My two high-school kids came by today. We’ve been trying to get a new teaching session together since early February, but they had a hell of a time all through February, and all our appointments ended up canceled with little or no notice; and then I spent March and April on tour.

We pressed on with knot theory. Today, we discussed knot sums, prime knots, knot tabulation, behavior of the one invariant (n-colorability) we know so far under knot sums, Dowker codes, and we got started on Conway codes for knots. Next week, I plan for us to finish up talking about the Conway knot notation, get the connection between rational knots and continued fractions down pat, and start looking into new invariants.

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Restarting high school topology

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First off, I’d ask your pardon for the lull in postings – this spring has been insane. It has been very much fun – traveling the world, talking about my research and meeting people I only knew electronically – and also very intense.

To break the lull, I thought I’d try to pick up what I did last summer: parallel computing on clusters. It’s been a bit of blog chatter about SAGE and how SAGE suddenly has transformed from a Really Good Idea to something that starts to corner out most other systems in usability and flexibility.

Matlab? SciPy bundled with SAGE and the Python integration seems to be at least as good, if not better.

Maple? Mathematica? Maxima? Singular? GAP? SAGE interfaces with all those that it doesn’t emulate.

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Parallel and cluster computing with MPI4Py

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*Edited to add Galway*

I’ll be doing a “US tour” in March / April. For the people who might be interested – here are my whereabouts, and my speaking engagements.

I’m booked at several different seminars to do the following:

Title: On the computation of A-infinity algebras and Ext-algebras

Abstract:

For a ring R, the Ext algebra carries rich information about the ring and its module category. The algebra is a finitely presented k-algebra for most nice enough rings. Computation of this ring is done by constructing a projective resolution P of k and either constructing the complex or equivalently constructing the complex . By diligent choice of computational route, the computation can be framed as essentially computing the homology of the differential graded algebra .
Being the homology of a dg-algebra, has an induced A-infinity structure. This structure, has been shown by Keller and by Lu-Palmieri-Wu-Zhang, can be used to reconstruct R from

.

I’m going to move on with the identification of geometric objects with functions from these objects down to a field soon enough, but I’d like to spend a little time nailing down the categorical language of this association. Basically, we have two functors I and V going back and forth between two categories. And the essential statement of the last post is that these two functors form an equivalence of categories.

Now, first off in this categorical language, I want to nail down exactly what the objects are. In the category the objects are solution sets of systems of polynomial equations. And in the category , the objects are finitely presented Noetherian reduced k-algebras.

The functor acts on objects by sending an algebra R to the solution set of the polynomial equations generating the ideal in a presentation of the algebra.

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Introduction to Algebraic Geometry (3 in a series)

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Read the full post (723 words, 49 images)
- February 21st, 2008
- 10:43 pm

I want to lead this sequence to the point where I am having trouble understanding algebraic geometry. Hence, I won’t take the usual course such an introduction would take, but rather set the stage reasonably quickly to make the transit to the more abstract themes clear.

But that’s all a few posts away. For now, recall that we recognized already that any variety is defined by an ideal, and that intersections and unions of varieties are given by sums and intersections or products of ideals.

This is the first page of what is known as the Algebra-Geometry dictionary. The dictionary is made complete by a pair of reasonably famous theorems. I won’t bother proving them – the proofs are a good chunk of any decent commutative algebra course – but I’ll quote the theorems and discuss why they matter.

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Introduction to Algebraic Geometry (2 in a series)

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Read the full post (565 words, 11 images)
- February 21st, 2008
- 12:33 pm

I’m growing embarrassed by my lack of understanding for the sheaf-theoretic approaches to algebraic (and differential) geometry. I’ve tried to deal with it several times before, and I’m currently reading up on Algebraic Geometry again to fill the void that the finished thesis, soon arriving travels and non-existent job application responses produce.

So, why not learn by teaching? It’s an approach that has been pretty darn good in the past. So I thought I’d write a sequence of posts on algebraic geometry, introducing what it’s supposed to be about and how the main viewpoints develop more or less naturally from the approaches taken.

## Varieties

The basic objective of algebraic geometry is to study solution sets to systems of polynomial equations. That is, we take some set of polynomials in some polynomial ring over some field . And we write for the set of all simultaneous roots to all these polynomials:

This is a preview of

Introduction to Algebraic Geometry (1 in a series)

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Read the full post (355 words, 13 images)
- February 21st, 2008
- 1:15 am

I saw the Cerebrate solve the first Scripting Games challenge: Pairing off. And immediately thought “I can do that in Haskell too”.

So, here it is.

import Data.List
cards = [(1,7),(0,5),(3,7),(2,7),(2,13)]
countpairs [] = 0
countpairs [a] = 0
countpairs (a:as) = length . filter (((snd a)==) . snd) $ as
pairingOff = sum . map countpairs . tails

And that’s that. Alas, the actual competition only takes Perl, VBScript and PowerShell, so I won’t be submitting this.

(79 words)

- February 15th, 2008
- 7:59 pm

Brent Yorgey wrote a post on using category theory to formalize patch theory. In the middle of it, he talks about the need to commute a patch to the end of a patch series, in order to apply a patch undoing it. He suggests a necessary condition to do this is that, given patches P and Q, we need to be able to find patches Q’ and P’ such that PQ=Q’P', and preferably such that Q’ and P’ capture some of the info in P and Q.

However, as such, this is not enough to solve the issue. For one thing, we can set Q’=P and P’=Q, and things are the way he asks for.

Now, I wonder whether we can solve this by using PROPs (or possibly di-operads or something like that). Let’s represent a document as a list of some sort of tokens. We’ll set the set of all lists of length , and we’ll set to denote operations that take a list of length n and returns a list of length m.

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PROPs and patches

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- February 15th, 2008
- 2:13 pm

In a mean push, these last two weeks my advisor has read three different drafts of my thesis. And I’ve worked on getting the corrections in quickly. The last push started yesterday, when I got a bunch of corrections in the morning, had the last draft ready at 4pm, and then sat reading it myself until 1am.

My advisor took it home with him, spent the evening on it, and had his batch of corrections in the morning.

Hence, today at 10-ish when I got myself in to the office, I had two batches of corrections in front of me, and a printer closing at 2pm. So I worked – and now, well, it’s done.

That’s it.

It’ll get printed.

Then read.

In May, we should get all the comments back from the external examiners.

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Thesis written

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- February 1st, 2008
- 2:27 pm

So, here’s the plan for my 10th grade topology students.

Today, we’ll abandon algebraic topology completely, and instead go into knot theory. I’ll want to discuss what we mean by a knot (embedding of in ), what we mean by a knot deformation (thus introducing isotopies while we’re at it) and the Reidemeister moves. Also we’ll discuss knot invariants – and their use analogous to topological invariants.

Later on, we’ll continue with other invariants; definitely including the Jones polynomial, and possibly even covering Khovanov homology. One possible end report would be to explain a bunch of knot invariants and show using examples how these have different coarseness.

*Edited to add:* I got myself some damn smart students. They figured out the Reidemeister moves on their own – as well as minimal crossing number in a projection being highly relevant – with basically no prompting from me. I’m impressed.

(149 words, 2 images)

- January 25th, 2008
- 5:58 pm

At the start of the German Year of Mathematics, the Oberwolfach research institute has released an exhibition and the software they used to produce it. The software, surfer, is a really nice GUI that sits on top of surf and lets you rotate and zoom your algebraic surfaces as well as pick colours very comfortably.

They have a whole bunch of Really Pretty Images at the exhibition website, and I warmly recommend a visit. If you can get hold of the exhibition, they also have produced real models – with a 3d-printer – of some of the snazzier surfaces, so that one could have a REALLY close encounter with them.

But also, I’d really like to show you some of my own minor experiments with the program.

This is the interior of a Klein Bottle, using the “standard” realization as an algebraic surface given by Mathworld. In other words, I’m using

(x^2+y^2+z^2+2*y-1)*((x^2+y^2+z^2-2*y-1)^2-8*z^2)+16*x*z*(x^2+y^2+z^2-2*y-1)=0

for the defining equation. It kinda looks a bit like a Sousaphone in my opinion.

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Algebraic surface toys!

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- January 18th, 2008
- 4:26 pm

http://arxiv.org/abs/0707.1637

Just got accepted for publication in the Journal of Homotopy and Related Structures.

Damn, this feels good!

(19 words)

- January 10th, 2008
- 8:41 am

Today, the congress ended.

I bought one book – Adams’ Knot book, with free shipping, for $22.

And I drooled over one more – Kozlov’s Combinatorial Algebraic Topology. The hardcover was down from $99 to $70 at the congress stand, but still was WAY outside my own budget capabilities.

Now, this book does algebraic topology on simplicial complexes. It does everything I’ve wanted a reference for with simplicial complexes. And at some point, I’ll REALLY need to get it.

I listened to a bunch of talks on Mathematics and Arts – including one on knitting hyperbolic pant crotches for toddlers – and one on an analysis of a combinatorial game on graphs: “Flee from the Zombies” – very entertaining.

I also spent an hour talking about the historical background of -algebras and bialgebras with one of Ron Umble’s students.

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AMS-MAA JMM 2008 Liveblogging, day 4 – final day

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- January 9th, 2008
- 8:35 am

The day started bad. I overslept, went to the convention center, and realized that I had forgotten my badge. Back to the hotel, and then back to the convention center. By the time I got there, the first talk I wanted to hear – one on a generalization of Kuratowski’s theorem to simplicial complexes – was already over by the time I got there.

So instead, I learned beading. I did two prototype versions of small and neat little Borromean rings in golden seed beads and blue, shimmering bugle beads. The SF fan / knitter / crafter who taught me was busy doing earrings in the shape of torus knots. Gorgeous. She has a plan for doing triple torus knots (solid spirals with bugle – seed – bugle – seed – bugle – seed) interlinked like Borromean rings.

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AMS-MAA JMM 2008 Liveblogging, day 3

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- January 8th, 2008
- 8:42 am

This was a packed day.

And yet, I had trouble finding anything in the talks I wanted to hear.

i woke up, went down to the employment schedule, and fetched my interview schedule. Then I went to Frank’s pancake house and ate their World Famous Apple Pancake. The thing was 20cm high, covered a full plate and incredibly delicious. It also cost more than I expected to spend on breakfasts, but splurging once is alright.

Then I walked around, doing nothing much, and checked out the universities I was assigned to interview with on the web. Small. Teaching oriented. And in small towns. Both of them.

First interview went well enough, though I doubt I’ll want to go there and I doubt they’ll want me either. I’m not convinced that a university whose main claim to desirability is their pre-veterinary and equestrian programs will agree with my severe horse allergy.

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AMS-MAA JMM 2008 Liveblogging, day 2

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- January 7th, 2008
- 4:30 pm

There’s a bunch of us math bloggers on site in San Diego. Hence, here, the call for a blogger meetup. We’ll convene by the entrance to Hall B (the one with the registration and the exhibitions) at 6pm on Tuesday 8th.

I’ll be there, and so will bit-player. Join in you too!

(53 words)

- January 7th, 2008
- 5:04 am

I’m exhausted.

I’m completely exhausted.

And I just got through the first day.

However, I also managed to meet up with S from the university interested in me. We had a really nice chat, and I feel rather good about it.

Other things done today – listened to an interesting talk generalizing Koszul algebras based on the highest degree ring generator of the Ext algebra. Listened to bits and pieces of a talk on Koszul and Verdier duality. Saw Flatland – The Movie (with Martin Sheen playing the main character, Arthur Square).

I also chatted with Cliff Stoll – whose sales pitch for the Klein Bottles is immensely entertaining; NSA – who don’t want me; Maplesoft – who are interested in me; Mathematica – who pointed me to their website; various e-Learning companies; and many many other exhibitors.

Also, got tired, hungry and WET. It’s bloody raining here.

(149 words)

- January 6th, 2008
- 7:47 am

The participation in the AMS-MAA Joint Mathematics Meeting sure got off to a smashing start. If nothing else, the storm that hit the Californian seaboard on January 4th ensured that.

I get out of bed at 3.30am, CET, not having been able to sleep particularly well at all. At 4am, I drag myself out to the taxi; which charges more to get me to the airport shuttle than the airport shuttle itself does to get me out to the airport. I don’t care that much – I need the coddling at that ungodly hour.

Checking in and going down to Frankfurt is uneventful. Every single passenger is transferring to either Eritrea or the US, and all but two have managed to check their luggage through as well. n

The remaining two – me and one more poor bastard – have our luggage rerouted to another conveyor belt. And no information about it. When, after an hour, the “Stockholm pending” turns into “Stockholm finished”, I go to lost baggage, where they scan my slip and direct me to the right conveyor belt. Where the bag happily reposes.

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AMS-MAA JMM 2008 Liveblogging, day 0

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- December 20th, 2007
- 1:51 pm

I’ll be in San Diego for the AMS-MAA Joint Mathematics Meetings, January 5-11. I would be happy to meet up with cool people, blog readers, blog writers and what not – regardless of whether you actually will participate in the meeting or not. Drop me an email (contact data in the [about] page here) and we’ll coordinate something.

Also, I’ll be speaking twice. Come listen – if you dare.

(70 words, 1 image)

- December 19th, 2007
- 12:57 pm

From each month, the first sentence of the first post.

January: I decided on a whim to look in at the Dilbertblog, where the top post at the moment has Scott Adams calling all atheists that discuss on the net irrational, using a rather neat strawman carbon copy of most discussions of faith between believers (i.e. mostly Christians) and atheists he has seen on the web.

February: The second carnival of mathematics is up over at Good Math, Bad Math.

March: I just met up with the workgroup in the Deutsche Mathematikervereinigung (German Association of Mathematicians) with interest spanning

(100 words)

- December 16th, 2007
- 10:34 am

I just received my first ever referee’s report. Yikes!

Suffice to say, the report did not, as some I’ve seen blogged about, tear me a new one. Far from it – it was civil, kind, and pointed out several areas where my article text overlapped known arguments from other people and was generally superfluous as well as several areas where my article was too curt and didn’t actually spell out the new ideas sticking in it.

Also, making the relation of my results and those I rely on to the results of the Grand Old Man in applying -techniques in group cohomology explicit and discuss these in more detail was requested.

I know I couldn’t expect to write The Perfect Article as my first submission ever. And it’s not a flat out denial. And it brings constructive comments about how to make this a better article. Still, I think my ego needs a little bit of training to learn to cope with this part of the review process.

(169 words, 1 image)

- December 14th, 2007
- 4:31 pm

The last meeting with my 10th grade topology kids this year just finished. We introduced singular homology, calculated the singular homology of a point and discussed homeomorphism invariance.

Next term, we’ll want to show homotopy invariance and that the singular and simplicial homology coincide when applicable. After that, we’ll change directions slightly.

The future after that holds knot theory, was decided today. We’ll want to introduce knots, look at Reidemeister moves and basic knot invariants. I use basic here in a pretty wide sense – we’ll probably do the Jones polynomial and we might even end up doing Khovanov homology if I feel particularly insane late spring.

(108 words)

- December 13th, 2007
- 3:05 pm

Last week, the news hit the blogosphere that Google had released a beta API for generating graphs using a reasonably easy and transparent GET parametrisation.

Inspired by this, and inspired by my early playing around with Ruby on Rails, I decided to whack together a Rails plugin that takes care of building the Google Charts IMG tag using what I hope is reasonably easy to use syntax.

I have a test-site using random data up for playing around with it.

The test-site as such runs on Ruby on Rails. The controller does some parsing and setting up of relevant arrays, and primarily generates random data for plotting.

The view has the following source code:

<%= google_chart

(@data,

@alt_text,

@options) %>

<p><% form_tag "" do %>

<label for="options[type]">Type</label>

<%= select_tag "options[type]", options_for_select(@typeopts,@options["type"])

%>

<label for="options[title]">Title</label>

<%= text_field_tag "options[title]", @options["title"] %>

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Riding the Google Charts API bandwagon

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Read the full post (253 words)
- December 9th, 2007
- 10:13 pm

So, there is this one big and neat framework called Rails, building on top of this one neat new programming language called Ruby.

And one of the things that makes Rails so Damn Neat is that if you only set things up the right way around, it guesses almost everything you need it to guess for you.

One of the ways it does this is by *pluralization*. Basically, the model `Foo`

has a model defined in `app/model/foo.rb`

and it accesses the database table `foos`

.

So, when talking a good friend through the basics, we created the table `persons`

and generated the model `Person`

. And promptly got an error from the framework.

It turns out that the pluralization of *person* is *people*. I wonder what else irregularities they built into the system. If I have a model called `Index`

, does Rails expect it to read from the database table `indexes`

or from `indices`

?

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Pluralization in Rails

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- December 5th, 2007
- 12:13 pm

The last postdoc carnival for 2007 is coming to town, and given my current position in my career, I thought I’d try to slowly edge into that arena as well.

A short background blurb for those who haven’t read this blog before – and for those who haven’t heard the story: I’m a mathematics PhD student from Sweden in Germany, living apart from my wife for about 2

(69 words)

- December 3rd, 2007
- 8:52 am

So, there is this one condition called synaesthesia, where basically perception gets crosslinked. Most commonly, numbers, letters, and words get colours coupled to them. This way around, I have a few friends who I know have it.

The more exotic varieties couple more or other senses to each other.

The whole thing gets Really Interesting, and ties in to quite a bit of philosophy as well, when you start coming near the really odd cases. Qualia are the philosophical term for “how things are perceived by us”. Basically, it boils down to the following: if I see something red, is this intrinsic to the object, or something existing in my perceptive neurons only?

And so far, arguing about it has been more or less all there was. At least known to me.

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Synaesthesia and cognition

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- December 1st, 2007
- 10:54 pm

Issue # 21 in the Carnival of Mathematics series is up now over at the (not so) Secret Blogging Seminar.

The resulting discussion there amuses at least me.

(29 words)

- November 20th, 2007
- 6:12 pm

In a recent column at The Chronicle of Higher Education, the columnist writes

I’m a latecomer to it, in part because I have a very hit-or-miss interest in new technologies. (I still don’t own a cell phone, for example, though I check my e-mail 4,000 times a day.)

Now. There are 24 hours in a day. 1 440 minutes. 86 400 seconds. Thus, checking e-mail 4 000 times in a day would require you to check your inbox every 21.6 seconds. Day and night.

Either the author is innumerate or hyperactive.

(92 words)

- November 19th, 2007
- 4:41 pm

Due to a spectacular spam storm incited by akismet.com being unreachable from the webserver, I have decided to globally shut off commenting for the time being.

This should be a temporary state, and I hope that the akismet issue solves itself soon.

(43 words)

- November 16th, 2007
- 4:34 pm

Today, I told my two bright students about abstract and geometric simplicial complexes, about the boundary map and the chain complex over a ring R associated with a simplicial complex Δ, and assigned them reading out of Hatcher’s Algebraic Topology.

The next couple of weeks will be spent doing homology of simplicial complexes, singular homology, equivalence of the two, neat things you can do with them; and then we’ll start moving towards a Borsuk-Ulam-y topological combinatorics direction.

I might end up pulling combinatorics papers from my old “gang” in Stockholm on graph complexes, and graph property complexes, and poke around those with them.

(104 words)

- November 12th, 2007
- 12:34 pm

I tried out an idea from Khymos recently when inviting a bunch of friends over for a party. We took six slices, about 1100g, of beef entrec

(28 words)

- October 29th, 2007
- 10:11 pm

In a conversation on IRC, I started prodding at low-order wreath products. It turned out to be quite a lot of fun doing it, so I thought I’d try to expand it into a blog post.

First off, we’ll start with a **definition**:

The wreath product is defined for groups G,H and a G-set X by the following data. The elements of are tuples . The trick is in the group product. We define

(or possibly with a lot of inverses sprinkled into those indices)

Consider, first, the case of with the nontrivial G-action defined by gx=1, g1=x. We get 8 elements in the wreath product . Thus, the group is one of the groups with 8 elements – . We shall try to identify the group in question using orders of elements as the primary way of recognizing things. Consider an element ((x,y),z).

- September 26th, 2007
- 4:25 am

dynkin:~/magma> magma
Magma V2.14-D250907 Wed Sep 26 2007 13:19:51 on dynkin [Seed = 1]
Type ? for help. Type -D to quit.
Loading startup file "/home/mik/.magmarc"
> Attach("homotopy.m");
> Attach("assoc.m");
> Aoo := ConstructAooRecord(DihedralGroup(4),10);
> S := CohomologyRingQuotient(Aoo`R);
> CalculateHighProduct(Aoo,[x,y,x,y]);
z
> exit;
Total time: 203.039 seconds, Total memory usage: 146.18MB

And this is one major reason for the lack of updates recently.

(65 words)

- September 18th, 2007
- 2:26 am

No mathematical content today. However, I do note that the mathematics department in Sydney is located in a building as drab and boring as the Stockholm University main building. Its main architectural feature is the pale, washed out blue panels on the upper parts of the hollow concrete slab.

Just a short way away, though, we find the Quadrangle – a cathedral in the religion of learning, and the main building of Sydney campus. Complete with stained glass windows and stucco heraldic designs, all dedicated to the branches of scholarship.

Alas, the splendour suffers slightly from the extensive road construction work, which has just about managed to fence in and tear up almost all the tarmac in this corner of campus.

(122 words)

- September 9th, 2007
- 12:19 pm

However, I am enjoying the Scottish countryside and just – today – turned years of age.

(17 words, 1 image)

Trying to make the time until my flight leaves tomorrow go by, I played around a bit with the proof assistant Coq. And after wrestling a LOT with the assistant, I ended up being able to prove some pretty basic group theory results.

And this is how it goes:

Section Groups.

Variable U : Set.

Variable m : U -> U -> U.

Variable i : U -> U.

Variable e : U.

Hypothesis ass : forall x y z : U, m x (m y z) = m (m x y) z.

Hypothesis runit : forall x : U, m x e = x.

Hypothesis rinv : forall x : U, m x (i x) = e.

This sets the stage. It defines a group as a group object in Set, but without the diagonal map. It produces a minimal definition – the left identity and inverse follow from the right ones, which we shall prove immediately.

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Coq and simple group theory

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First off, Alexander Borovik has been writing a couple of times about a REALLY nice-sounding mathematical village in Turkey.

And it turns out, the village got closed this summer, with the government officials citing “education without permission” as their reason to close it.

Alexander is sending a petition to the prime minister. You should sign it.

In other news, I’m currently just waiting for Monday to come along. Why Monday? Because that’s the day I’m going back to Stockholm again. Once there, I’ll spend a couple of weeks spending time with friends and family, and then I will go and vow fidelity and those other things. The 25th of August, in case you’re about to ask.

All in all, this means that posting will be sparse if existent until mid-September – when I arrive, fresh out of my honeyforthnight, to Sydney; where the Magma research group host me for some 5-odd weeks. There I expect to have office space, an internet connection and a computer.

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Politics and absences

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Today I received an email kind of convincing me that my blog gets seen. It offered me $35 to put up an add for a phone service on one of my old blog posts.

What differentiated this offer from all other spam I get was that it was actually written well enough, and tailored enough, that I believe this guy would even go through with it. Only …

I am not interested.

I run this blog because I like running it. I do system admin myself too. The domain name is mine since my family wants it, and my parents chip in. The net connection also is something that the family chips in on, and is handled without significant cost.

All in all, I do not NEED ads to keep this place up and running.

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Advertising policy

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… or another bout of more-or-less shameless self-promotion.

I took the initiative, and invited some of the relevant Powers That Be to start an -themed group blog: The Infinite Seminar.

I also perceived a lack of blog aggregators, so I started Planet Math Blogseminars to aggregate group blogs in mathematics.

While I was at it, I bought the blogseminar.net domain. I’d be happy to allocate subdomains of this to decent enough blogs that wants in on it.

(78 words, 1 image)

The new carnival of mathematics is up over at PolyMathematics.

Yours truly is featured, but other than that, there seems to be heavy overweight on the educator side.

Do we have the volume for a Carnival of Research Mathematics?

(40 words)

One thing that has been bugging me for quite some time with AucTeX (which I love, in general) has been that I wasn’t able to reset the bloody hot key for math mode input.

The original setting maps to Shift-key left of backspace-space, since it’s an accent key which I occasionally use for .. y’know .. accenting letters, and thus don’t want immediate output from. And `M-x set-variable LaTeX-math-abbrev-prefix` didn’t do anything close to what I expected.

Today, I, on a whim, go and search the auctex mailing list archives for this. And lo and behold! One of the first messages tells me that I need to do `M-x customize-variable LaTeX-math-abbrev-prefix`. So I do, and it has my changes already, but not committed, so after committing the changes I try it out and it just works!

This should speed up usage of Emacs for me a bit.

(148 words)

These are the times that eat my productivity. The times that ensure that entire days go by and I afterwards feel nothing have happened at all. These times that are too short for productive work – where I know from the beginning that I cannot sit down and *do something* – too little time for reading, for coding, for writing, for .. well .. anything. And yet, while trying to get through them, they are obviously too long. An hour here, an hour there, interspersed with lunch, then coffee, then a seminar, and all of a sudden out of an 8 hour workday, the only vaguely productive thing that got done was hearing the seminar.

Fragmentation kills my productivity. With a fragmented workday, I have the time available neatly chopped up in pieces of free time that fall in-between. That are too short, but yet cover almost the entire workday.

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In-between times

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ComplexZeta asked me about the origins of my intuitions for homological algebra in my recent post. The answer got a bit lengthy, so I’ll put it in a post of its own.

I find Weibel very readable – once the interest is there. It’s a good reference, and not as opaque as, for instance, the MacLane + Hilton-Stammbach couplet can be at points.

The interest, however, is something I blame my alma mater for. Once upon a time, Jan-Erik Roos went to Paris and studied with Grothendieck. When he got back, he got a professorship at Stockholm University without having finished his PhD. He promptly made sure that nowadays (when he’s an Emeritus stalking the halls) there is not a single algebraist at Stockholm University without some sort of intuition for homological algebra.

So, my MSc advisor, J

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This term of teaching ends next week.

When I got back from T’bilisi, just over a month ago, I had research leads that I expect will end in three different publications.

I was slated with writing one LARP report for a swedish gaming magazine, and a series of various popular mathematics articles for the local student-run mathematics magazine here.

All in all, very many things converged this June/July for me.

It has started paying off though – the gaming article is published, and yesterday I submitted the first of the T’bilisi articles to the Journal of Homotopy and Related Structures as well as to the arXiv.

I now am listed on the arXiv with three papers, out of which one is already published, one is rejected (not unjustly so), and one is just submitted for review.

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Slumps and crunches

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I seem to have become the Goto-guy in this corner of the blogosphere for homological algebra.

Our beloved Dr. Mathochist just gave me the task of taking care of any readers prematurely interested in it while telling us all just a tad too little for satisfaction about Khovanov homology.

And I received a letter from the Haskellite crowd – more specifically from alpheccar, who keeps on reading me writing about homological algebra, but doesn’t know where to begin with it, or why.

I have already a few times written about homological algebra, algebraic topology and what it is I do, on various levels of difficulty, but I guess – especially with the carnival dry-out I’ve been having – that it never hurts writing more about it, and even trying to get it so that the non-converts understand what’s so great about it.

So here goes.

This is a preview of

The why and the what of homological algebra

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They simply do not end. Now, Cornell grads and pre-grads have started the Everything Seminar – which has absolutely brilliant discussions about the forbidden minor theorem in graph theory as well as a fascinating overview over constructing homological algebra as embedded in the theory of modules over .

Connected to this comes the observation that by constructing calculus using the tricks used in synthetic differential geometry, we end up with – again – modules over , and some very fascinating discussions are sparked as to subtle and interesting connections between these two viewpoints!

How on earth I am going to keep up with the interesting sprouting discussion group blogs I shall never know. Maybe it’s getting to the point where we’ll start an -blog?

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Too harried to blog.

Will miss this carnival.

Bugger.

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Is now up at Math Notations. The current host further suggests a split in undergrad+ and undergrad- categories – with the simpler and didactics focused posts in one carnival and the research and/or advanced mathematical posts in another. Personally, I think the momentum the carnival has is a good thing, and that a split should wait until we habitually turn away more posts than we’re comfortable with. This volume is not yet actually there – wherefore I’d be against a split.

Enjoy.

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right here – at least if you’re wondering what happened with my recent interview.

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All the cool kids are doing it, so I’ll tag in too.

There’s a secret blogging seminar going on. And the people seem to be writing interesting things – what little they managed to write before the hushed rumour mill started.

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