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 ...
read moreI 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 has played a growing role in politics for many years ...
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 ...
read moreI ran across this problem in a reddit side-bar job-ad, and was intrigued by the task (description paraphrased to decrease googleability):
read moreWrite 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 ...
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 ...
read moreI 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 ...
read moreSo, 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 ...
read moreFirst 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 ...
read moreThis 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 ...
read moreThis 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 ...
read moreThis 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.
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 ...
read moreA 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.
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 ...
read moreInspired 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 ...
read moreEric 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 ...
read moreThese 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.
First off, a few words on ...
Now up: Lecture 10 with the definition of a topos and a derivation of internal, inutitionistic logic within a topos.
read moreLecture 7, featuring the introduction of monads based in adjoints, with the connection between the monoid of endofunctors and the ...
read moreAnd, 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.
read moreLecture 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?
read moreThe third lecture is up on the haskell wiki.
read moreI've been maddeningly slow lately. With everything.
Since last week Wednesday, the second lecture is up on the Haskell wiki.
read moreThe 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
read moreCategory 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 ...
read moreDear 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 ...
read moreWhat 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 ...
read moreI 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 ...
read more
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 ...
read moreI 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 ...
read moreTech 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 ...
read moreI 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 ...
read moreThis 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.
http://www.thesun.co.uk/sol/homepage/features/article2011061.ece
This is a rather atrocious article giving yet another ad hoc "formula" to compute some numeric measurement of something-or-other. In this particular case, it's about cleavage, and how to avoid showing too much of it, but these "formulae" plague ...
read moreI've tweaked the layout of my blog a little bit. Among the more notable additions to it is the little box with a list of the major travel plans in my future.
This box is connected to a Google Calendar, public, and maintained from my normal calendar program, in ...
read moreFollowing the featuring of the internal political structure of Lichtenstein on the Strange Maps blog, Brian Hayes asks for the chromatic number of Lichtenstein.
Rahul pointed out that I made errors in transferring the map to a graph. Specifically, I missed the borders Schellenberg-Eschen and Vaduz-Triesen. The post below changes ...
read moreThis post is a walkthrough through a computation I just did - and one of the main reasons I post it is for you to find and tell me what I've done wrong. I have a nagging feeling that the cup product just plain doesn't work the way I ...
read moreThis is extremely early playing around. It touches on things I'm going to be working with in Stanford, but at this point, I'm not even up on toy level.
We'll start by generating a dataset. Essentially, I'll take the trefolium, sample points on the curve, and ...
read moreAs John Armstrong said, I didn't know he was still alive!
On the algebraic topology mailing list, the announcement came today that Henri Cartan, once co-founder of Nicholas Bourbaki, died August 13, 2008:
La Sociread more
The last of my thesis results has reached article form. The paper Blackbox computation of A-infinity algebras has now hit the arXiv and been submitted to the Kadeishvili Festschrift issue of the Georgian Mathematics Journal.
read moreAfter about 5 semesters, one paper, one erratum (submitted to JHRS) and one thesis, and after taking two oral exams and delivering one 30 minute talk on my research, I am now (modulo the week or two it takes to produce my certificate) entitled to the title of doctor rerum ...
read moreBased on the extensive discussion at the Secret Blogging Seminar on tools for long-distance collaborations, Scott Morrison writes an introduction to source control with subversion for research collaborators.
In this post, Scott also offers, quite magnanimously, to setup and host subversion repositories for any mathematician who happens to want to ...
read moreJag har varit en god medborgare. Jag har b
read moreI seem, lately, to be so densely planned that all I can do for my blog is to react on blog posts from Ben Webster at the Secret Blogging Seminar.
He has, recently, written a post inspired by the xkcd comic on purity in the sciences. The comic is funny ...
read moreMy 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 ...
read moreFirst 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 ...
read moreEdited 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:
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 ...
read moreI 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 ...
read moreI'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 ...
read moreI 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 ...read more
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 ...
read moreIn 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 ...
read moreSo, 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 [tex]S^1[/tex] in [tex]S^3[/tex]), what we mean by ...
read moreAt 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 ...
read moreDamn, this feels good!
read moreToday, 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 moreThe 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 moreThis 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 moreThere'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 moreI'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 moreThe 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 moreI'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 moreFrom 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 moreI 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 moreThe 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 moreLast 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 moreSo, 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 moreThe 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 moreSo, 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 moreIssue # 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.
read moreIn 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
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 moreToday, 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 moreIn 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:
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 ...
read more
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 moreHowever, I am enjoying the Scottish countryside and just - today - turned [tex]3^3[/tex] years of age.
read moreTrying 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
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 ...
read moreToday 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 ...
read more... 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 [tex]*_\infty[/tex]-themed group blog: The Infinite Seminar.
I also perceived a lack of blog aggregators, so I started Planet Math Blogseminars to aggregate group ...
read moreDo we have the volume for a Carnival of Research Mathematics?
read moreOne 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 ...
read moreThese 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 ...
read moreComplexZeta 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 ...
read moreThis 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 ...
read moreI 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 ...
read moreThey 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 [tex]\mathbb C[\epsilon ...
read moreIs 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 ...
read moreright here - at least if you're wondering what happened with my recent interview.
read moreAll 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.
read moreIMPORTANT: Note that the implementation herein is severely flawed. Do not use this.
One subject I spent a lot of time thinking about this spring was taking tensor products of A∞-algebras. This turns out to actually already being solved - having a very combinatorial and pretty neat solution.
Recall that ...
read moreSo, Heiligendamm just outside Rostock in northern Germany these days hosts both the G8 meeting and the numerous protest activities. This setup would have me ranting on and on about the violent left and failure to admonish extremists on your own side.
But that is not the issue that makes ...
read moreFirst off, I have a travellog of sorts over at my Livejournal.
Further on, jd2718 just posted the newest Carnival of Mathematics, as so often otherwise, I do feature.
read moreI 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.
read moreToday, 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 ...
read moreThe website/forumsite Mathetreff, run by the Bezirksregierung (region government) D
read moreThis post is dedicated to Janine K
read morenextLookSay = foldr (\xs -> ([length xs, head xs]++)) [] . group lookSay = iterate nextLookSay [1]
Conway's Look-and-say sequence
read moreI 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.
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 ...
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 ...
read moreThe 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.
read moreMany interesting groups have a very geometrical definition: transformations that fix certain symmetries is one of the historical origins of group theory.
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 ...
read moreToday, 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 ...
read moreThe second carnival of mathematics is up over at Good Math, Bad Math. It's again a nice, good read. Go.
The third carnival of mathematics is to be hosted by yours truly on the International Women's Day (maybe we can get a theme going? Women in mathematics, anyone ...
read moreThese badges are also displayed on my About page, but the explanation why merits a blog post of its own.
While I'm still on the subject of writing code with the PFP library, I may as well join in on a discussion that got pulled into the Carnival of Mathematics exposition.
Heath Raftery writes about weird probabilities in dice discussions, a problem very much reminiscent of the Monty Hall ...
read moreSyntaxfree 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 ...
read moreOver at Alon's place, Abstract Nonsense, the first issue of the forthnightly Carnival of Mathematics is up.
Go there. Read. There's a LOT of good blog posts there.
read moreI have previously calculated the A:sub:`∞-structure for the cohomology ring of D8 <http://blog.mikael.johanssons.org/archive/2006/11/an-a-structure-on-the-cohomology-of-d8/>`__. Now, while trying to figure out how to make my work continue from here, I tried working out what algebra this would have come from ...
read moreAlon 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.
read moreI 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 ...
read moreInspired 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 ...
read moreAs 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 [tex]H^*(D_8,\mathbb F_2)[/tex].
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)[/tex] and [tex]H^*(C_2\times C_2,\mathbb F_2)[/tex].
We will find the A∞-structures on the group cohomology ring by ...
read moreThe 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 ...
read moreI 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 ...
read moreIn 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 ...
read moreThe 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 ...
read moreThis 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 ...
read moreThis 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
read moreI 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.
read moreI 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 ...
read moreAs 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 ...
read moreSince the content rate of haskell-related posts is going up, the feed of this blog will get added to Planet Haskell. Hi, Planet!
read moreAfter 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 ...
read moreI 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 ...
read moreSo, 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 ...
read moreGot 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.
Accomplished:
The weekly reports have been dead for a while. Reason? The blog has been dead for a while.
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 ...
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 ...
read moreIn a previous installment, we calculated [tex]H^*(D_8)[/tex] with some amount of success. For that post, I said that I was going to calculate the cohomologies of [tex]D_8[/tex] and of [tex]U(\mathbb H)[/tex] by hand - and I've been at it for the latter ...
read moreThis 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!
read moreIt'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 ...
read moreMy advisor told me to go hit [tex]D_8[/tex] and [tex]U(\mathbb H)[/tex] 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 ...
read moreI 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 ...
read moreI 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 [tex]H^*(C_8,\mathbb F_2)[/tex] and give explicitly in a series of ways the product structure - as Yoneda splices, as chain map ...
read moreThis 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 ...
read moreI'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 ...
read moreI 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 ...
read moreRight. 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 ...
read moreSuppose we have a presheaf [tex]\mathcal F[/tex] of abelian groups over [tex]M[/tex] and pick a point [tex]x[/tex]. On the collection of all abelian groups defined over some neighbourhood of [tex]x[/tex] (disjoint union) we put an equivalence relation which identifies [tex]f\in ...
read moreMy 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 moreI 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 moreNow 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 moreOnce 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 moreA paper recently up on arXiv details the errors committed by an author of a paper in Non-Linear Analysis, who, by ignoring basic conditions of theorems manages to prove most of mathematics and substantial parts of physics inconsistent.
This is the second insufficiently reviewed paper at that Journal causing some ...
read moreFor 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 moreI 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 moreThis 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 moreSo 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 moreSo, 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 moreAfter 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 moreTodays webbrowsing led me to John Baez finds in mathematical physics for week 226, which led me to snoop around John Baez homepage, which in turn led me to stumble across the Geometry of Computation school and conference in Marseilles right now.
This, in turn, leads to several different themes ...
read moreSince 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 moreBreaking 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 moreIf 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 moreSo, 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 moreI'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 moreStumbling 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 moreIn 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 moreIn 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 moreYou may have seen some of these before...
[tex]\frac{1\cancel{6}}{\cancel{6}4}=\frac{1}{4}[/tex]
[tex]\frac{1\cancel{9}}{\cancel{9}5}=\frac{1}{5}[/tex]
[tex]\frac{\partial}{\partial x}\sin^2(x)=\sin(2x)[/tex] -- just move down the 2.
read moreTillbehör: Färska frukter och bär
Mikael Johansson, Susanne Vejdemo
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.
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 ...
read moreThe 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 ...
read moreBlanda, rulla små bollar, lägg på plåt, platta till, baka.
read more
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