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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 two and the week inbetween my fiancĂ©e, have been visiting me in Jena. Thus, I have covered more ground in these three weeks when it comes to tourism than I probably will be able to do in several months. I have seen the Blue Man Group in Berlin (WOW!), I have seen the Dornburg, the Feengrotten and Weimar. I have eaten at the expensive luxurious restaurant at the top of the old university tower in Jena (it’s bloody scary, but quite cool – the restaurant is on the 29th floor; in a city where only one single house goes above 10 floors).
This is a preview of
Weekly Report: Power tourism
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My advisor told me to go hit and 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 of with , he walked me through his Shiny! Gröbner base method to get resolutions with free modules over finite p-group algebras. Armed with the minimal resolution, I sat down and started hunting products; and finally found the cohomology ring.
Or … to be exact, I found and then peeked into Carlson, et.al. for the Big List of 2-group cohomologies to see that all interesting stuff happens in anyway.
So for the benefit of any and all readers who want to see what it looks like, I’m going to walk through it again here. Nonono, you don’t need to flee all of you – just skip this entry if it’s that scary!
This is a preview of
More group cohomology
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I just received in the mail a bunch of prints. Of my article “Computation of PoincarĂ©-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 di Istituto Matematico di Universita di Trieste, on pages 85-94 of Vol. XXXVII (2005).
Damn, it feels good. Reviewed and everything. If you’re curious, my manuscript can be found at http://math.su.se/~mik/torino.pdf or at the arXiv as math.AC/0502348.