Conferences are important

I am not a great mathematician. I have many deficiencies. The deficiency I am going to focus on today is that I am not very good at generating my own research questions. But I have some ideas on how to get better below.

(Note: I am not a great mathematician, but I am an okay mathematician. This is because I have some amount of the most important quality for a mathematician: tenacity. I am not work efficiently and I may not have the background I should, but I am willing to sit down most every day and work. This is really huge).

First, I went to the Zassenhaus Group Theory Conference last weekend (I am one of the giants in the back of the picture). I was reminded how important these conferences are. For one, I got a lot of ideas for research questions from listening to other presenters speak. Some of these ideas were given to me directly by the speaker, and other ideas were tangential to what the presenter was actually discussing. But I also was a presenter, and I presented on a problem that I am stuck on. I received several great suggestions on how to proceed.

Second, I have been working with a collaborator for the past semester on a problem. Something clicked today about one problem I have: I search for a solution a little too directly. But reading my collaborator’s ideas, I realize that he plays with the ideas much more, collecting a bunch of ideas that may or may not be useful to the problem at hand. This seems like it would be enormously useful, and I am shocked that I do not do it already.

My goal is to play more. This is what I ask my students to do, and they sometimes just do not get it. Apparently, neither do I. I am hoping that

  1. I can work past this and
  2. I can learn what it took for me to work past this, so that I can help me students to learn to play more.
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6 Responses to “Conferences are important”

  1. Adam Glesser Says:

    Speaking of research questions, I’m in Virginia right now for the retirement conference for Leonard Scott and an interesting question came up today that you might like. Lenny Jones conjectured that for any symmetric group, the number of irreducible characters of maximal degree is at most 2. He claims to have checked it for all S_n with n < 73.

    I don't have a good feeling for why it would be true, but I only learned how to use the abacus two days ago, so that doesn't mean much.

    • bretbenesh Says:

      Hi Adam,

      How is the conference? Also, I should look at your papers—maybe we have some overlap in interests?

      I don’t know how to use an abacus at all. The question sounds interesting, although the theme of my talk was “Bret does not know any representation or character theory” (which is almost true). If Lenny Jones cannot solve it, I doubt I can.

      But…I am going to put it on my “problem list.” I am fortunate enough now to have way too many questions to work on (thanks, in large part, to the conference). But it is always good to have a store of questions.

      Thanks, Adam! Bret

      • Adam Glesser Says:

        Hi Bret,

        The conference was a lot of fun although, being that Lie theory is well outside my area of expertise, I did feel lost most of time. I would have felt much more comfortable (mathematically) at the Zassenhaus conference, I suspect. From the conference photo, I immediately recognize Mark Lewis, James Cossey, and Alexandre Turull, so there were definitely enough people in the audience who knew rep’n theory to compensate for any of your perceived lack of expertise!

        I looked at your paper with Newton and the problem you presented at the conference (at least for the Family 2 examples) and my first question is whether you have good reason to believe there is a nice relationship. The first example I looked at was (7,21) and I already got stuck.

        Adam

      • bretbenesh Says:

        Hi Adam,

        Thanks for looking at my problem. I am stuck too, although Arturo Magidin and Mark Lewis independently gave me some hope. They told me to think of these maximal symmetric groups as stabilizers of…something. If I find what that something is, then I might be able to reverse engineer the proof of The Branching Rule to figure out what is going on. But I have another problem right now that is a higher priority.

        I hope to see you at Ohio State-Denison next year or in North Carolina (for Zassenhaus) the year after that! Bret

  2. sunilchetty Says:

    I just want to say that I am reminded often that I recommend things to my students that I do not do well myself…. I too must learn to find ways to play with a problem so that I can see new angles of attack.

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