March 21, 2012
Exact completions and small sheaves
Posted by Mike Shulman
At long last, the following paper is on the arXiv:
This was the subject of my talk at CT2011 last July, but it’s taken me this long to massage it into publishable form. (To be sure, I got distracted with other stuff, like hunting for a job and writing other papers.) For a brief overview, you can look at the slides from my CT2011 talk.
March 19, 2012
Circles Disturbed
Posted by David Corfield
Apostolos Doxiadis and Barry Mazur have edited a book with Princeton University Press called Circles Disturbed: The Interplay of Mathematics and Narrative. Its chapters are largely provided by participants of a workshop held in Delphi in 2007, whose number included John Baez and myself.
John posted about his talk Why Mathematics Is Boring. However, he didn’t develop it into a chapter for the book. I posted about the meeting here, and you can read a draft of my chapter.
The introduction to the book is available. As it mentions, the accompanying interviews, which were conducted by workshop participants on each other, are to be made available. Two are already uploaded, including my interview of Barry Mazur.
Reader Survey: log|x| + C
Posted by Tom Leinster
The semester is nearly over here — just one more week of teaching to go! I’m profoundly exhausted, but as the end comes into sight, I feel my spirits lifting. As soon’s as it’s over, I’ll be heading to Ohio to spend a couple of weeks working with Mark Meckes. The trip is close enough now that I’m starting to get that excited anticipation; soon I’ll be back exploring the wide world of new ideas.
But not so fast: there’s one teaching-related matter to deal with first.
Have you ever taught calculus? If so, what did you tell your students was the answer to $\displaystyle\int \frac{1}{x} d x$?
Here we tell them that it’s $\log|x| + C$, where $C$ is the famous ‘constant of integration’. I’m pretty sure that’s what I was taught myself.
But it’s wrong. At least, it’s wrong if you interpret the question and the answer in what I think is the obvious way. It’s wrong for reasons that won’t surprise many readers, and although I’ll explain those reasons, I don’t think that’s such an interesting point in itself.
What I’m more interested in hearing about is the pedagogy. If you think it’s bad to teach students things that are flat-out incorrect, what do you do instead? I’m not talking about advanced students here: these are 17- and 18-year-olds, many of whom won’t take any further math courses. What do you tell them about $\displaystyle\int \frac{1}{x} d x$?
6th Scottish Category Theory Seminar
Posted by Tom Leinster
We are pleased to announce the sixth meeting of the Scottish Category Theory Seminar, from 2.00 to 5.30 on Friday 25 May, at the University of Strathclyde (Glasgow). All are welcome to attend. We have two invited talks:
- Thomas Streicher (Darmstadt): On univalent foundations
- Eric Finster (EPFL, Lausanne): Revisiting the opetopes: applications in computer science and type theory
We are also looking for contributed talks. If you wish to attend the meeting, would like to have dinner with us, or would like to give a contributed talk, then please email the organisers at scotcatsATcis.strath.ac.uk.
ScotCats 6 will receive financial support from the SICSA’s Complex Systems Engineering Theme.
The local organizer is Neil Ghani, and the other ScotCats organizers are me and Alex Simpson.
March 16, 2012
New Perspectives in Topological Field Theories
Posted by Urs Schreiber
This summer, August 27 - 31 (2012), the Center for Mathematical Physics in Hamburg hosts the coference:
New Perspectives in Topological Field Theories
From their website:
In this conference we will bring together researchers in mathematics and theoretical physics which are involved in recent developments related to topological field theories. Specifically, the topics covered are higher categories, Khovanov homology, non-compact Chern-Simons theory, and topological conformal field theory. The spectrum of topics is chosen to provide enough common ground between participants from these fields to stimulate intensive interaction. Namely, from a mathematical perspective, all topics are related to structures in representation theories and their categorifications. On the physics side, structures inspired or derived from string theory are the unifying link.
See here for further contact information.
March 6, 2012
The Multiplicativity of Fixed-Point Invariants
Posted by Mike Shulman
Kate Ponto and I have just posted a new paper on the arXiv: The multiplicativity of fixed-point invariants. We’re pretty excited about this, because it’s the first time we’ve been able to use Kate’s machinery of “bicategorical traces” to prove something new, rather than just find new ways to prove something old.
Amazingly, I haven’t ever blogged here about bicategorical traces, although Kate and I have been working on them for quite some years now. But the appearance of this paper is a perfect opportunity for such a blog post, precisely because the paper itself does not go into any of the category theory. Since it’s aimed at fixed-point theorists, not category theorists, it has a long chatty introduction and eschews categorical language as much as possible, preferring concrete proofs to abstract ones. But readers of this blog will probably want to know the categorical underpinnings, so let me bend your ears in that direction.