Catalan’s conjecture after Mihăilescu (CCAM)

The Fall 2021 learning seminar studied Catalan’s conjecture, following the work of Mihăilescu as presented in René Schoof’s book. The seminar met online on Fridays at 4pm.

schedule

• 9/3 - Outline of proof, following Schoof’s Introduction (including exercises!, Daniel)

• 9/10 - The cases q=2 and p=2 (following Chapters 2 and 3, Zack)

• 9/17 - The nontrivial solution and context around elliptic curves (following Chapter 4, Raemeon)

• 9/24 - Runge’s method (following Chapter 5, Paco)

• 10/1 - Cassels’ Theorem (following Chapter 6, Santana)

• 10/8 - An obstruction group, and small p or q (following chapters 7-8, Arvind)

• 10/15 - The Stickelberger ideal (following Chapter 9, Tyler)

• 10/22 - The double Wiefrich criterion and the minus argument (Chapters 10/11, Haiyang)

• 10/29 - Discussion session

• 11/5 - The plus argument (black-boxing formal group-theoretic facts) (Chapters 12-14, Simon)

• 11/12 - The density theorem (Chapter 15, Freddy)

• 11/19 - Thaine’s theorem (Chapter 16, Sasha)