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Speaker: Arata Minamide
Title: Explicit Estimates in Inter-universal Teichm¨uller Theory I, II
Abstract: In the final paper of a series of papers concerning inter-universal Teichm¨uller
theory, Mochizuki verified various numerically non-effective versions of the Vojta, ABC,
and Szpiro Conjectures over number fields. In this series of two talks, we will give various
numerically effective versions of Mochizuki’s results. This is joint work with Shinichi
Mochizuki, Ivan Fesenko, Yuichiro Hoshi, and Wojciech Porowski.

Speaker: Wojciech Porowski
Title: Overview of IUT theory
Abstract: In this talk we will give a brief overview of the structure of IUT theory and
explain a role played by individual papers. We will also discuss various notions such as
´etale-like and Frobenius-like structures, holomorphic vs. mono-analytic structures and
indeterminacies.

Speaker: Christian T´afula Santos
Title: From ABC to L: On singular moduli and Siegel zeroes
Abstract: In 2000, using analytical, algebraic, and arithmetical ideas, Granville and Stark
showed that the “uniform” ABC for number fields implies that odd Dirichlet L-functions
have no “Siegel zeroes”, which are a severe type of (not yet unconditionally ruled out)
counterexample to the Generalized Riemann Hypothesis. In this talk we are going to
focus on the structure of their main argument, and discuss recent work that allows us to
get more precise relations between the analysis (zero-free regions of L-functions) and the
arithmetics (heights of singular moduli).

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