We now interrupt your regularly scheduled radio silence…

It has been nearly two years since my last post here, and several things of note have occurred or are about to occur.  My Ph.D was conferred last December.  My dissertation, Categories in Control:  Applied PROPs, is available on the arXiv and via eScholarship.  In the meantime I have been teaching as adjunct faculty at Victor Valley College in the Mathematics and Physics departments, keeping an eye on conferences of interest and postdoc positions.

Since I last wrote, there are two new countries’ stamps on my passport, and in a few days I’ll finally be adding one from a country that shares a land border with the U.S.  Less cryptically, I will be spending next week in Canada, attending a conference on Hopf Algebras and other things in a title that is longer than this description at the Perimeter Institute.  I would like to take this opportunity to thank Tobias Fritz for bringing the conference to my attention and Daniel Gottesman for providing the Perimeter Institute invitation.  Saying the invitation covers practically all the expenses is putting it mildly.

I have been in courtship with a postdoc position since about the beginning of June with the Air Force Research Laboratory in Dayton, Ohio.  There is a close connection there with a group at Penn led by Daniel Koditschek.  I have been invited to give a talk and spend a couple of days at Penn in early September so we can get to know each other better, both personally and mathematically.

A little bit farther in the future, I am looking with interest at the upcoming AMS sectional meeting in November at UC Riverside and the upcoming Joint Math Meeting in January in San Diego.  I still need to submit an abstract for the Applied Category Theory session at the sectional meeting.  I plan to simply attend the JMM—it will be 14 years since the last time I went to a JMM, when it was last in Phoenix.  It will be nice to have a fresh look from a more mathematically mature perspective.

AMS talk 10/24/15

About two months ago I gave a talk at the AMS Fall Western Sectional Meeting.  While I could have safely rehashed my QPL talk, I decided to push forward instead.  That may or may not have been the best idea – the results were certainly less polished.  On the other hand, I was able to describe controllability and observability of a control system in terms of string diagrams.  This is something that was painfully missing from my QPL talk’s results in July.  Seeing the nontrivial constants in the string diagrams the quantum folk were using provided the key insight, and I wanted to capitalize on it as soon as possible.

The punchline of the AMS talk is that the duality between controllability and observability noticed by Kalman in the late 50s and early 60s can be expressed in terms of a PROP, which is a kind of symmetric monoidal category.  In particular, this PROP includes a subPROP of finite-dimensional vector spaces and linear relations, which is basically what Paweł Sobociński deals with here under the name of Interacting Hopf monoids.  Okay, so the actual punchline is that the duality Kalman noticed six and a half decades ago between controllability and observability? it’s simply time-reversed bizarro duality.

Bizarro is Sobociński’s term (seen in episode 7 of his blog), but I’m kind of partial to it.