Math 296Z: Tools in Resolution of Singularities (Harvard, Spring Semester 2024/25)

Meets: Every Monday and Wednesday, 3-4:15PM at Science Center 120

Brief course description: This course is an invitation to resolution of singularities. I will briefly introduce the classical methods and discuss the complications that arise in the classical algorithm of Hironaka. I will then discuss the recent work of Abramovich—Temkin—Włodarczyk and McQuillan. They demonstrated that complications in the classical algorithm can be better resolved by working more broadly with algebraic stacks instead of schemes. As a result, they were able to construct an iterative procedure to embedded resolution of singularities in characteristic zero, where at every step, one blows up the ​"most singular locus", and immediately witnesses an improvement in singularities. If time permits, I will cover some adjacent topics. 

Some typed notes will be posted on this space soon.