tag:blogger.com,1999:blog-178977942011-04-21T19:44:44.340+02:00Mathematics. Algebraic topology. Homological algebra. Algebraic geometry. K-theory. Category theory. Surgery theory. Abstract nonsense.rodennoreply@blogger.comBlogger31100tag:blogger.com,1999:blog-17897794.post-36956669662139700172007-08-16T10:59:00.000+02:002007-08-16T11:00:14.966+02:00(On the melody of "My Favourite Things" from "Sound Of Music".)<br /><br />Functors, espec'ly of higher dimensions<br />Infinite spectra of loops and suspensions<br />A topological theory on strings<br />These are a few of my favourite things.<br /><br />Finally grokking the bar resolution<br />Solving equations by guessing solutions<br />zero-dimensional Gorenstein rings<br />These are a few of my favourite things<br /><br />When a conference,<br />a real good one, ends<br />Then I'm feeling sad<br />But then I remember my favourite things<br />And then I don't feel so bad<br /><br />Posing a question without hesitation<br />Knowing the proof and in four variations<br />Dreams of the future, what ever it brings<br />These are a few of my favourite things<br /><br />When a complex<br />is too complex<br />driving me insane<br />I take a good look at my favourite things<br />and know this work's not in vain<div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/17897794-3695666966213970017?l=therealsqrt.blogspot.com' alt='' /></div>rodennoreply@blogger.com2tag:blogger.com,1999:blog-17897794.post-1163244271109913102006-11-11T12:08:00.000+01:002006-11-11T12:26:15.506+01:00Feeling like an almost full-grown mathematician, I now have performed my first mathematics lecture.<br /><br />Actually, I 'performed' quite some weeks ago, but I came to remember that I hadn't told you guys.<br /><br />The lecture was a part of a course on representation theory, where we had just gone through complex representations, character tables, and stuff like that.<br /><br />The topic was perfect for me: The correspondence between complex group representations and modules over the complex group ring.<br /><br />Some of the younger maths students who were gatherd there (younger as in number of theorems understood, not as in age), and thus I was to introduce them to the concept of 'modules' for the fist time of their lives. I am positive, that they or at least some of them came to love modules just a little bit. Or at least like them. Just a little.<br /><br />As usual, the lecture notes are available to you, by simply clicking the blog-topic.<br />Note that I use "R-module map" as a word for an R-morphism of R-modules in the exercise.<br /><br />And by the way: if this made you love modules over the group ring just a little bit more: tell me! ;)<br /><br />See you.<div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/17897794-116324427110991310?l=therealsqrt.blogspot.com' alt='' /></div>rodennoreply@blogger.com2tag:blogger.com,1999:blog-17897794.post-1154440361531970652006-08-01T14:19:00.000+02:002006-08-01T16:29:57.146+02:00Hi, and welcome to my new maths blog.<br /><br />I recently finished my "thesis" on <span style="font-weight:bold;">Group Cohomology</span>. <br /><br /><blockquote name=abstract>In this thesis we describe the basic properties of homology and cohomology with coefficients. Induction and coinduction is shown to coincide when the subgroup has finite index. We then proceed with a proof of Shapiro's Lemma.<br /><br />We study the group algebra over a field and prove Maschke's theorem. The group algebra over a field is a self-injective ring, and we notice that the group algebra of a p-group over a field of characteristic p is a local Gorenstein ring.</blockquote><br /><br />Click the title of this entry to download the pdf.<div class="blogger-post-footer"><img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/17897794-115444036153197065?l=therealsqrt.blogspot.com' alt='' /></div>rodennoreply@blogger.com0