## April 7, 2011

### The 4th Scottish Category Theory Seminar

#### Posted by Tom Leinster

On Friday 13 May, the Scottish Category Theory Seminar will meet for the fourth time at the University of Glasgow. We’re delighted to have as our speakers:

See the seminar website for further information.

Posted at April 7, 2011 2:09 AM UTC

TrackBack URL for this Entry:   http://golem.ph.utexas.edu/cgi-bin/MT-3.0/dxy-tb.fcgi/2381

### Re: The 4th Scottish Category Theory Seminar

I’m ll actually be in Univ Glasgow coming from the States. Is this seminar open to non-students who want to hear the guest speakers?

Posted by: Career Test on April 7, 2011 9:08 AM | Permalink | Reply to this

### Re: The 4th Scottish Category Theory Seminar

I think the comment I’m replying to is spam. The commenter’s name, “Career Test”, sounds like spam, and the name was linked to a commercial website until I removed the link using my superpowers. (The object of such spam is to generate links to the site in question, thus raising its rank on search engines.)

But on the off-chance that it’s not spam, here’s the answer: as usual for academic seminars, we welcome anyone interested in the subject matter.

Posted by: Tom Leinster on April 7, 2011 10:46 AM | Permalink | Reply to this

### Re: The 4th Scottish Category Theory Seminar

I’ve noticed spam has been getting much cleverer of late. They pay some attention to what’s been said in the thread.

Posted by: David Corfield on April 7, 2011 8:08 PM | Permalink | Reply to this

### Re: The 4th Scottish Category Theory Seminar

I am wondering if Bruno Valette will talk about his latest work on “minimal models” for BV-operads. He has been giving talks on this elsewhere, recently.

On his website there is a link to a pdf for a preprint on this with Gabriel Drummond-Cole, but the link seems to be broken. At least I could not open the file. Does anyone know where to get it?

Posted by: Career Test on April 9, 2011 12:06 PM | Permalink | Reply to this

### Re: The 4th Scottish Category Theory Seminar

Posted by: jim stasheff on April 9, 2011 12:42 PM | Permalink | Reply to this

### Re: The 4th Scottish Category Theory Seminar

Someone is very witty…

I will let Bruno know that the world is clamouring for his preprint.

Posted by: Tom Leinster on April 9, 2011 12:57 PM | Permalink | Reply to this

### Re: The 4th Scottish Category Theory Seminar

So, is Career Test a real person after all? The suspense is killing me. (I’d rather die more dramatically to be honest.)

Posted by: Eugenia Cheng on April 10, 2011 6:02 PM | Permalink | Reply to this

### Re: The 4th Scottish Category Theory Seminar

The first Career Test was probably not a real person: or rather, a real person, but a real spamming person. The second Career Test was, I believe, a fellow host playing a funny joke on me. I don’t know who, but I have my suspicions.

Either that or spammers these days are really sophisticated.

Posted by: Tom Leinster on April 11, 2011 7:06 AM | Permalink | Reply to this

### Re: The 4th Scottish Category Theory Seminar

At first I thought Career Test was joking that ‘BV-operad’ stands for ‘Bruno Valette operad’!

Posted by: John Baez on April 12, 2011 4:07 PM | Permalink | Reply to this

### Re: The 4th Scottish Category Theory Seminar

The second Career Test was, I believe, a fellow host playing a funny joke on me.

Yes, it was me! You inspired me, when starting a conversation with a spammer

on the off-chance that it’s not spam.

Just imagine: a spammer looking around for threads to deposit his spam in ends up getting actually interested in the discussion, gives up spamming and becomes an expert on homotopy operads. What a career test!

Posted by: Urs Schreiber on April 11, 2011 9:31 AM | Permalink | Reply to this

### Re: The 4th Scottish Category Theory Seminar

Ha! That’s surely a movie waiting to be made.

Posted by: Tom Leinster on April 11, 2011 2:30 PM | Permalink | Reply to this

### Re: The 4th Scottish Category Theory Seminar

Sorry to make you wait for the preprint. It is almost finished. We just have to polish the last two pages … I hope to be able to put a version online before the end of the week-end. (Anyway, thank you for your interest !)

Posted by: Bruno Vallette on April 9, 2011 2:50 PM | Permalink | Reply to this

### Re: The 4th Scottish Category Theory Seminar

Sorry to make you wait for the preprint. It is almost finished. We just have to polish the last two pages … I hope to be able to put a version online before the end of the week-end.

Hi Bruno, I would say: take your time with the preprint, that does not want to be rushed. But rush to let us know what you will speak about in Glasgow.

Posted by: Urs Schreiber on April 11, 2011 9:36 AM | Permalink | Reply to this

### Re: The 4th Scottish Category Theory Seminar

Posted by: Tom Leinster on April 12, 2011 11:20 PM | Permalink | Reply to this

### Re: The 4th Scottish Category Theory Seminar

Thanks. That now answers CareerTest’s question: the talk will not be about current research, but will be an introduction to homotopy operad theory.

By the way, I tend to disagree, if you allow and if that makes sense, with the title of the talk, which apparently is

Algebra + homotopy = higher structure .

It seems to me that Algebra + homotopy gives higher algebra and that there are higher structures that want to be called higher geometry instead of higher algebra. But maybe the idea is that one reflects the other (which it does).

Also, I think it is not quite fair to say that the mathematical notion that models homotopical algebra is that of an operad (by which is implicitly meant an $\infty$-operad, really, presented by the standard model structure on operads enriched in simplicial sets/topological spaces or in chain complexes for the simpler cases). There is instead a trinity

in that there is, if not quite an equivalence, large overlap between the three notions and their $\infty$-algebras (just as in 1-category theory).

Sometimes it is useful to pass back and forth between these three notions. For instance $E_\infty$-algebras (rings) are traditionally maybe mostly conceived as $\infty$-algebras over (a cofibrant resolution of the) commutative operad, but there is also a simple and useful incarnation of the corresponding $(\infty,1)$-Lawvere theory (here): It is in fact just a $(2,1)$-theory: namely the $(2,1)$-category $Span(FinSet)$ of spans of finite sets. From that one sees immediately that the free $E_\infty$-algebra in $\infty Grpd$ is the union of the delooping of all the symmetric groups $\Sigma_n$

\begin{aligned} Free_{E_\infty}(\ast) &\simeq Span(FinSet)(\ast,\ast) \\ & \simeq Core(FinSet) \\ & \simeq \coprod_{n \in \mathbb{N}} \mathbf{B}\Sigma_n \end{aligned} \,.

In order to get the same insight with operads, one has to construct explicitly the Barrat-Eccles-resolution of $Comm$. Maybe not a big deal either, but I think the structure of the free $E_\infty$-algebra is more immediate in the perspective of the $(\infty,1)$-algebraic theory (well, maybe one could say that this is a tautology, since like algebraic theories, these are by their very nature controled by the free objects).

Finally a question: I wasn’t aware that there is any application of operad theory to Gröbner bases. (But then, I have only faint recollection of Gröbner base theory in the first place.) What is the relation?

Posted by: Urs Schreiber on April 13, 2011 9:37 AM | Permalink | Reply to this

### Re: The 4th Scottish Category Theory Seminar

Urs wrote:

the talk will not be about current research, but will be an introduction to homotopy operad theory.

Right. And this gives me an opportunity to say a bit more about the purpose of this seminar series.

Scotland’s mathematical community is not enormous, but there are actually quite a lot of people with some kind of interest in category theory, and they’re extremely varied. A lot of them are not primarily mathematicians, or not in mathematics departments: they’re computer scientists, or at least in computer science departments. People with this background probably know a lot about type theory and logic, but might have only a hazy idea of what, say, homology is. (That’s not true of all these computer scientists, but I think it is true of some of them.)

On the other hand, you’ve got algebraists and algebraic geometers and topologists who use things like derived categories or operads. They might have literally never heard of the subject called “type theory”, and might have only a hazy idea of what, say, first order logic is.

So our speakers have a tough job. We try to mix together the different communities, and we try to arrange speakers with broad appeal. It’s probably true that some of the most successful talks have been of a survey-like nature. Giving a talk at our seminar is something like giving a colloquium, but to an audience who all know some category theory.

Posted by: Tom Leinster on April 13, 2011 11:05 AM | Permalink | Reply to this

### Re: The 4th Scottish Category Theory Seminar

Bruno’s paper on the minimal model of BV (with Gabriel Drummond-Cole) is now on the arXiv.

Posted by: Tom Leinster on May 11, 2011 12:46 PM | Permalink | Reply to this