I am hoping to return to a semi-regular posting schedule—hopefully one to two posts per week.
My last month thus far has consisted mostly of two things: preparing my third year review file and working with my excellent student researcher.
I decided to ignore most everything else to get a draft of my third year review done. I now have 93 pages that I could hand in, if needed. However, there are major sections I know I will change (e.g. my teaching statement), and others will suggest many changes when they informally review it for me. But I have something that I think I could hand in without getting fired, and it is barely July (it is due in November).
This process has given me some time to reflect on my classes; some of my thoughts will be featured here at symmetricblog.
My student is researching the relationship between the number of conjugacy classes of a finite group and the number of conjugacy classes of its Sylow -subgroups. He has already answered our question for nilpotent groups, dihedral groups, cube-free groups, and symmetric groups (I think that alternating groups will fall within the week). Next up: either dicyclic groups or supersolvable groups.