3. Postdoctoral Program - MSRI

EXTERNAL POSTDOCTORAL FELLOW REPORT
December 2009
-------- Original Message --------
Subject: Re: mid year report for teh NSF
Date: Tue, 22 Dec 2009 10:20:35 -0700 (MST)
From: Scott Crofts
To: Hélène Barcelo
References:
After graduating in May, my first objective was to turn the results of my thesis into a
paper. After looking at things carefully, I decided to first attempt to extend the results to a
more general setting. I made significant progress on this over the first few months of the
summer and I now believe that this work will result in two papers. I completed the first
paper and submitted it to the electronic journal 'Representation Theory'. It is a pretty long
paper (~75 pages) and according to the editor, I should hear something by April. It is
available on the arXiv at:
Vogan Duality for ~Spin(p,q) I - arXiv:0908.1976v1 [math.RT]
Although, I have made significant progress on the second paper, there is still more work
to do there. I expect to return to this sometime next year.
Over the summer I also attended a workshop/conference on the computational
representation theory of real groups. Although I did not give a talk, I
was responsible for coordinating evening sessions during the workshop for graduate
students.
My mentor at UCSC is Martin Weissman. Marty's research interests are similar to mine,
only he works mostly over p-adic fields. Since I know very little about p-adic
representation theory, I have been trying to learn as much as I can from Marty. I spent a
significant amount of time trying to understand his recent paper on metaplectic tori and
trying to relate it to my own work. Interestingly, we now believe that the main
results of his paper do not include a case that will be important for the results of my
second paper. This isn't something we understand well at this point.
Finally, I spent a week in Maryland visiting Jeffrey Adams. I gave a talk in the
representation theory seminar on my own research and had a very productive visit with
Jeff. I believe we have an interesting project to work on and it has already led to some
nice results. I am hopeful that I can begin writing a paper on these topics early next year.