Thursday, September 20, 2018, 3-4:30 p.m. Taylor Dupuy, Mochizuki's Inequality and the ABC Conjecture Mochizuki's approach to the ABC conjecture is to prove an inequality which implies the Szpiro inequality for elliptic curves under certain technical hypotheses called "initial theta data" show that these technical restrictions don't matter. The aim of this talk is to explain exactly what step 1 is all about. Roughly, for an elliptic curve in "initial theta data", Mochizuki's inequality says that the size of one region (encoding one side of Szpiro) is less than the size of a "blurry" region (encoding the other side of Szpiro).
I will explain what these regions are and how they relate to Szpiro explicitly. In particular we will discuss "indeterminacies", "q-pilots", "theta-pilots", and "initial theta data". Later in the semester we will discuss the anabelian constructions that go into the "blurry construction". This talk is supposed to set up future talks down the road. Much of this project of making these inequalities explicit is joint work with Anton Hilado.
Thursday, October 18, 2018, 3-4:30 p.m. Taylor Dupuy, Log Volume Computations We are going to continue discussing Mochizuki's inequality. In particular we will discuss the indeterminacies Ind1,Ind2,Ind3 and start in on the log-volume computations which give rise to a version of Szpiro's inequality for elliptic curves sitting in initial theta data.
Thursday, November 15, 2018, 3-4:30 p.m. Taylor Dupuy, More Log Volume Computations We will perform computations similar to the computations in IUT4 using Mochizuki's Inquality (Corollary 3.12 of IUT3) and the definitions of the indeterminacies therein to give a Szpiro-type inequality for Elliptic Curves in initial theta data (Theorem 1.10 of IUT4).
