VIGRE REPORT PART II · SPRING 2010

JOHN KERL

The period of support (spring 2010) completed the fifth and final year of my PhD program in mathematics at the University of Arizona. My activities were as follows.

Principally, I completed my doctoral research. With all high-performance computing runs complete, I updated, with smaller error bars, experimental determination of critical temperature T_{c} as a function of α. This had been more crudely computed near the end of the fall semester. I then used the estimated critical exponents for 𝔼[ℓ_{max}]/N and f_{I} to test the hypothesis that the GRU quotient 𝔼[ℓ_{max}]/Nf_{I} is constant in T for T < T_{c}. (Off-lattice computations, as well as use of non-Ewens cycle weights, are a postdoctoral research topic.) I finished several chapters of my dissertation which had been incomplete. I defended my dissertation March 22, and completed revisions on April 10.

I submitted a condensed version of my dissertation to the Journal of Statistical Physics in December, in time for job applications. In early March, the paper was accepted with revisions. I submitted those revisions after my defense; the paper is now in publication.

I recently spoke with Jan Wehr about publishing percolation results described in my summer/fall 2009 proposal. I intend to finish this work this summer; I did not complete this task in time for the end of VIGRE support.

I continued to work with Tom Kennedy’s bridge group. My contributions were (in my opinion) quite small.

(1) I did some ad hoc software mentoring with various members of the group. (2) I wrote a few shell scripts which enabled Tom Kennedy’s SAW-pivot code (as customized by members of the group) to run in the background on a compute server. (3) I wrote a program to exhaustively count, using a backtracking algorithm, location-constrainted self-avoiding walks of length N in the plane, for N up to 20 or so. This was intended to complement Tom’s software which examined location-constratined self-avoiding walks of much longer lengths, using sampling methods. I found that the achievable walk lengths were too small to confirm Tom’s results.

Along with Tom Kennedy, I co-organized the weekly mathematical physics seminar.

I gave a talk on my dissertation research at the AMS/MAA Joint Meetings in San Francisco in January. Of course, my primary purpose for attending this year’s meetings was the job search; I had three interviews there, two of which led to offers of on-site interviews.

I also attended the 23rd Annual Workshop on Recent Developments in Computer Simulation Studies in Condensed Matter Physics at the end of February at the University of Georgia. I gave a contributed talk on the worm-algorithm portion of my dissertation. I made several professional contacts. As well, I obtained advice on the worm algorithm’s stopping-time problem — alas, too late to implement for my dissertation research.

Spring job-seeking efforts included attendance at the Joint Meetings, several on-site interviews, and one job offer, which I accepted. Academic employers were not interested in me; one acknowledges that it is a tight job market this year. A mathematical-consulting defense contractor, who recruited me at the Joint Meetings, as well as three financial firms I applied to, brought me on-site for interviews. One of the latter made me an offer, which I accepted. I will be working as a quantitative software developer in New York, starting in mid-June.

Date: May 11, 2010.

VIGRE support was particularly helpful in permitting me to focus on the job search. I extend my appreciation to the VIGRE committee.