http://infinity.blogseminar.net Blogging ... up to homotopy. Fri, 25 Jul 2008 17:16:46 +0000 http://backend.userland.com/rss092 en My paper on blackbox computation of A-infinity algebra structures, submitted to the Kadeishvili Festschrift issue of the Georgian Mathematics Journal, is now on the arXiv. http://infinity.blogseminar.net/2008/07/25/blackbox-computation-on-the-arxiv/ Since the thesis is now defended, and the degree provisionally granted, I present to you my doctoral thesis. http://infinity.blogseminar.net/2008/07/17/computation-of-a-infinity-algebra-structures-in-group-cohomology/ In the arXiv mailing from today, February 2nd 2008, there was a large chunk of $A_\infty$-related preprints from Lyubashenko and Manzyuk. Most of these preprints are getting published in journals, or in Max-Planck-Institute report series. For reference, the arXiv posts I'll be talking about here are: http://arxiv.org/abs/0802.2885 http://arxiv.org/abs/math/0211037 http://arxiv.org/abs/math/0306018 http://arxiv.org/abs/math/0312339 http://arxiv.org/abs/math/0701165 In general sweeps - acquired from ... http://infinity.blogseminar.net/2008/02/21/lyubashenko-manzyuk-on-the-arxiv-some-additional-thoughts/ In my doctoral thesis (soon to be released to the general public), I spend some time discussing a blackbox technique for computing A-infinity structures on Ext algebras using Kadeishvili's proof of the minimality theorem as an inspiration for an algorithmic approach. Basically, we build up a quasi-isomorphism from $H^{*}A$ to $A$ ... http://infinity.blogseminar.net/2008/02/06/blackbox-computation-of-a-infinity-structures/ arXiv:0711.4499 Steffen Sagave - DG-algebras and derived A-infinity algebras In this paper, the theory of $A_{\infty}$-algebras as sketched in Kellers survey papers is developed to give bigraded (homological and "original") resolutions of dg-algebras, and construct minimal models for dg-algebras using an extended notion of $A_{\infty}$-algebras called derived $A_{\infty}$-algebras. These take a ... http://infinity.blogseminar.net/2007/12/10/infinity-preprints-on-the-arxiv-november-28-december-10-2007/ There is a paper by Loday on the arXiv since about a month ago, entitled The diagonal of the Stasheff polytope. The basic idea of the paper is to introduce a new operad $AA_\infty$, built on the simplicial chains of Lodays triangulation of the associahedron, and using the relative simplicity ... http://infinity.blogseminar.net/2007/11/09/associahedral-diagonals/ towards-relative-symplectic-field-theory-report.pdf http://infinity.blogseminar.net/2007/10/01/partial-report-on-aim-workshop-towards-relative-symplectic-field-theory/ A sneak preview of my current project -- which will end up as about a third of my PhD thesis: 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 ... http://infinity.blogseminar.net/2007/09/27/computational-projects/ AJ Tolland links to some seminar notes he took from a seminar by Kevin Costello on $A_\infty$-algebras in topological string theory. Thanks to AJ for telling me what I got wrong in the first take. http://infinity.blogseminar.net/2007/09/21/a-infinity-at-the-secret-blogging-seminar/ Ben Webster asked, in a comment to the post Question for the audience for pointers to literature on the computation of $A_\infty$-structures. Since I'm still out traveling, and far from a university, I won't give any real pointers, but rather stick to namedropping. It's not very difficult, using the names, ... http://infinity.blogseminar.net/2007/08/29/overview-of-the-computation-of-a-infinity-structures/