1. # Classifying spaces and Haskell

Published: Thu 15 May 2014

I've been talking with some topologists lately, and seen interesting constructions. I think these may potentially have some use in understanding Haskell or monads.

Simplicial objects

A simplicial object in a category is a collection of objects $C_n$ together with n maps $d_j:C_n\to C_{n-1}$ and n ...

2. # Topology of Politics — Popular topology lecture

Published: Fri 21 September 2012

I will be speaking on my research into topological data analysis for political data sets at the University of Edinburgh, at 4:10pm on 15th October, in Room 6206, James Clerk Maxwell Building.

## Data Analysis on politics data

Data analysis has played a growing role in politics for many years ...

3. # Jonas Thente och innumeracy

Published: Mon 02 July 2012

Jonas Thente har tyckt till på DN. Matematik är ett föråldrat skolämne, eftersom alla har miniräknare.

Jag har en historia jag hörde idag, som jag skulle vilja ta upp. En god vän (och universitetslärare i matematik) till mig förklarade hur han gör för att hantera fuskare på hans matematiktentor. Han ...

4. # Recursively counting numbers with fixed bit counts

Published: Sun 13 May 2012

I ran across this problem in a reddit side-bar job-ad, and was intrigued by the task (description paraphrased to decrease googleability):

Write a function
 uint64_t bitsquares(uint64_t a, uint64_t b);
such that it return the number of integers in [a,b] that have a square number of bits set to ...
5. # ATMCS 5 in Edinburgh

Published: Thu 22 March 2012

## ATMCS 5 - Algebra and Topology, Methods, Computing, and Science

### Second Announcement

This meeting will take place in the period July 2-6, at the ICMS in Edinburgh, Scotland. The theme will be applications of topological methods
in various domains. Invited speakers are
J.D. Boissonnat (INRIA Sophia Antipolis) (Confirmed)
R. Van ...
6. # BibLaTeX — why haven't I used this earlier!?

Published: Wed 07 March 2012

As any reader of this (now rather occasional) blog might have guessed by now, I do quite a lot of writing in LaTeX. It comes with the territory — I do mathematics research, so I write in LaTeX. I do quite a bit of research, so I spend a lot of ...

7. # Collaborative tools

Published: Fri 17 February 2012

I do quite a bit of collaboration. In fact, since after my PhD research, I have written exactly one preprint that does NOT spring from a collaboration. And there is quite a bit of technological support that flows into a good collaboration of mine. Here are some of the tools ...

8. # A quick python hack for a mathematical puzzle

Published: Sat 12 November 2011

So, today I saw this in my Twitter feed:

«Phil Harvey wants us to partition {1,…,16} into two sets of equal size so each subset has the same sum, sum of squares and sum of cubes.» -- posted by @MathsJam and retweeted @haggismaths.

Sounds implausible was my first though. My ...

9. # Some thoughts on fire photography

First off: I would like to apologize to the readers I still have that I never get around to updating here. I am aware that I'm writing less than once I was planning to.

Aaaaanyway.

I have grown very interested in photography, as those of you who have seen ...

10. # Geometric realization of simplicial sets

Published: Tue 01 March 2011

This post is an expansion of all the details I did not have a good feeling for when I started with for page 7 of Goerss-Jardine, where the geometric realization of simplicial sets is introduced.

The construction works by constructing a few helpful categories, and using their properties along the ...

11. # The Topology of Politics

Published: Tue 04 January 2011

This is a typed up copy of my lecture notes from the seminar at Linköping, 2010-08-25. This is not a perfect copy of what was said at the seminar, rather a starting point from which the talk grew.

In my workgroup at Stanford, we focus on topological data analysis — trying ...

12. # Species, derivatives of types and Gröbner bases for operads

Published: Sat 18 December 2010

This is a typed up copy of my lecture notes from the combinatorics seminar at KTH, 2010-09-01. This is not a perfect copy of what was said at the seminar, rather a starting point from which the talk grew.

In some points, I've tried to fill in the most ...
13. # Teaching and seminars up ahead

I'll be talking quite a bit in the next couple of weeks; here's a “heads up” for those who might want to come and listen.

25 August, 1pm, Linköpings Universitet. The topology of Politics.

1 September, 10am, KTH. Combinatorial species, Haskell datatypes and Gröbner bases for operads.

1 ...

14. # Itinerary for the Summer

A few things that may interest people.

1. I'm going on the job market in the fall. I'm looking for lectureships, tenure tracks, possibly 2 year postdocs if they are really interesting.

15. # Repeal the nth amendment

Published: Wed 24 March 2010

Inspired by this post over at Making Light, here, have a chart:

First, Second, ...

1st, 2nd, ...

And, because this chart is kinda tricky to read, here's the log-scaled version of the same chart:

For the log-chart, I stopped stacking the numbers.

ETA: Changed the log-chart from a line-chart to ...

16. # Another kind of sports reporting

Published: Tue 23 February 2010

Inspired by John Allen Paulos, who just now tweeted

Obvious, but NBC hasn't said: Canada, Norway, Germany way ahead of US in Olympic medals per capita. Many ways to rank: Cf. Arrow's theorem.

I decided to redo the medals list. Here, the number of medals per capita among ...

17. # Testing out the wplatex package

Published: Wed 03 February 2010

Eric Finster, over at Curious Reasoning has built a python script to allow you to write Wordpress posts entirely in LaTeX , and upload them. The script parses the LaTeX code and generates HTML that expresses the same structure.

This, here, is me trying it out. With any luck, the appearance ...

18. # Coordinatization with hom complexes

Published: Mon 07 December 2009

These are notes from a talk given at the Stanford applied topology seminar by Gunnar Carlsson from 9 Oct 2009. The main function of this blog post is to get me an easily accessible point of access for the ideas in that talk.

## Coordinatization

First off, a few words on ...

19. # [MATH198] Lecture 10 (last lecture) posted

Now up: Lecture 10 with the definition of a topos and a derivation of internal, inutitionistic logic within a topos.

20. # [MATH198] Lecture 9 posted and lectured

Lecture 9: Catamorphisms, Anamorphisms, more from that zoo; adjunctions, some properties and some examples.

21. # [MATH198] Multiple lectures posted

I have been remiss in updating here. Since the last time I posted, I have posted:
Lecture 6, featuring some interesting limits and colimits, culminating in the introduction of adjoints.

Lecture 7, featuring the introduction of monads based in adjoints, with the connection between the monoid of endofunctors and the ...

22. # [MATH198] Lecture 5 is up

And, as it turns out, my logic-fu is lacking. Next time around, it's likely I talk about the CCC = typed λ-calculus correspondence, but won't try to actually produce the correspondence explicitly.

23. # [MATH 198] Lecture 4 and a question for the community

Lecture 4 was held, and the notes are up on the wiki: Lecture 4 notes

During class, and in unrelated conversations afterwards, though, the question emerged:

If Formally differentiating datatypes gives us zippers? What happens if we formally integrate datatypes?

24. # [MATH 198] Second lecture

I've been maddeningly slow lately. With everything.

Since last week Wednesday, the second lecture is up on the Haskell wiki.

25. # [MATH198] Lecture 1 now online

The first lecture has been successfully held. The notes - which may well be augmented once I get hold of the students' notes - are online on the Haskell Wiki

26. # [Stanford] MATH 198: Category Theory and Functional Programming

Published: Sat 29 August 2009

Category theory, with an origin in algebra and topology, has found use in recent decades for computer science and logic applications. Possibly most clearly, this is seen in the design of the programming language Haskell - where the categorical paradigm suffuses the language design, and gives rise to several of the ...

Published: Wed 22 July 2009

Dear blogosphere,

come this fall, I shall be teaching. My first lecture course, ever.

The subject shall be on introducing Category Theory from the bottom up, in a manner digestible for Computer Science Undergraduates who have seen Haskell and been left wanting more from that contact.

And thus comes my ...

28. # Guess the plots!

What do these depict?

Here are two others. Different data source, different point in time, but what are they?

They are all linked in pairs - one coloured and one black linked together. They are not sports related. And they are taken from real world data. The colours are relevant and ...

29. # Mapping zipcodes in R

Published: Wed 13 May 2009

I started fiddling around with R again, and ended up playing with a zipcode database.

So, first I downloaded the zipcode database at Mapping Hacks, and unpacked the zipfile in my working directory.

Then, I loaded the data into R

> zips <- read.table("zipcode.csv",sep=",",quote="\"",header=TRUE)
> names ...
30. # Gröbner bases for Operads — or what I did in my vacation

Published: Fri 08 May 2009

This post is to give you all a very swift and breakneck introduction to Gröbner bases; not trying to be a nice and soft introduction, but much more leading up to announcing the latest research output from me.

Recall how you would run the Gaussian algorithm on a matrix. You ...

31. # 1-manifolds and curves

Published: Sat 02 May 2009

I have been painfully remiss in keeping this blog up and running lately. I wholeheartedly blame the pretty intense travel schedule I've been on for the last month and a half.

To get back into the game, I start things off with a letter from a reader. Rodolfo Medina ...

32. # Applied knot theory

Published: Mon 16 March 2009

Tech note: All figures herewithin are produced in SVG. If you cannot see them, I recommend you figure out how to view SVGs in your browser.

A few weeks ago, my friend radii was puzzling in his server hall. He asked if it was possible to prove that what he ...

33. # Picking fights over religion

I suspect this will be a flame war magnet. On the other hand I feel compelled to write it.

First a bit of backstory. My wife enjoys, often and with engagement, discussing theology with her new friends. One of them, a pentecostal christian, gave her the book I don't ...

34. # Homological Inclusion-Exclusion and the Mayer-Vietoris sequence

Published: Fri 09 January 2009

This blogpost is inspired to a large part by comments made by Rob Ghrist, in connection to his talks on using the Euler characteristic integration theory to count targets detected by sensor networks.

He pointed out that the underlying principle inducing the rule

57. # Building my academic persona

Published: Fri 18 January 2008
Just got accepted for publication in the Journal of Homotopy and Related Structures.

Damn, this feels good!

58. # AMS-MAA JMM 2008 Liveblogging, day 4 - final day

Published: Thu 10 January 2008

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 ... read more 59. # AMS-MAA JMM 2008 Liveblogging, day 3 Published: Wed 09 January 2008 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 ... read more 60. # AMS-MAA JMM 2008 Liveblogging, day 2 Published: Tue 08 January 2008 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 ... read more 61. # JMM Blogger Meetup! Published: Mon 07 January 2008 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 ... read more 62. # AMS-MAA JMM 2008 Liveblogging, day 1 Published: Mon 07 January 2008 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 ... read more 63. # AMS-MAA JMM 2008 Liveblogging, day 0 Published: Sun 06 January 2008 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 ... read more 64. # Calling all San Diego participants and Californians Published: Thu 20 December 2007 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 ... read more 65. # The year 2007 in review Published: Wed 19 December 2007 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 ... read more 66. # Papers status Published: Sun 16 December 2007 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 ... read more 67. # Planning the future Published: Fri 14 December 2007 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 ... read more 68. # Riding the Google Charts API bandwagon Published: Thu 13 December 2007 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 ... read more 69. # Pluralization in Rails Published: Sun 09 December 2007 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 ... read more 70. # Reaching for the postdoc world doorknocker Published: Wed 05 December 2007 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 ... read more 71. # Synaesthesia and cognition Published: Mon 03 December 2007 In Blogs. 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 ... read more 72. # Checking email 4000 times a day Published: Tue 20 November 2007 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 ... read more 73. # Comments temporary disabled Published: Mon 19 November 2007 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. read more 74. # High school topology restarting Published: Fri 16 November 2007 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 ... read more 75. # Beef sous vide 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 read more 76. # Wreath products Published: Mon 29 October 2007 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 $$H ... read more 77. # Progress Published: Wed 26 September 2007 dynkin:~/magma> magma Magma V2.14-D250907 Wed Sep 26 2007 13:19:51 on dynkin [Seed = 1] Type ? for help. Type -D to quit. Loading startup file "/home/mik/.magmarc" > Attach("homotopy.m"); > Attach("assoc.m"); > Aoo := ConstructAooRecord(DihedralGroup(4),10); > S := CohomologyRingQuotient(AooR); > CalculateHighProduct(Aoo,[x,y,x ... read more 78. # Settling in in Sydney No mathematical content today. However, I do note that the mathematics department in Sydney is located in a building as drab and boring as the Stockholm University main building. Its main architectural feature is the pale, washed out blue panels on the upper parts of the hollow concrete slab. Just ... read more 79. # Still away However, I am enjoying the Scottish countryside and just - today - turned [tex]3^3$$ years of age. read more 80. # Coq and simple group theory Published: Sun 05 August 2007 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 ... read more 81. # Advertising policy Published: Wed 01 August 2007 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 ...

82. # New additions to the blogosphere

Published: Sun 29 July 2007

... 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 $$*_\infty$$-themed group blog: The Infinite Seminar.

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

83. # 13 on a friday

Published: Fri 27 July 2007
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?

84. # AucTeX hackery

Published: Tue 17 July 2007

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 ...

85. # In-between times

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 ...

86. # Today seems to be a day for posting...

Published: Thu 12 July 2007

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 ...

87. # Slumps and crunches

Published: Thu 12 July 2007

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 ...

88. # The why and the what of homological algebra

Published: Thu 12 July 2007

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 ...

89. # Blogging seminars - a new fad!

Published: Fri 06 July 2007

97. # 8th Carnival of Mathematics

Published: Sat 19 May 2007

Is up at the GeomBlog.

This fortnight has a lot of goodies, among those a call for reading Grothendieck and a blogpost by Ian Stewart.

98. # 7th Carnival of Mathematics

Published: Fri 04 May 2007

I have been somewhat remiss in announcing these lately - but over at nOnoscience, the 7th Carnival of Mathematics just got posted.

I'm featured again - as are many other very readable bloggers. Go. Read.

99. # Young Topology: The fundamental groupoid

Published: Fri 04 May 2007

Today, with my bright topology 9th-graders, we discussed homotopy equivalence of spaces and the fundamental groupoid. In order to get the arguments sorted out, and also in order to give my esteemed readership a chance to see what I'm doing with them, I'll write out some of the ...

100. # Interview with a blogger

Published: Mon 30 April 2007

The website/forumsite Mathetreff, run by the Bezirksregierung (region government) D

101. # Modular representation theory - when Maschke breaks down

Published: Sat 21 April 2007

This post is dedicated to Janine K

102. # looksay - today's Haskell snippet

Published: Wed 18 April 2007
nextLookSay = foldr (\xs -> ([length xs, head xs]++)) [] . group
lookSay = iterate nextLookSay [1]
`

Conway's Look-and-say sequence

103. # iTeX2MML not activated

Published: Fri 06 April 2007

I just tried installing the iTeX2MML plugin from Jacques Distler. This is what the n-Category Cafe use for their mathematics, and it gives a neated display than the LaTeXrender plugin I've been using so far.

It turns out, though, that
1. The plugin jumps on quoted perl code, interpreting ...
104. # Modular representation theory: Simple and semisimple objects

Published: Mon 02 April 2007

## Representations of categories

The basic tenet of representation theory is that we have some entity - the group representation theory takes a group, the algebra representation theory most often a quiver, and we look at ways to view the elements of the structure as endomorphisms of some vectorspace. The attentive reader ...

105. # Sudden responsibilities

I just met up with the workgroup in the Deutsche Mathematikervereinigung (German Association of Mathematicians) with interest spanning "Information and Communication" - which turns out to mean that they care about libraries, about communicative tools for mathematicians, and spend their time thinking about these things, and meeting at conferences.

Met up ...

106. # 4th Carnival of Mathematics posted

Published: Fri 23 March 2007

The fourth Carnival of Mathematics is up at EvolutionBlog.

Featured this time around are homological algebra, representation theory, Rubik's cube solutions, Bernoulli processes, topology, number theory, and much much more.

107. # Representation theory - basics

Published: Wed 21 March 2007

Many interesting groups have a very geometrical definition: transformations that fix certain symmetries is one of the historical origins of group theory.

Thus, one of the most interesting classes of finite groups are the rotation and reflection symmetries of a regular polygon. These are called $$D_n$$, for a ...
108. # Carnival of Mathematics #3

Published: Fri 09 March 2007

And it is with pride that I welcome you all to my first issue, and the third issue all in all, of the Carnival of Mathematics. I probably should apologize as well - my announcement stated March 8th, but that was before I really looked at the dates involved, so we ...

109. # Bright students and topology

Published: Fri 02 March 2007

Today, I started an experiment together with the local specialised secondary school. I'll be taking care of two of their brightest students, meeting them roughly once a week, and taking them on a charge through algebraic topology. At the far end shimmers knot theory and other funky applications; and ...

110. # The Order of the Science Scouts of Exemplary Repute and Above Average Physique

These badges are also displayed on my About page, but the explanation why merits a blog post of its own.

For one thing, I blog about the stuff. I also was a radio speaker at the time that Radio Unga Forskare ...
111. # More silly random text

Published: Fri 09 February 2007

Syntaxfree writes over at his blog about a silly little toy he wrote, using the PFP library, to generate random text.

Now, his text is unreadable. I mean, it's even unpronounceable. Why? Because he's looking at bigram distributions of letter.

Great, I thought, I'll do him one ...

112. # Announcing the Carnival of Mathematics

Published: Fri 02 February 2007

Alon Levy, over at Abstract Nonsense has just announced the first issue of a brand new Blog Carnival: the Carnival of Mathematics.

Go take a look. Submit your own blog posts. And then check it out in a week - the carnival is scheduled for the 9th.

113. # On religion

Published: Sat 27 January 2007

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 ...

114. # Retrospection 2006

Published: Sat 30 December 2006

Inspired by other bloggers on Planet Haskell, I thought I'd just sit down and write a retrospection post, reviewing the past year - primarily from angles such as mathematics, computers and my generic life situation.

It divides neatly into two different sections: the months as a commercial programmer and the ...

115. # An A∞-structure on the cohomology of D8

Published: Thu 30 November 2006

As a first unknown (kinda, sorta, it still falls under the category of path algebra quotients treated by Keller) A-calculation, I shall find the A-structure of $$H^*(D_8,\mathbb F_2)$$.

To do this, I fix the group algebra
$$\Lambda=\mathbb F_2[a,b]/(a^2 ... read more 116. # A∞-algebras and group cohomology Published: Thu 23 November 2006 In which the author, after a long session sweating blood with his advisor, manages to calculate the A-structures on the cohomology algebras [tex]H^*(C_4,\mathbb F_2)$$ and $$H^*(C_2\times C_2,\mathbb F_2)$$.

We will find the A-structures on the group cohomology ring by ...

117. # Why Blog?

Published: Thu 16 November 2006

The Community College Dean has written about why he blogs, and asks any and all readers to tack on to his effort.

My blog is not very anonymous. It is occasionally personal, occasionally political and throughout a venting location for thoughts, and a place where I formulate myself in higher ...

118. # A∞ for the layman

Published: Tue 07 November 2006

I recently had reason to describe my PhD work in complete laymans terms while writing letters to my grandparents. This being a good thing to do in order to digest your ideas properly, I thought I might try and write it up here as well.

It will, however, push through ...

119. # Prototyping thought

Published: Sat 28 October 2006

In a recent post, pozorvlak reminded me of one of the reason it is important to have a good, obvious, and quick-to-write programming language around.

He, as I, is a mathematician, spending his time thinking, finding patterns, and trying to formulate (more or less) absolute proof that his patterns hold ...

120. # Weekly Report: Parties and lectures

Published: Sun 22 October 2006

The term has started. In full force. No seating in the lunch cafeteria, lot's of people all over the place, lot's and lot's of new students, and lectures and examples classes kicking off all over the place.

I'm leading an example class this year: linear algebra ...

121. # A-infinity and Hochschild cocycles

Published: Fri 20 October 2006

This blogpost is a running log of my thoughts while reading a couple of papers by Bernhard Keller. I recommend anyone reading this and feeling interest to hit the arXiv and search for his introductions to A-algebras. Especially math.RA/9910179 serves as a basis for this post.

If ...

122. # Computational Group Theory in Haskell (1 in a series)

Published: Wed 18 October 2006

This term, I'm listening to a lecture course on Computational Group Theory. As a good exercise, I plan to implement everything we talk about as Haskell functions as well.

The first lecture was mainly an introduction to the area, ending with a very na

Published: Tue 10 October 2006

I just submitted a paper to a journal.

Based on research I have done during my time as a PhD student.

Wish me luck.

Update:If you want to read the paper, I suggest you go look at arXiv:math.GR/0610374.

124. # Weekly Report: Settling down again

Published: Sun 08 October 2006

I get the feeling that my pledge to write the weekly reports regularily has been less than successful. So I'll try to renew that pledge: I shall try to keep up the regularity of my weekly report.

Since last authored, I have been running a mathematics camp for 10th ...

125. # OpenGL programming in Haskell, a tutorial (Part 2)

Published: Tue 19 September 2006

As we left off the last installment, we were just about capable to open up a window, and draw some basic things in it by giving coordinate lists to the command renderPrimitive. The programs we built suffered under a couple of very infringing and ugly restraints when we wrote them ...

Published: Thu 14 September 2006

Since the content rate of haskell-related posts is going up, the feed of this blog will get added to Planet Haskell. Hi, Planet!

127. # OpenGL programming in Haskell - a tutorial (part 1)

Published: Thu 14 September 2006

After having failed following the googled tutorial in HOpenGL programming, I thought I'd write down the steps I actually can get to work in a tutorial-like fashion. It may be a good idea to read this in parallell to the tutorial linked, since Panitz actually brings a lot of ...

128. # Monthly Report: Conference summer draws to an end

Published: Mon 11 September 2006

I haven't really been updating much here - and especially not the category Weekly Report. Slowly, it's time to get around to it.

Now, there is a specific reason updates have been slow: I've been travelling. A lot. With very varying internet access and even more varying energy ...

129. # Localisation and ring depth

Published: Tue 05 September 2006

So, we're back at the point where I'm hesitating whether what I tried to work out even made sense or not. So I'll do a write up of all the things I feel certain about asserting, and ask my loyal readership to hunt my errors for me ...

130. # Carry bits and group cohomology

Published: Thu 27 July 2006

Got treated today to a really nice workout in group cohomology; most of which is well worth sharing, since seeing it done once gave me a lot of insight.

So, if we pick $$\mathbb Z/10$$ and view it as the set 0,1,2,3,4,5 ...
131. # Todo and accomplishments

Published: Mon 24 July 2006

Accomplished:

• I am done with the coursework for the past semester. Sent off the TeXed up solution sheets to the webmaster today.
• My pattern observation seems to hold up surprisingly well - there seems to be a theorem to fetch out there somewhere.
• I have done most of the dishes. Go ...
132. # Weekly Report: Back up again

Published: Sun 23 July 2006

The weekly reports have been dead for a while. Reason? The blog has been dead for a while.

## Hardware woes

The old computer running this website had some problem all of a sudden about 3 weeks ago. These problems appeared as a complete lockdown of the system - no response to ...

133. # Triangulated categories

Published: Mon 17 July 2006

One predominant tendency in the algebra/category theory camp is to seek out the minimal set of conditions needed to be able to perform a certain technique, and then codifying this into a specific axiomatic system. Thus, you only need to verify the axioms later on in order to get ...

134. # Group cohomology revisited: Quaternionic unit group

Published: Tue 20 June 2006

In a previous installment, we calculated $$H^*(D_8)$$ with some amount of success. For that post, I said that I was going to calculate the cohomologies of $$D_8$$ and of $$U(\mathbb H)$$ by hand - and I've been at it for the latter ...

Published: Mon 19 June 2006

This blog just migrated to WP 2.0. Should anything be odd, please notify me.

The migration was to a large portion motivated by commenting problems I've been told about. I hope that my readers out there will be able to comment now; possibly even without logging in!

136. # Weekly Report: Power tourism

Published: Sun 18 June 2006

It's been a while since I managed to write one of these. The reason is simple enough - my weekends have been packed; and I don't get around to it during the weeks.

During the last three weekends, first my parents and my brother, and then for the last ...

137. # More group cohomology

Published: Thu 08 June 2006

My advisor told me to go hit $$D_8$$ and $$U(\mathbb H)$$ as my next two cohomology calculation projects; try to do them with resolutions by hand so that I get a feeling for what's going on. After failing spectacularily both at getting a resolution ...

Published: Tue 06 June 2006

I just received in the mail a bunch of prints. Of my article "Computation of Poincaré-Betti series for monomial rings", produced from my Master's thesis for the "School and workshop on computational algebra for algebraic geometry and statistics" in Torino 2004. It is now being published in the Rendiconti ...

139. # My first group cohomology - did I screw up?

Published: Sun 21 May 2006

I thought the seminar on tuesday would possibly benefit from something not very often seen - explicit examples. So I started working through one. I wanted to calculate $$H^*(C_8,\mathbb F_2)$$ and give explicitly in a series of ways the product structure - as Yoneda splices, as chain map ...

140. # Weekly Report: From 0 to 100 in 6 seconds flat!

Published: Sat 20 May 2006

This is the second weekend in a row spent to more or less large part in the office, working with the product structures on cohomology. Reason for this is that I'm getting my share of the department seminars now - I'm to walk us through the Yoneda cohomology product ...

141. # Weekly Report: Mathematics makes my ears bleed

Published: Sun 14 May 2006

I'm back in Jena now. The last week was spent working myself to the brink of unconsciousness trying to grasp homotopical algebra, simplicial objects, model categories and any and all things Alex sent my way. With some 6-8 hours each day spent on lectures and discussions explicitly held to ...

142. # Weekly Report: Preparing to leave

Published: Sun 07 May 2006

I left Jena going to Stockholm on Saturday. Thus, much of the week past has been spent in preparation for the trip - reading up on homotopical algebra; getting all the paperwork together and getting my things together for the trip.

Along with "Make sure you learn homotopical algebra" and "Get ...

143. # Weekly Report: Forgot all about it!

Published: Thu 04 May 2006

Right. It's thursday. And I had some sort of hopes to do my weekly reports on saturdays. Only, last saturday found me back in Nuremburg, in the middle of a marathon party-after-party session with the RPG crowd there.

Last week was very much characterized by getting various conditions for ...

144. # Reading Merkulov: Differential geometry for an algebraist (4 in a series)

Published: Mon 24 April 2006

Suppose we have a presheaf $$\mathcal F$$ of abelian groups over $$M$$ and pick a point $$x$$. On the collection of all abelian groups defined over some neighbourhood of $$x$$ (disjoint union) we put an equivalence relation which identifies $$f\in ... read more 145. # Weekly report: Settling in Published: Sat 22 April 2006 My first week has passed. Today is saturday; and the move took place monday. So far, I've been running around doing bureaucracy and little else (I managed to leaf through the first 5 pages of Evens: Cohomology of Groups). Along the lines - I've received a summons to appear ... read more 146. # Question for the mathematical audience Published: Thu 20 April 2006 I have now been staring at this particular sentence for way too long, and thus will start using any and all communication lines I can find to get assistance. Either I'm being way too stupid, or the author neglects to mention some salient detail. Setup: [tex]\phi\colon G ... read more 147. # Weekly posts - a new feature at this blog Published: Sat 15 April 2006 Now that my blog returns to its status of a PhDiary as I actually got a PhD position, I will introduce one flavour of regular postings. Instead of keeping in touch with people by mailing lists, livejournal, and everywhere else, there will be weekly postings here about life as a ... read more 148. # Why I keep organizing congresses Published: Wed 05 April 2006 Once upon a time, I wasn't passionate about mathematics. Up to grade 6, I even disliked it quite a bit - it consisted of only mechanical plugging away of numbers, and training of multiplication tables that I had the feeling I already mastered. Then something changed. Subtly at first - in ... read more 149. # Report from Villars (5 in a series) Published: Sun 12 March 2006 For the last two half-days of the conference, I managed to take a break in skiing precisely when the conditions were at their very worst; with sight down to a few meters and angry winds. Miles Gould and Arne Weiner, however, managed to sit in a chair lift that kept ... read more 150. # Report from Villars (4 in a series) Published: Wed 08 March 2006 I haven't been able to get around to skiing since the last update - I may, or may not, go out in the slopes after this updates. The weather is growing warmer and wetter; and doesn't really invite to skiing as it previously did. However, we have had more ... read more 151. # Report from Villars (3 in a series) Published: Tue 07 March 2006 This post will concern tuesday morning. Tuesday evening will be in a later post. With the morning thus came, again, the pain in the legs. However, I'm told it'll be better if I keep on skiing. The mathematics in this report will come sooner than in the last ... read more 152. # Report from Villars (2 in a series) Published: Mon 06 March 2006 So we hit the pistes during monday morning, those of us who actually already are here. Me, Bruno Vallette (Hi Stockholm!), Arne Weiner, Miles Gould, Paul Eugene Parents and Jonathan Scott, Dev Sinha and Muriel Livernet. Skiing was MARVELOUS. Me, Arne and Miles shot off on our own, and damn ... read more 153. # Report from Villars (1 in a series) Published: Sun 05 March 2006 So, I've arrived in Villars sur Ollon for the Alpine Operad Workshop. The travel was long and at times annoying, mainly because the heavy snowfall over München and Zürich and some other places in the region triggered extreme delays. As we were supposed to board, the poor attendant at ... read more 154. # Anti-spam measures Published: Tue 21 February 2006 After having a visit of some 5+ spams (I'm known by the spam bots! Is that good?) I just installed a captcha-like plugin. It requires some basic arithmetic skills from y'all; but on the other hand, I -am- a math blog after all. read more 155. # Reading Merkulov: Differential geometry for an algebraist (3 in a series) Published: Mon 13 February 2006 Since I cannot concentrate anyway, here comes the third installment of my reading Merkulov. We now get to the funky stuff - introducing sheaves and getting to what should be at the very start of basically any modern geometry course. At least if I am to believe the geometers I know ... read more 156. # This came faster than expected... Published: Mon 13 February 2006 Breaking news! Just in from /. According to this article, there is a Cincinnati-based company that just had two of its employees implant glass-encapsulated RFIDtags in their biceps as a part of the access control system to their datacenter. And we're one step closer to the artificial linking of identity ... read more 157. # Reading John M. Lee - Introduction to Smooth Manifolds (1 of 1) Published: Sun 12 February 2006 If I'm going to take this renewed interest in trying to understand differential geometry more seriously, I might as well read more than one source on it. So, I'll start a sequence of posts on this book as well. Just as Merkulov, Lee starts with a short definition ... read more 158. # Reading Merkulov: Differential geometry for an algebraist (2 in a series) Published: Sat 11 February 2006 So, in the last installment, we got to know smooth manifolds and charts, atlases and some nice topological tricks and tweaks. For this round, we follow Merkulov onward, and pretty soon stumble across category theory and sheaves. The notes I'm following here are from the link on Merkulov's ... read more 159. # Reading Merkulov: Differential geometry for an algebraist (1 in a series) Published: Sat 11 February 2006 I'll do this in posts and not pages on further thought... Sergei Merkulov at Stockholm University gives during the spring 2006 a course in differential geometry, geared towards the algebra graduate students at the department. The course was planned while I was still there, and so I follow it ... read more 160. # New blog found! Published: Fri 10 February 2006 Stumbling across the blog Epsilon-Delta with a brilliant article series on mathematics as key to effective programming. This in itself merits a closer look at the blog; which in turn merits it a place in my blogroll. Go and read it you too! read more 161. # Borsuk-Ulam and West Wing Published: Tue 07 February 2006 In West Wing 4x20, CJ states that there are two antipodal points with identical temperature on the earth, as an argument why it should be possible to imagine that an egg could stand on its end at the spring equinox. This particular plotline also has her most emphatically claiming that ... read more 162. # Introduction to Algebraic Topology and related topics (I) Published: Sun 01 January 2006 In the spirit of writing some sort of introductory posts to the things related to what I'm about to spend several years thinking and writing about, I thought I'd try to make a (more or less) layman friendly introduction to Homology and Homotopy. It's all residing in ... read more 163. # Some math-y jokes Published: Sun 01 January 2006 You may have seen some of these before... [tex]\frac{1\cancel{6}}{\cancel{6}4}=\frac{1}{4}$$

$$\frac{1\cancel{9}}{\cancel{9}5}=\frac{1}{5}$$

$$\frac{\partial}{\partial x}\sin^2(x)=\sin(2x)$$ -- just move down the 2.

Published: Sat 31 December 2005
Botten:
100g hasselnötter
1 msk kakao
3 tsk farinsocker
(1 msk rom)
30g smält smör
Fyllning:
30g smör
3 äggulor

Tillbehör: Färska frukter och bär

Samtliga botteningredienser mixas i ...
165. # The role of almonds in Swedish marital trends

Published: Fri 30 December 2005

## The role of almonds in Swedish marital trends

Mikael Johansson, Susanne Vejdemo

### Abstract

In this paper, we investigate the Swedish folkloristic belief that almonds in the Christmas rice porridge will lead to marriage. We offer a falsification of this hypothesis.
Keywords: Christmas traditions, almonds, porridge, marriage

### Introduction

One old folk ...
166. # Calligraphy before christmas

Published: Fri 23 December 2005

I sat down and started my calligraphy again recently. A few of the things I've done have not been saved for posteriority, but a few of them have been scanned and are available for display.

All images are clickable for the full version.

First, a sampling of the inks ...
167. # EU Parliament clubbing Big Brother light

Published: Thu 15 December 2005

Since roughly september, a resolution has been making its way through the EU bureaucracy to institute mandatory storage times for, among other things, internet traffic logs with ISPs. Throughout the discussions, the image has been coming through that the resolution would in endeffect require ISPs to log more or less ...

168. # New directions!

Published: Tue 06 December 2005

The byline is probably the most basic motivation for the blog. I want a place to write where I can expound upon themes I don't write in my LiveJournal - where I write articles rather than notes, where I publish creations I happened to make (I've started calligraphy - expect ...

169. # Thettes Kolakakor

Published: Wed 04 May 2005
300g smör
3dl socker
3msk vaniljsocker
3msk sirap
3tsk bakpulver
7dl vetemjöl

Blanda, rulla små bollar, lägg på plåt, platta till, baka.