I presented a group talk for my QFT II class on Peskin and Schroeder section 16.6, explaining the background field method and using it to derive the QCD beta function. I found the section in P&S to be utterly incomprehensible–they don’t really give you any clues to what they’re doing or how anything is defined or what is actually going on. Hopefully the attached notes go some way towards a decent explanation of the background field method. I found Schwartz’s QFT textbook to be much better on this point if you want to read more.
I gave a talk at the UM HET journal club on the Extended Press-Schechter formalism, which describes the number density distribution of halos (galaxy clusters) in ΛCDM. It starts from basic cosmology but assumes some results from inflationary theory without demonstration. The Press-Schechter formalism was a mildly accurate formalism with some problems; these problems are resolved in the extended formalism. Thanks to Dragan Huterer, my cosmology professor, for notes and to the very clear textbook MBW. You can access the lecture notes here.