: I'm not sure I got your "as" right, but the tenor of your comment still seems to be that you are admonishing the OP for going public. And I just don't agree with that.
    $endgroup$
    – darij grinberg
    May 23 at 13:21






  • 3




    $begingroup$
    @darijgrinberg we indeed disagree on this. This was not considered as offensive towards the OP (and the OP doesn't claim this). Also I don't blame public accusation of the advisor, since it's anonymous. All the benefit I see from this is an anonymous depreciation of some field, and this can be offensive to people working in this field.
    $endgroup$
    – YCor
    May 23 at 13:29














  • 13




    $begingroup$
    @Ycor The advior said this in public meeting of undergraduate students with the research staff.
    $endgroup$
    – Tyrell
    May 23 at 11:11






  • 6




    $begingroup$
    Anyway it was addressed to a few undergrads and I'm not sure it is very useful to overspread, apart from being offensive to possible people working on it. It's an advisor's responsibility not to send students in active areas, and they do it according to their own knowledge and possibly bias. I remember having been told to avoid some directions before PhD and this turned out, I think, to be good advice, and also heard that some directions are dead, which turned out to be false. It makes sense to ask other people as you do here about research in these directions, without copying all this.
    $endgroup$
    – YCor
    May 23 at 11:31






  • 21




    $begingroup$
    @YCor: There being no -1 for comments, I'm recording one here. Academic conversations are not commonly understood to be Deep Background, at least not where I am. Second opinions are almost always worth getting when considering research subjects to choose. MathOverflow is as good as any other place for getting these second opinions, and may be the most accessible one (the OP isn't necessarily at a major university and even then may be too shy to ask a question like this).
    $endgroup$
    – darij grinberg
    May 23 at 13:14






  • 9




    $begingroup$
    @YCor: I'm not sure I got your "as" right, but the tenor of your comment still seems to be that you are admonishing the OP for going public. And I just don't agree with that.
    $endgroup$
    – darij grinberg
    May 23 at 13:21






  • 3




    $begingroup$
    @darijgrinberg we indeed disagree on this. This was not considered as offensive towards the OP (and the OP doesn't claim this). Also I don't blame public accusation of the advisor, since it's anonymous. All the benefit I see from this is an anonymous depreciation of some field, and this can be offensive to people working in this field.
    $endgroup$
    – YCor
    May 23 at 13:29








13




13




$begingroup$
@Ycor The advior said this in public meeting of undergraduate students with the research staff.
$endgroup$
– Tyrell
May 23 at 11:11




$begingroup$
@Ycor The advior said this in public meeting of undergraduate students with the research staff.
$endgroup$
– Tyrell
May 23 at 11:11




6




6




$begingroup$
Anyway it was addressed to a few undergrads and I'm not sure it is very useful to overspread, apart from being offensive to possible people working on it. It's an advisor's responsibility not to send students in active areas, and they do it according to their own knowledge and possibly bias. I remember having been told to avoid some directions before PhD and this turned out, I think, to be good advice, and also heard that some directions are dead, which turned out to be false. It makes sense to ask other people as you do here about research in these directions, without copying all this.
$endgroup$
– YCor
May 23 at 11:31




$begingroup$
Anyway it was addressed to a few undergrads and I'm not sure it is very useful to overspread, apart from being offensive to possible people working on it. It's an advisor's responsibility not to send students in active areas, and they do it according to their own knowledge and possibly bias. I remember having been told to avoid some directions before PhD and this turned out, I think, to be good advice, and also heard that some directions are dead, which turned out to be false. It makes sense to ask other people as you do here about research in these directions, without copying all this.
$endgroup$
– YCor
May 23 at 11:31




21




21




$begingroup$
@YCor: There being no -1 for comments, I'm recording one here. Academic conversations are not commonly understood to be Deep Background, at least not where I am. Second opinions are almost always worth getting when considering research subjects to choose. MathOverflow is as good as any other place for getting these second opinions, and may be the most accessible one (the OP isn't necessarily at a major university and even then may be too shy to ask a question like this).
$endgroup$
– darij grinberg
May 23 at 13:14




$begingroup$
@YCor: There being no -1 for comments, I'm recording one here. Academic conversations are not commonly understood to be Deep Background, at least not where I am. Second opinions are almost always worth getting when considering research subjects to choose. MathOverflow is as good as any other place for getting these second opinions, and may be the most accessible one (the OP isn't necessarily at a major university and even then may be too shy to ask a question like this).
$endgroup$
– darij grinberg
May 23 at 13:14




9




9




$begingroup$
@YCor: I'm not sure I got your "as" right, but the tenor of your comment still seems to be that you are admonishing the OP for going public. And I just don't agree with that.
$endgroup$
– darij grinberg
May 23 at 13:21




$begingroup$
@YCor: I'm not sure I got your "as" right, but the tenor of your comment still seems to be that you are admonishing the OP for going public. And I just don't agree with that.
$endgroup$
– darij grinberg
May 23 at 13:21




3




3




$begingroup$
@darijgrinberg we indeed disagree on this. This was not considered as offensive towards the OP (and the OP doesn't claim this). Also I don't blame public accusation of the advisor, since it's anonymous. All the benefit I see from this is an anonymous depreciation of some field, and this can be offensive to people working in this field.
$endgroup$
– YCor
May 23 at 13:29




$begingroup$
@darijgrinberg we indeed disagree on this. This was not considered as offensive towards the OP (and the OP doesn't claim this). Also I don't blame public accusation of the advisor, since it's anonymous. All the benefit I see from this is an anonymous depreciation of some field, and this can be offensive to people working in this field.
$endgroup$
– YCor
May 23 at 13:29










5 Answers
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I cannot answer the question of whether the field of $q$-series is dead. I would make this a comment, but I lack sufficient reputation.



I am a Banach space theorist, and Banach space theory is not fully dead. However, it is sufficiently unfashionable as to make it terribly difficult for me to find a job (even with a very strong research record). In fact, I have been completely unable to find employment, and I am now forced to leave academia because of it. Granted, geographical factors, personal connections, and luck may all be different for you. However, I made the mistake of choosing my research area only because of its intellectual interest to me, without any practical consideration of the job market, and I would caution you against doing the same. If your advisor says the area is dead, I would listen.



I would also say that, if you like that area, you can study it as much as you want after you find a permanent position.






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  • 7




    $begingroup$
    I was in a similar situation, if you want to discuss it please drop me a line.
    $endgroup$
    – Tomek Kania
    May 24 at 5:52



















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Jehanne Dousse has recently obtained a sought-after CNRS position. From what I remember seeing, she was inundated with job interviews. This should disprove the death of q-series, at least as far as partition-like series are concerned. Certain subfields may be worse off.



If you want to discreetly ask specific people inside the field whether the field is alive enough to support a career, a good approach seems to me to state the question positively: Ask what the most interesting currently existing questions are, what the most exciting recent work is about, etc. With some luck you may get a good research project in return :)






share|cite|improve this answer









$endgroup$















  • $begingroup$
    is it hard to get a CNRS position?
    $endgroup$
    – user140765
    May 23 at 14:19






  • 11




    $begingroup$
    @kartop_man: From what I know, yes. These are permanent positions with no teaching required!
    $endgroup$
    – darij grinberg
    May 23 at 14:24






  • 12




    $begingroup$
    @kartop_man Darij is correct, these are extremely competitive and sought after. They don't carry any teaching duty, but usually you can choose to teach a light load for an increase in salary. Moreover after 3-5 years you can ask (and are usually granted) the possibility to move to any CNRS research unit, in France or abroad. To give an idea, this year there were 11 positions in total for all of pure and applied math (+ 3 designated for applied math only). The only downside is the salary, which is slightly lower than lecturers', which is itself not competitive internationally.
    $endgroup$
    – Najib Idrissi
    May 23 at 15:34








  • 1




    $begingroup$
    @Najib I'm a CNRS researcher and the time you have to wait if you want to move to a different institution is only one year. I have a young colleague who recently did that. Plus you can change topic as soon as you have the position.
    $endgroup$
    – Ratbert
    May 23 at 20:01






  • 2




    $begingroup$
    @Ratbert You can ask every year, but do you get the permission every year? I was at a meeting for newly recruited mathematicians last month, and the vice director of the Insmi told us that 3-5 years was the "reasonable" delay (but if you have a good reason they can make exceptions).
    $endgroup$
    – Najib Idrissi
    May 24 at 9:25





















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The opinions that certain areas of mathematics are dead are frequently stated but in many cases incorrect. Some areas experience declines in activity and then revivals. Many examples can be given.



On the other hand, my recommendation to a PhD student would be: do what your adviser says. When you obtain a permanent position you will be free to pursue whatever topic you yourself find interesting. Until that time you have to take into account various things other than intrinsic interest of the topic.



Example. In the early 1980th my friend, then a graduate student, discussed with his adviser possible directions of research. The adviser himself contributed to classical complex functions theory and to holomorphic dynamics. He said that holomorphic dynamics is dead, and recommended to
work in classical function theory (the area which was not the most popular at that time either). It is almost exactly at that time (1982) when the revolution in holomorphic dynamics happened, suddenly this become one of the most fashionable area in whole mathematics, and it preserves this status to this day. But in 1960-80 the adviser was almost alone, working in holomorphic dynamics.






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  • 3




    $begingroup$
    "Many examples can be given" - maybe you could give at least one, so that the answer is more self-contained?
    $endgroup$
    – user140765
    May 23 at 18:14



















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The reports of the death of the field of $q$-series and special functions are greatly exaggerated. George Andrews wrote a book Q-Series on the subject published in 1986. He and Bruce Berndt last year completed the publication of a five volume edition about the results in Ramanujan's Lost Notebook. An important subject for Ramanujan was $q$-series and special functions. George Andrews is a former President of the AMS with many awards.



Ken Ono, the Vice President of the AMS, has done research on Rogers-Ramanujan identities, Mock theta functions, and recently he and his coworkers have proved the Umbral Moonshine Conjecture. In joint work with Jan Bruinier, he discovered a finite algebraic formula for computing partition numbers. The partition numbers are the coefficients of the reciprocal of the fundamental $q$-series $(q;q)_infty$. There are many other examples that I could cite, but this should be enough.






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    8












    $begingroup$

    I think that (properly understood) theory of $q-$series is one of the most fashionable areas of mathematics right now. One reason is the appearance of $q-$series in topology. Namely, Turaev-Viro TQFT associates to each $3-$manifold with boundary a $q-$special function, defined for $q$ being a root of unity. These functions are expected to be $q-$holonomic, so should satisfy interesting difference equations. The building block for these invariants is so-called quantum $6j-$symbol, which coincides with ${}_4F_3-$ basic hypergeometric series with general parameters at $z=1$.






    share|cite|improve this answer









    $endgroup$
























      5 Answers
      5






      active

      oldest

      votes








      5 Answers
      5






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes









      49












      $begingroup$

      I cannot answer the question of whether the field of $q$-series is dead. I would make this a comment, but I lack sufficient reputation.



      I am a Banach space theorist, and Banach space theory is not fully dead. However, it is sufficiently unfashionable as to make it terribly difficult for me to find a job (even with a very strong research record). In fact, I have been completely unable to find employment, and I am now forced to leave academia because of it. Granted, geographical factors, personal connections, and luck may all be different for you. However, I made the mistake of choosing my research area only because of its intellectual interest to me, without any practical consideration of the job market, and I would caution you against doing the same. If your advisor says the area is dead, I would listen.



      I would also say that, if you like that area, you can study it as much as you want after you find a permanent position.






      share|cite|improve this answer









      $endgroup$











      • 7




        $begingroup$
        I was in a similar situation, if you want to discuss it please drop me a line.
        $endgroup$
        – Tomek Kania
        May 24 at 5:52
















      49












      $begingroup$

      I cannot answer the question of whether the field of $q$-series is dead. I would make this a comment, but I lack sufficient reputation.



      I am a Banach space theorist, and Banach space theory is not fully dead. However, it is sufficiently unfashionable as to make it terribly difficult for me to find a job (even with a very strong research record). In fact, I have been completely unable to find employment, and I am now forced to leave academia because of it. Granted, geographical factors, personal connections, and luck may all be different for you. However, I made the mistake of choosing my research area only because of its intellectual interest to me, without any practical consideration of the job market, and I would caution you against doing the same. If your advisor says the area is dead, I would listen.



      I would also say that, if you like that area, you can study it as much as you want after you find a permanent position.






      share|cite|improve this answer









      $endgroup$











      • 7




        $begingroup$
        I was in a similar situation, if you want to discuss it please drop me a line.
        $endgroup$
        – Tomek Kania
        May 24 at 5:52














      49












      49








      49





      $begingroup$

      I cannot answer the question of whether the field of $q$-series is dead. I would make this a comment, but I lack sufficient reputation.



      I am a Banach space theorist, and Banach space theory is not fully dead. However, it is sufficiently unfashionable as to make it terribly difficult for me to find a job (even with a very strong research record). In fact, I have been completely unable to find employment, and I am now forced to leave academia because of it. Granted, geographical factors, personal connections, and luck may all be different for you. However, I made the mistake of choosing my research area only because of its intellectual interest to me, without any practical consideration of the job market, and I would caution you against doing the same. If your advisor says the area is dead, I would listen.



      I would also say that, if you like that area, you can study it as much as you want after you find a permanent position.






      share|cite|improve this answer









      $endgroup$



      I cannot answer the question of whether the field of $q$-series is dead. I would make this a comment, but I lack sufficient reputation.



      I am a Banach space theorist, and Banach space theory is not fully dead. However, it is sufficiently unfashionable as to make it terribly difficult for me to find a job (even with a very strong research record). In fact, I have been completely unable to find employment, and I am now forced to leave academia because of it. Granted, geographical factors, personal connections, and luck may all be different for you. However, I made the mistake of choosing my research area only because of its intellectual interest to me, without any practical consideration of the job market, and I would caution you against doing the same. If your advisor says the area is dead, I would listen.



      I would also say that, if you like that area, you can study it as much as you want after you find a permanent position.







      share|cite|improve this answer












      share|cite|improve this answer



      share|cite|improve this answer










      answered May 23 at 10:31







      user78375


















      • 7




        $begingroup$
        I was in a similar situation, if you want to discuss it please drop me a line.
        $endgroup$
        – Tomek Kania
        May 24 at 5:52














      • 7




        $begingroup$
        I was in a similar situation, if you want to discuss it please drop me a line.
        $endgroup$
        – Tomek Kania
        May 24 at 5:52








      7




      7




      $begingroup$
      I was in a similar situation, if you want to discuss it please drop me a line.
      $endgroup$
      – Tomek Kania
      May 24 at 5:52




      $begingroup$
      I was in a similar situation, if you want to discuss it please drop me a line.
      $endgroup$
      – Tomek Kania
      May 24 at 5:52











      21












      $begingroup$

      Jehanne Dousse has recently obtained a sought-after CNRS position. From what I remember seeing, she was inundated with job interviews. This should disprove the death of q-series, at least as far as partition-like series are concerned. Certain subfields may be worse off.



      If you want to discreetly ask specific people inside the field whether the field is alive enough to support a career, a good approach seems to me to state the question positively: Ask what the most interesting currently existing questions are, what the most exciting recent work is about, etc. With some luck you may get a good research project in return :)






      share|cite|improve this answer









      $endgroup$















      • $begingroup$
        is it hard to get a CNRS position?
        $endgroup$
        – user140765
        May 23 at 14:19






      • 11




        $begingroup$
        @kartop_man: From what I know, yes. These are permanent positions with no teaching required!
        $endgroup$
        – darij grinberg
        May 23 at 14:24






      • 12




        $begingroup$
        @kartop_man Darij is correct, these are extremely competitive and sought after. They don't carry any teaching duty, but usually you can choose to teach a light load for an increase in salary. Moreover after 3-5 years you can ask (and are usually granted) the possibility to move to any CNRS research unit, in France or abroad. To give an idea, this year there were 11 positions in total for all of pure and applied math (+ 3 designated for applied math only). The only downside is the salary, which is slightly lower than lecturers', which is itself not competitive internationally.
        $endgroup$
        – Najib Idrissi
        May 23 at 15:34








      • 1




        $begingroup$
        @Najib I'm a CNRS researcher and the time you have to wait if you want to move to a different institution is only one year. I have a young colleague who recently did that. Plus you can change topic as soon as you have the position.
        $endgroup$
        – Ratbert
        May 23 at 20:01






      • 2




        $begingroup$
        @Ratbert You can ask every year, but do you get the permission every year? I was at a meeting for newly recruited mathematicians last month, and the vice director of the Insmi told us that 3-5 years was the "reasonable" delay (but if you have a good reason they can make exceptions).
        $endgroup$
        – Najib Idrissi
        May 24 at 9:25


















      21












      $begingroup$

      Jehanne Dousse has recently obtained a sought-after CNRS position. From what I remember seeing, she was inundated with job interviews. This should disprove the death of q-series, at least as far as partition-like series are concerned. Certain subfields may be worse off.



      If you want to discreetly ask specific people inside the field whether the field is alive enough to support a career, a good approach seems to me to state the question positively: Ask what the most interesting currently existing questions are, what the most exciting recent work is about, etc. With some luck you may get a good research project in return :)






      share|cite|improve this answer









      $endgroup$















      • $begingroup$
        is it hard to get a CNRS position?
        $endgroup$
        – user140765
        May 23 at 14:19






      • 11




        $begingroup$
        @kartop_man: From what I know, yes. These are permanent positions with no teaching required!
        $endgroup$
        – darij grinberg
        May 23 at 14:24






      • 12




        $begingroup$
        @kartop_man Darij is correct, these are extremely competitive and sought after. They don't carry any teaching duty, but usually you can choose to teach a light load for an increase in salary. Moreover after 3-5 years you can ask (and are usually granted) the possibility to move to any CNRS research unit, in France or abroad. To give an idea, this year there were 11 positions in total for all of pure and applied math (+ 3 designated for applied math only). The only downside is the salary, which is slightly lower than lecturers', which is itself not competitive internationally.
        $endgroup$
        – Najib Idrissi
        May 23 at 15:34








      • 1




        $begingroup$
        @Najib I'm a CNRS researcher and the time you have to wait if you want to move to a different institution is only one year. I have a young colleague who recently did that. Plus you can change topic as soon as you have the position.
        $endgroup$
        – Ratbert
        May 23 at 20:01






      • 2




        $begingroup$
        @Ratbert You can ask every year, but do you get the permission every year? I was at a meeting for newly recruited mathematicians last month, and the vice director of the Insmi told us that 3-5 years was the "reasonable" delay (but if you have a good reason they can make exceptions).
        $endgroup$
        – Najib Idrissi
        May 24 at 9:25
















      21












      21








      21





      $begingroup$

      Jehanne Dousse has recently obtained a sought-after CNRS position. From what I remember seeing, she was inundated with job interviews. This should disprove the death of q-series, at least as far as partition-like series are concerned. Certain subfields may be worse off.



      If you want to discreetly ask specific people inside the field whether the field is alive enough to support a career, a good approach seems to me to state the question positively: Ask what the most interesting currently existing questions are, what the most exciting recent work is about, etc. With some luck you may get a good research project in return :)






      share|cite|improve this answer









      $endgroup$



      Jehanne Dousse has recently obtained a sought-after CNRS position. From what I remember seeing, she was inundated with job interviews. This should disprove the death of q-series, at least as far as partition-like series are concerned. Certain subfields may be worse off.



      If you want to discreetly ask specific people inside the field whether the field is alive enough to support a career, a good approach seems to me to state the question positively: Ask what the most interesting currently existing questions are, what the most exciting recent work is about, etc. With some luck you may get a good research project in return :)







      share|cite|improve this answer












      share|cite|improve this answer



      share|cite|improve this answer










      answered May 23 at 13:19









      darij grinbergdarij grinberg

      19.1k3 gold badges74 silver badges195 bronze badges




      19.1k3 gold badges74 silver badges195 bronze badges















      • $begingroup$
        is it hard to get a CNRS position?
        $endgroup$
        – user140765
        May 23 at 14:19






      • 11




        $begingroup$
        @kartop_man: From what I know, yes. These are permanent positions with no teaching required!
        $endgroup$
        – darij grinberg
        May 23 at 14:24






      • 12




        $begingroup$
        @kartop_man Darij is correct, these are extremely competitive and sought after. They don't carry any teaching duty, but usually you can choose to teach a light load for an increase in salary. Moreover after 3-5 years you can ask (and are usually granted) the possibility to move to any CNRS research unit, in France or abroad. To give an idea, this year there were 11 positions in total for all of pure and applied math (+ 3 designated for applied math only). The only downside is the salary, which is slightly lower than lecturers', which is itself not competitive internationally.
        $endgroup$
        – Najib Idrissi
        May 23 at 15:34








      • 1




        $begingroup$
        @Najib I'm a CNRS researcher and the time you have to wait if you want to move to a different institution is only one year. I have a young colleague who recently did that. Plus you can change topic as soon as you have the position.
        $endgroup$
        – Ratbert
        May 23 at 20:01






      • 2




        $begingroup$
        @Ratbert You can ask every year, but do you get the permission every year? I was at a meeting for newly recruited mathematicians last month, and the vice director of the Insmi told us that 3-5 years was the "reasonable" delay (but if you have a good reason they can make exceptions).
        $endgroup$
        – Najib Idrissi
        May 24 at 9:25




















      • $begingroup$
        is it hard to get a CNRS position?
        $endgroup$
        – user140765
        May 23 at 14:19






      • 11




        $begingroup$
        @kartop_man: From what I know, yes. These are permanent positions with no teaching required!
        $endgroup$
        – darij grinberg
        May 23 at 14:24






      • 12




        $begingroup$
        @kartop_man Darij is correct, these are extremely competitive and sought after. They don't carry any teaching duty, but usually you can choose to teach a light load for an increase in salary. Moreover after 3-5 years you can ask (and are usually granted) the possibility to move to any CNRS research unit, in France or abroad. To give an idea, this year there were 11 positions in total for all of pure and applied math (+ 3 designated for applied math only). The only downside is the salary, which is slightly lower than lecturers', which is itself not competitive internationally.
        $endgroup$
        – Najib Idrissi
        May 23 at 15:34








      • 1




        $begingroup$
        @Najib I'm a CNRS researcher and the time you have to wait if you want to move to a different institution is only one year. I have a young colleague who recently did that. Plus you can change topic as soon as you have the position.
        $endgroup$
        – Ratbert
        May 23 at 20:01






      • 2




        $begingroup$
        @Ratbert You can ask every year, but do you get the permission every year? I was at a meeting for newly recruited mathematicians last month, and the vice director of the Insmi told us that 3-5 years was the "reasonable" delay (but if you have a good reason they can make exceptions).
        $endgroup$
        – Najib Idrissi
        May 24 at 9:25


















      $begingroup$
      is it hard to get a CNRS position?
      $endgroup$
      – user140765
      May 23 at 14:19




      $begingroup$
      is it hard to get a CNRS position?
      $endgroup$
      – user140765
      May 23 at 14:19




      11




      11




      $begingroup$
      @kartop_man: From what I know, yes. These are permanent positions with no teaching required!
      $endgroup$
      – darij grinberg
      May 23 at 14:24




      $begingroup$
      @kartop_man: From what I know, yes. These are permanent positions with no teaching required!
      $endgroup$
      – darij grinberg
      May 23 at 14:24




      12




      12




      $begingroup$
      @kartop_man Darij is correct, these are extremely competitive and sought after. They don't carry any teaching duty, but usually you can choose to teach a light load for an increase in salary. Moreover after 3-5 years you can ask (and are usually granted) the possibility to move to any CNRS research unit, in France or abroad. To give an idea, this year there were 11 positions in total for all of pure and applied math (+ 3 designated for applied math only). The only downside is the salary, which is slightly lower than lecturers', which is itself not competitive internationally.
      $endgroup$
      – Najib Idrissi
      May 23 at 15:34






      $begingroup$
      @kartop_man Darij is correct, these are extremely competitive and sought after. They don't carry any teaching duty, but usually you can choose to teach a light load for an increase in salary. Moreover after 3-5 years you can ask (and are usually granted) the possibility to move to any CNRS research unit, in France or abroad. To give an idea, this year there were 11 positions in total for all of pure and applied math (+ 3 designated for applied math only). The only downside is the salary, which is slightly lower than lecturers', which is itself not competitive internationally.
      $endgroup$
      – Najib Idrissi
      May 23 at 15:34






      1




      1




      $begingroup$
      @Najib I'm a CNRS researcher and the time you have to wait if you want to move to a different institution is only one year. I have a young colleague who recently did that. Plus you can change topic as soon as you have the position.
      $endgroup$
      – Ratbert
      May 23 at 20:01




      $begingroup$
      @Najib I'm a CNRS researcher and the time you have to wait if you want to move to a different institution is only one year. I have a young colleague who recently did that. Plus you can change topic as soon as you have the position.
      $endgroup$
      – Ratbert
      May 23 at 20:01




      2




      2




      $begingroup$
      @Ratbert You can ask every year, but do you get the permission every year? I was at a meeting for newly recruited mathematicians last month, and the vice director of the Insmi told us that 3-5 years was the "reasonable" delay (but if you have a good reason they can make exceptions).
      $endgroup$
      – Najib Idrissi
      May 24 at 9:25






      $begingroup$
      @Ratbert You can ask every year, but do you get the permission every year? I was at a meeting for newly recruited mathematicians last month, and the vice director of the Insmi told us that 3-5 years was the "reasonable" delay (but if you have a good reason they can make exceptions).
      $endgroup$
      – Najib Idrissi
      May 24 at 9:25













      17












      $begingroup$

      The opinions that certain areas of mathematics are dead are frequently stated but in many cases incorrect. Some areas experience declines in activity and then revivals. Many examples can be given.



      On the other hand, my recommendation to a PhD student would be: do what your adviser says. When you obtain a permanent position you will be free to pursue whatever topic you yourself find interesting. Until that time you have to take into account various things other than intrinsic interest of the topic.



      Example. In the early 1980th my friend, then a graduate student, discussed with his adviser possible directions of research. The adviser himself contributed to classical complex functions theory and to holomorphic dynamics. He said that holomorphic dynamics is dead, and recommended to
      work in classical function theory (the area which was not the most popular at that time either). It is almost exactly at that time (1982) when the revolution in holomorphic dynamics happened, suddenly this become one of the most fashionable area in whole mathematics, and it preserves this status to this day. But in 1960-80 the adviser was almost alone, working in holomorphic dynamics.






      share|cite|improve this answer











      $endgroup$











      • 3




        $begingroup$
        "Many examples can be given" - maybe you could give at least one, so that the answer is more self-contained?
        $endgroup$
        – user140765
        May 23 at 18:14
















      17












      $begingroup$

      The opinions that certain areas of mathematics are dead are frequently stated but in many cases incorrect. Some areas experience declines in activity and then revivals. Many examples can be given.



      On the other hand, my recommendation to a PhD student would be: do what your adviser says. When you obtain a permanent position you will be free to pursue whatever topic you yourself find interesting. Until that time you have to take into account various things other than intrinsic interest of the topic.



      Example. In the early 1980th my friend, then a graduate student, discussed with his adviser possible directions of research. The adviser himself contributed to classical complex functions theory and to holomorphic dynamics. He said that holomorphic dynamics is dead, and recommended to
      work in classical function theory (the area which was not the most popular at that time either). It is almost exactly at that time (1982) when the revolution in holomorphic dynamics happened, suddenly this become one of the most fashionable area in whole mathematics, and it preserves this status to this day. But in 1960-80 the adviser was almost alone, working in holomorphic dynamics.






      share|cite|improve this answer











      $endgroup$











      • 3




        $begingroup$
        "Many examples can be given" - maybe you could give at least one, so that the answer is more self-contained?
        $endgroup$
        – user140765
        May 23 at 18:14














      17












      17








      17





      $begingroup$

      The opinions that certain areas of mathematics are dead are frequently stated but in many cases incorrect. Some areas experience declines in activity and then revivals. Many examples can be given.



      On the other hand, my recommendation to a PhD student would be: do what your adviser says. When you obtain a permanent position you will be free to pursue whatever topic you yourself find interesting. Until that time you have to take into account various things other than intrinsic interest of the topic.



      Example. In the early 1980th my friend, then a graduate student, discussed with his adviser possible directions of research. The adviser himself contributed to classical complex functions theory and to holomorphic dynamics. He said that holomorphic dynamics is dead, and recommended to
      work in classical function theory (the area which was not the most popular at that time either). It is almost exactly at that time (1982) when the revolution in holomorphic dynamics happened, suddenly this become one of the most fashionable area in whole mathematics, and it preserves this status to this day. But in 1960-80 the adviser was almost alone, working in holomorphic dynamics.






      share|cite|improve this answer











      $endgroup$



      The opinions that certain areas of mathematics are dead are frequently stated but in many cases incorrect. Some areas experience declines in activity and then revivals. Many examples can be given.



      On the other hand, my recommendation to a PhD student would be: do what your adviser says. When you obtain a permanent position you will be free to pursue whatever topic you yourself find interesting. Until that time you have to take into account various things other than intrinsic interest of the topic.



      Example. In the early 1980th my friend, then a graduate student, discussed with his adviser possible directions of research. The adviser himself contributed to classical complex functions theory and to holomorphic dynamics. He said that holomorphic dynamics is dead, and recommended to
      work in classical function theory (the area which was not the most popular at that time either). It is almost exactly at that time (1982) when the revolution in holomorphic dynamics happened, suddenly this become one of the most fashionable area in whole mathematics, and it preserves this status to this day. But in 1960-80 the adviser was almost alone, working in holomorphic dynamics.







      share|cite|improve this answer














      share|cite|improve this answer



      share|cite|improve this answer








      edited May 23 at 18:23

























      answered May 23 at 12:39









      Alexandre EremenkoAlexandre Eremenko

      53.5k6 gold badges153 silver badges273 bronze badges




      53.5k6 gold badges153 silver badges273 bronze badges











      • 3




        $begingroup$
        "Many examples can be given" - maybe you could give at least one, so that the answer is more self-contained?
        $endgroup$
        – user140765
        May 23 at 18:14














      • 3




        $begingroup$
        "Many examples can be given" - maybe you could give at least one, so that the answer is more self-contained?
        $endgroup$
        – user140765
        May 23 at 18:14








      3




      3




      $begingroup$
      "Many examples can be given" - maybe you could give at least one, so that the answer is more self-contained?
      $endgroup$
      – user140765
      May 23 at 18:14




      $begingroup$
      "Many examples can be given" - maybe you could give at least one, so that the answer is more self-contained?
      $endgroup$
      – user140765
      May 23 at 18:14











      12












      $begingroup$

      The reports of the death of the field of $q$-series and special functions are greatly exaggerated. George Andrews wrote a book Q-Series on the subject published in 1986. He and Bruce Berndt last year completed the publication of a five volume edition about the results in Ramanujan's Lost Notebook. An important subject for Ramanujan was $q$-series and special functions. George Andrews is a former President of the AMS with many awards.



      Ken Ono, the Vice President of the AMS, has done research on Rogers-Ramanujan identities, Mock theta functions, and recently he and his coworkers have proved the Umbral Moonshine Conjecture. In joint work with Jan Bruinier, he discovered a finite algebraic formula for computing partition numbers. The partition numbers are the coefficients of the reciprocal of the fundamental $q$-series $(q;q)_infty$. There are many other examples that I could cite, but this should be enough.






      share|cite|improve this answer











      $endgroup$




















        12












        $begingroup$

        The reports of the death of the field of $q$-series and special functions are greatly exaggerated. George Andrews wrote a book Q-Series on the subject published in 1986. He and Bruce Berndt last year completed the publication of a five volume edition about the results in Ramanujan's Lost Notebook. An important subject for Ramanujan was $q$-series and special functions. George Andrews is a former President of the AMS with many awards.



        Ken Ono, the Vice President of the AMS, has done research on Rogers-Ramanujan identities, Mock theta functions, and recently he and his coworkers have proved the Umbral Moonshine Conjecture. In joint work with Jan Bruinier, he discovered a finite algebraic formula for computing partition numbers. The partition numbers are the coefficients of the reciprocal of the fundamental $q$-series $(q;q)_infty$. There are many other examples that I could cite, but this should be enough.






        share|cite|improve this answer











        $endgroup$


















          12












          12








          12





          $begingroup$

          The reports of the death of the field of $q$-series and special functions are greatly exaggerated. George Andrews wrote a book Q-Series on the subject published in 1986. He and Bruce Berndt last year completed the publication of a five volume edition about the results in Ramanujan's Lost Notebook. An important subject for Ramanujan was $q$-series and special functions. George Andrews is a former President of the AMS with many awards.



          Ken Ono, the Vice President of the AMS, has done research on Rogers-Ramanujan identities, Mock theta functions, and recently he and his coworkers have proved the Umbral Moonshine Conjecture. In joint work with Jan Bruinier, he discovered a finite algebraic formula for computing partition numbers. The partition numbers are the coefficients of the reciprocal of the fundamental $q$-series $(q;q)_infty$. There are many other examples that I could cite, but this should be enough.






          share|cite|improve this answer











          $endgroup$



          The reports of the death of the field of $q$-series and special functions are greatly exaggerated. George Andrews wrote a book Q-Series on the subject published in 1986. He and Bruce Berndt last year completed the publication of a five volume edition about the results in Ramanujan's Lost Notebook. An important subject for Ramanujan was $q$-series and special functions. George Andrews is a former President of the AMS with many awards.



          Ken Ono, the Vice President of the AMS, has done research on Rogers-Ramanujan identities, Mock theta functions, and recently he and his coworkers have proved the Umbral Moonshine Conjecture. In joint work with Jan Bruinier, he discovered a finite algebraic formula for computing partition numbers. The partition numbers are the coefficients of the reciprocal of the fundamental $q$-series $(q;q)_infty$. There are many other examples that I could cite, but this should be enough.







          share|cite|improve this answer














          share|cite|improve this answer



          share|cite|improve this answer








          edited May 24 at 3:46

























          answered May 24 at 2:52









          SomosSomos

          1,5092 silver badges14 bronze badges




          1,5092 silver badges14 bronze badges


























              8












              $begingroup$

              I think that (properly understood) theory of $q-$series is one of the most fashionable areas of mathematics right now. One reason is the appearance of $q-$series in topology. Namely, Turaev-Viro TQFT associates to each $3-$manifold with boundary a $q-$special function, defined for $q$ being a root of unity. These functions are expected to be $q-$holonomic, so should satisfy interesting difference equations. The building block for these invariants is so-called quantum $6j-$symbol, which coincides with ${}_4F_3-$ basic hypergeometric series with general parameters at $z=1$.






              share|cite|improve this answer









              $endgroup$




















                8












                $begingroup$

                I think that (properly understood) theory of $q-$series is one of the most fashionable areas of mathematics right now. One reason is the appearance of $q-$series in topology. Namely, Turaev-Viro TQFT associates to each $3-$manifold with boundary a $q-$special function, defined for $q$ being a root of unity. These functions are expected to be $q-$holonomic, so should satisfy interesting difference equations. The building block for these invariants is so-called quantum $6j-$symbol, which coincides with ${}_4F_3-$ basic hypergeometric series with general parameters at $z=1$.






                share|cite|improve this answer









                $endgroup$


















                  8












                  8








                  8





                  $begingroup$

                  I think that (properly understood) theory of $q-$series is one of the most fashionable areas of mathematics right now. One reason is the appearance of $q-$series in topology. Namely, Turaev-Viro TQFT associates to each $3-$manifold with boundary a $q-$special function, defined for $q$ being a root of unity. These functions are expected to be $q-$holonomic, so should satisfy interesting difference equations. The building block for these invariants is so-called quantum $6j-$symbol, which coincides with ${}_4F_3-$ basic hypergeometric series with general parameters at $z=1$.






                  share|cite|improve this answer









                  $endgroup$



                  I think that (properly understood) theory of $q-$series is one of the most fashionable areas of mathematics right now. One reason is the appearance of $q-$series in topology. Namely, Turaev-Viro TQFT associates to each $3-$manifold with boundary a $q-$special function, defined for $q$ being a root of unity. These functions are expected to be $q-$holonomic, so should satisfy interesting difference equations. The building block for these invariants is so-called quantum $6j-$symbol, which coincides with ${}_4F_3-$ basic hypergeometric series with general parameters at $z=1$.







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered May 24 at 3:14









                  Daniil RudenkoDaniil Rudenko

                  1,70814 silver badges22 bronze badges




                  1,70814 silver badges22 bronze badges


















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Legend”originalet”Metallica, Slayer, Iron Maien Among Winners At Metal Hammer Awards””Metal Hammer Golden Gods Awards””Bullet For My Valentine Booed At Metal Hammer Golden Gods Awards””Metal Storm Awards 2006””Metal Storm Awards 2015””Slayer's Concert History””Slayer - Relationships””Slayer - Releases”Slayers officiella webbplatsSlayer på MusicBrainzOfficiell webbplatsSlayerSlayerr1373445760000 0001 1540 47353068615-5086262726cb13906545x(data)6033143kn20030215029