### Vesselin Dimitrov, Mochizuki's form of the ABC conjecture

I will explain how Mochizuki's inequality (III 3.12) encodes a version of the ABC conjecture. This concerns the log-shells log-volume computations of IUT IV. I will also discuss the implications of Mochizuki's inequality.

### Kiran Kedlaya, On Mochizuki's approach to Diophantine inequalities

We work backwards from Dimitrov's lecture, attempting to explain as concretely as possible the strategy proposed by Mochizuki to prove the main inequality in his theory (III 3.12). In so doing, we explain how to replace some nonstandard terminology used in the IUT papers with more conventional terminology. (Warning: no warranties about the correctness of any statements are implied!)

### Emmanuel Lepage, Theta functions and evaluation

We'll introduce Theta functions on Tate curves and discuss the anabelian behavior of its Kummer class. One gets a group-theoretic evaluation of the Theta function at some rational point of the Tate curve by pulling back the Kummer class along the Galois section of the fundamental group defined by this point. The Gaussian monoid is obtained by taking these group theoretical values at some torsion points, whose Galois sections can be recovered group-theoretically up to mild indeterminacy.

### Andrew Obus, Introduction to (model) Frobenioids

This talk will give an introduction to Frobenioids, particularly the "model" Frobenioids that are used in the development of IUT. While the categorical definition of a Frobenioid is somewhat complicated, the most important example is that of a "geometric Frobenioid," which is a categorical object that keeps track of a proper normal variety, its tower of finite Galois covers, their monoids of effective divisors, their groups of rational functions, and all the compatibilities that arise. We will discuss geometric Frobenioids in detail, as well as their arithmetic analogues. Time permitting, we will say a word about "tempered Frobenioids," which also take into account certain analytic covers when the variety is defined over a non-archimedean field. No previous familiarity with Mochizuki's work will be assumed.

### Carl Pomerance, Why the ABC conjecture

This survey will give some of the history of the ABC conjecture, why it was made, why it is likely to be "true", what has been proved, and why it is important.

### Kirsten Wickelgren, Galois groups and pi_1: What Do They Know? Do They Know Things?? Let's Find Out!, Part I

We'll define and discuss several of the fundamental objects and constructions (e.g., Kummer classes, evaluation of classes, cyclotomes, etc) and various reconstruction theorems.

### David Zureick-Brown, Galois groups and pi_1: What Do They Know? Do They Know Things?? Let's Find Out!, Part II

We'll define and discuss several of the fundamental objects and constructions (e.g., Kummer classes, evaluation of classes, cyclotomes, etc) and various reconstruction theorems.