Blog Profile / Theoretical Atlas
| URL : | http://theoreticalatlas.wordpress.com/ | |
|---|---|---|
| Filed Under: | Academics / Mathematics | |
| Posts on Regator: | 56 | |
| Posts / Week: | 0.2 | |
| Archived Since: | December 12, 2008 | |
Blog Post Archive
Seminar on the Cobordism Hypothesis and (Infinity,n)-Categories
Well, it’s been a while, but it’s now a new semester here in Hamburg, and I wanted to go back and look at some of what we talked about in last semester’s research seminar. This semester, Susama Agarwala and I are sharing the teaching in a topics class on “Category Theory for Geometry“, in which [...]
Moving to Hamburg; Talk in Brno: 2-Symmetry of Moduli Spaces
Hamburg Since I moved to Hamburg, Alessandro Valentino and I have been organizing one series of seminar talks whose goal is to bring people (mostly graduate students, and some postdocs and others) up to speed on the tools used in Jacob Lurie’s big paper on the classification of TQFT and proof of the Cobordism [...]
“Observer Space”: Cartan Geometry and Lifting General Relativity
This entry is a by-special-request blog, which Derek Wise invited me to write for the blog associated with the International Loop Quantum Gravity Seminar, and it will appear over there as well. The ILQGS is a long-running regular seminar which runs as a teleconference, with people joining in from various countries, on various topics which [...]
Higher Structures in China
Since the last post, I’ve been busily attending some conferences, as well as moving to my new job at the University of Hamburg, in the Graduiertenkolleg 1670, “Mathematics Inspired by String Theory and Quantum Field Theory”. The week before I started, I was already here in Hamburg, at the conference they were organizing “New Perspectives [...]
Paper on the Categorified Heisenberg Algebra
This blog has been on hiatus for a while, as I’ve been doing various other things, including spending some time in Hamburg getting set up for the move there. Another of these things has been working with Jamie Vicary on our project on the groupoidified Quantum Harmonic Oscillator (QHO for short). We’ve now put the [...]
Cohomology, Groupoidification, and TQFT
I’ve written here before about building topological quantum field theories using groupoidification, but I haven’t yet gotten around to discussing a refinement of this idea, which is in the most recent version of my paper on the subject. I also gave a talk about this last year in Erlangen. The main point of the paper [...]
Representations and Categories – Part II (Erlangen)
Well, as promised in the previous post, I’d like to give a summary of some of what was discussed at the conference I attended (quite a while ago now, late last year) in Erlangen, Germany. I was there also to visit Derek Wise, talking about a project we’ve been working on for some time. (I’ve [...]
Two Workshops on Representations and Categories – Part I
So I’ve been travelling a lot in the last month, spending more than half of it outside Portugal. I was in Ottawa, Canada for a Fields Institute workshop, “Categorical Methods in Representation Theory“. Then a little later I was in Erlangen, Germany for one called “Categorical and Representation-Theoretic Methods in Quantum Geometry and CFT“. Despite [...]
2-Erlangen Program; Manifold Calculus talk (Pedro Brito)
(Note: WordPress seems to be having some intermittent technical problem parsing my math markup in this post, so please bear with me until it, hopefully, goes away…) As August is the month in which Portugal goes on vacation, and we had several family visitors toward the end of the summer, I haven’t posted in a [...]
Quasigroups (Loops), and Relativity
So apparently the “Integral” gamma-ray observatory has put some pretty strong limits on predictions of a “grain size” for spacetime, like in Loop Quantum Gravity, or other theories predicting similar violations of Lorentz invariantsShow More Summary
Dan Christensen on Diffeological Spaces and Homotopy Theory
So Dan Christensen, who used to be my supervisor while I was a postdoc at the University of Western Ontario, came to Lisbon last week and gave a talk about a topic I remember hearing about while I was there. This is the category of diffeological spaces as a setting for homotopy theory. Just to [...]
Benabou on Spans and Profunctors/Distributors
So I recently got back from a trip to the UK – most of the time was spent in Cardiff, at a workshop on TQFT and categorification at the University of Cardiff. There were two days of talks, which had a fair amount of overlap with our workshop in Lisbon, so, being a little worn [...]
Explanation, Fundamentals, an Agrippa-type Trilemma
There is no abiding thing in what we know. We change from weaker to stronger lights, and each more powerful light pierces our hitherto opaque foundations and reveals fresh and different opacities below. We can never foretell which of our seemingly assured fundamentals the next change will not affect. H.G. Wells, A Modern Utopia So [...]
Relativity of Localization
One talk at the workshop was nominally a school talk by Laurent Freidel, but it’s interesting and distinctive enough in its own right that I wanted to consider it by itself. It was based on this paper on the “Principle of Relative Locality”. Whereas Einstein’s gravity describes a regime where Newton’s gravitational constant is important [...]
HGTQGR – Part IIIb (Workshop)
As usual, this write-up process has been taking a while since life does intrude into blogging for some reason. In this case, because for a little less than a week, my wife and I have been on our honeymoon, which was delayed by our moving to Lisbon. We went to the Azores, or rather to [...]
HGTQGR – Part IIIa (Workshop)
Now for a more sketchy bunch of summaries of some talks presented at the HGTQGR workshop. I’ll organize this into a few themes which appeared repeatedly and which roughly line up with the topics in the title: in this post, variations on TQFT, plus 2-group and higher forms of gauge theory; in the next post, [...]
HGTQGR Workshop – Part IIb (School)
Continuing from the previous post, there are a few more lecture series from the school to talk about. Higher Gauge Theory The next was John Huerta’s series on Higher Gauge Theory from the point of view of 2-groups. John set this in the context of “categorification”, a slightly vague program of replacing set-based mathematical ideas [...]
HGTQGR Workshop – Part IIa (School)
I’d like to continue describing the talks that made up the HGTQGR workshop, in particular the ones that took place during the school portion of the event. I’ll save one “school” session, by Laurent Freidel, to discuss with the talks because it seems to more nearly belong there. This leaves five people who gave between [...]
HGTQGR Workshop – Part I (Pre-school)
So I had a busy week from Feb 7-13, which was when the workshop Higher Gauge Theory, TQFT, and Quantum Gravity (or HGTQGR) was held here in Lisbon. It ended up being a full day from 0930h to 1900h pretty much every day, except the last. We’d tried to arrange it so that there were [...]
Tomasz Brzezinski – “Toward Synthetic Non-Commutative Geometry”
So there’s a lot of preparations going on for the workshop HGTQGR coming up next week at IST, and the program(me) is much more developed – many of the talks are now listed, though the schedule has yet to be finalized. This week we’ll be having a “pre-school school” to introduce the local mathematicans to [...]