I have to admit that I try to read more than I actually do, in particular blog posts. In this post I give you some links from 2010 that I now read skimmed a few weeks ago and found to be fresh enough to be shared again.

Continue reading «From the Backlog 2010»

The new term has begun! And with it a new academic year in Freiburg.

In the past I used to put extensive notes online, for any talks I gave (mostly in local seminars at my university). I have changed this to posting blog posts instead, but sometimes I also have some teXed talk notes. The quality of the teXed notes is usually bad, as I didn't intend to publish them. This is a compilation of talk notes from the last academic year.

Goal for the next year: focus :-)

• Seminar on Systolic Geometry: Aspherical Manifolds and Essential Manifolds.
• Seminar on Perverse Sheaves: Introduction to 6 functor formalism. I also blogged some stuff even more elementary about 4 functors before.
• Seminar on Geometric Langlands: From Langlands for Function Fields to Geometric Langlands; I have blogged an introduction and also some of the talk on Geometric Langlands here.
• Seminar on Cobordism: Bordism, Cobordism and Spectra (there's a blog post). There are also slides on the cobordism spectrum, though I remember it was definitely on a blackboard.
• Seminar on Mapping Class Groups: Spectra and Infinite Loop Spaces (these notes are actually not that bad).
• Seminar on Galois Representations: Grothendieck's Monodromy Theorem. I have written a small note on supernatural numbers, which appear in Tate's proof. There are also (bad, uncorrected) talk notes on Weil-Deligne representations in german.
• Seminar on Multiple Zeta Values: Upper bounds on periods (link goes to full lecture notes, which are quite good now).
• Student's conference of the german math society: 20 minutes on A¹-fundamental groups of isotropic groups.

This is a list of resources available on the web for research mathematicians, which used to be updated regularly. The first version was published May 5, 2012. The last update was on March 12, 2015, marked by [UPDATE 15-03-12]. It is now no longer actively maintained.

Continue reading «Mathematics Resources»

The term Web 2.0 was coined by Darcy DiNucci in 1999 and popularised by Tim O'Reilly in a 2004 conference named Web 2.0. In the beginning, it wasn't totally clear what Web 2.0 really meant for the ordinary web consumer. Then it crystallised out that users associate with the term Web 2.0 an interactive internet. During that time, the first large collaborative dynamic websites were seen, such as Wikipedia and YouTube. Web 1.0 are static HTML pages that don't allow interaction.

Continue reading «Math 2.0»

Today in the series "How to do XYZ with software?":

How to manage bookmarks?

Probably you've once had the moment in your life when you installed some new browser, re-installed you computer or something like that - and all your browser bookmarks were lost. How to do better?

Continue reading «Managing bookmarks»

I decided to post some background needed in order to understand Morel-Voevodsky's paper "A¹-homotopy theory". I explain some notions of simplicial sets, topoi, monoidal categories, enriched categories and simplicial model categories.

I tried to give many more references I found useful.
Continue reading «Categorical background for A¹-homotopy theory (simplicial model categories)»