Tom:

I failed to schedule a meeting between you, me, & Daniel before Daniel left
town.  However, here is a list of things I will/should be doing for summer and
fall:

* Of course, my VIGRE proposal remains the big picture:

  http://math.arizona.edu/~kerl/rcm/VIGRE_App_PartII.pdf

* I will be presenting a contributed talk at the conference on Stochastic
  Processes and Their Applications at the end of this month in Berlin.  I will
  spend some time beforehand preparing for that talk.  This is more of a
  mathetmatics conference than a simulation conference:  my main goal is to
  present the model of spatial permutations in a way that will pique the
  interest of probabilists in the audience.  I'll include a couple sentences
  indicating that I'll be glad to chat in the hallway with anyone having
  expertise in MCMC methods.

* Daniel has two collaborators in Marseille:  Daniel Gandolfo and Jean Ruiz.
  I will spend three days with them and Daniel U. the week before the
  conference.  Our main goal is to investigate some questions involving the
  maximum cycle length with a view toward a known result for non-spatial
  permutations (1966 paper of Shepp and Lloyd); we will focus less on the
  questions involving shift in critical temperature which my dissertation
  research has focused on up to this point.  We hope to get a paper out of
  this.  Gandolfo and Ruiz, like me, are experimentalists, and so we hope to
  obtain similar results from their & my separate software implementations.  If
  we can get the same answer in two different ways, our confidence will be
  (even more) increased.

* In preparation for that, before I leave I will be typing up a dissertation
  chapter which describes one of the less obvious (and more recent) changes
  I've made, namely, the optimization technique of caching permutation cycle
  lengths.

* In other software work this summer, I've just completed (and am now
  running regression tests on) batched means.

* In addition to the above-mentioned simulational work with Gandolfo, Ruiz, and
  Ueltschi, I am completing some simulation runs which estimate the shift in
  critical temperature as function of cycle-interaction parameter for the
  two-cycle and Ewens interaction models.  These should lend supporting weight
  to the ongoing theoretical work of Ueltschi and Betz.

* In theoretical work for this summer, I need to understand more about
  optimal choices of batch size and number of batches.  There is a good recent
  paper (Flegal & Jones 2009) on this subject.

* Theoretical work for the fall:  Note that there are many known results
  (Suto as well as Ueltschi & Betz) for spatial permutations with points
  distributed on the continuum, largely due to the use of the Fourier method.
  For points distributed on the lattice, the Fourier method is not available
  and simulation methods are used.

  For my dissertation, I am focusing on the latter.  However, there are a
  couple things currently not known for points distributed on the continuum:
  distribution of the length of the longest cycle, and monotonicity of
  correlation length as a function of temperature.

  This fall, I will digest the Fourier method and see what I can say about
  these two questions.

* Simulational work for the fall:  Daniel and I have sketched out some
  ("quenched") models for holding point positions fixed, but off the lattice,
  as well as ("annealed") models allowing point positions to move during a
  simulation.

  The greater goal is to sample from the true distribution for the Bose gas.
  There are two key components:  (1) allow spatial point motion; (2) find the
  correct interaction strength.  Ueltschi and Betz are engaged in work aiming
  to find the correct cycle weights for the Bose gas.  I don't know whether
  they will have this by the end of next year, when I intend to graduate, so I
  don't want to insist on including this point-motion work in my thesis.

* The AMS/MAA Joint Meetings are coming up, where I'll be job-shopping and
  therefore giving a talk.  I need to get an abstract out by the end of July.

* Likewise, there is what sounds like it will be a very good simulational
  conference hosted by David Landau's group at UGA in February.  So, I will
  need to apply soon.  (They don't yet have an abstract-submission deadline.)

* I'll begin job-hunting work in August.

Please let me know if I forgot anything ...

----------------------------------------------------------------
John Kerl
Graduate student, University of Arizona Department of Mathematics
kerl@math.arizona.edu
http://math.arizona.edu/~kerl